Research ArticleLattice Boltzmann Simulation of Airflow and MixedConvection in a General Ward of Hospital

Taasnim Ahmed Himika Md Farhad Hasan and Md Mamun Molla

Department of Mathematics amp Physics North South University Dhaka 1229 Bangladesh

Correspondence should be addressed to Md Mamun Molla mamunmollanorthsouthedu

Received 16 January 2016 Accepted 11 April 2016

Academic Editor Mrsquohamed Souli

Copyright copy 2016 Taasnim Ahmed Himika et alThis is an open access article distributed under theCreativeCommonsAttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

In the present investigation the airflow and heat transfer for mixed convection have been simulated for a model general ward ofhospital with six beds and partitions using the Lattice Boltzmann Method (LBM) Three different Reynolds numbers 100 250 and350 have been considered Bounce-back condition has been applied at the wall Results have been represented in three differentcase studies and the changes have been discussed in terms of streamlines and isotherms Code validation has also been includedbefore going through the simulation process and it shows good agreement with previously published papers when the comparisonis made on average Nusselt number Results show that the pattern of indoor airflow is varied in each and every case study due tothe effect of mixed convection flow and placement of partition In addition the changes in average rate of heat transfer indicatethat patients closer to inlet get the most air and feel better and if any patient does not need much air he or she should be kept nearthe outlet to avoid temperature related complications

1 Introduction

The study of mixed convection fluid flows has become anattention-grabber due to considerable practical interest inmany engineering applications such as nuclear reactors [1]crystal growth solar collectors [2] and reservoirs and lakes[3] Apart from these mixed convection appears to be a con-cerning issue while designing modern ventilation system inhigh-rise buildings and health care centersThemain purposeof room air-ventilation system is to provide comfortable andgood indoor air quality with minimum energy consumptionso that the residents inside do not feel stuffy or uncom-fortable So to design efficient ventilation system necessarydesigning or simulation tools are required in order to accu-rately visualize the airflow pattern and know the appropriatepositions of inlets and outlets in any complex geometry

The combined effect of natural and forced convectionin fluid flows has been analyzed by many researchers overdecades The fact behind their curiosity lies in the buoyancyeffect that can be the dominant factor in determining heattransfer Since experimental scalemodeling is very expensiveresearchers continued their study with the aid of traditional

Computational Fluid Dynamics (CFD) model simulationtechnique But the main problem with this traditionalmethod involves solving the Navier-Stokes (NS) equationsthat needs more CPU time and memory Researchers foundthat the solution lies in the Lattice Boltzmann Model (LBM)an alternative Computational Fluid Dynamics (CFD) modelthat does the same job by solving discrete Boltzmann equa-tion which is a faster process than solving the NS equations[4] LBM has originated from Lattice Gas Automata (LGA)[5] which is used to simulate fluid dynamics by tracing themovement of single-particle distribution function consider-ing the space time and particle velocities to be discrete

The reasons behind LBMrsquos popularity are as followsbecause it has simple mathematical modeling of any complexsystem the boundaries are treated in simple manner it is asuitable model for parallel computation and apparently itsaves 30 percent of the total CPU timewhichwould have beenoccupied by nonlinear Riemann problem in CFD [6] LBMis also considered to be very easy and efficient method overfinite volume finite-difference and finite element techniquesMany experiments and researches were performed to explorethe effectiveness of LBM Peng et al [7] simplified thermal

Hindawi Publishing CorporationJournal of Computational EngineeringVolume 2016 Article ID 5405939 15 pageshttpdxdoiorg10115520165405939

2 Journal of Computational Engineering

LBM to study incompressible thermal flows Lee et al[8] researched the incompressible lattice Bhatnagar-Gross-Krook (BGK) model to simulate axisymmetric geometrySidik [9] calculated the temperature field and velocity fieldutilizing two different distribution functions for each fieldand developed an incompressible 2D and 3D thermohydro-dynamics for the LBM The main aim of Mondal and Lirsquos[10] investigation was to observe the effect that volumetricradiation has on the natural convection in a square cavitycontaining an absorbing emitting and scattering mediumSzucki and Suchy [11] studied a method concerning localviscosity changes in single-relaxation time (SRT) LBMMoreover LBM was successful in various fluid dynamicalproblems including flows in porous media [12] magnetohy-drodynamics [13] immiscible fluids [14] and turbulence [15]LBM can also be applied to investigate indoor airflow In 2002Crouse et al [16] were the first and probably the only ones toimplement LBM in indoor convective airflow analysis

An investigation was carried out by Zhang et al [17] whostudied the airflow inside an airliner ward performing exper-imental mathematics and numerical simulations The wardwas assumed to be half occupied with 28 seats and twin-aisleThe authors used the Reynolds averaged Navier-Stokes equa-tions based on theRNG 119896minus120598model to solve the air velocity airtemperature and gas contaminant concentration and applieda Lagrangian technique to model the particle transport Thenumerical results showed good agreement quantitativelywiththeir experimental data However they confessed that it isvery challenging and difficult to achieve a complete andaccurate validation for the complex flow in a ward LaterZhang and Lin [18] used LBM to analyze indoor airflowsThey worked on low Reynolds number indoor airflow fieldsin amodel room building a partition and their computationalresults of LBM were found to be in agreement with theexperimental data in terms of airflow velocitiesThey appliedLBM in a relatively more complex environment that is amodel ward with 10 beds Although their works were solelyon fluid flow they did not consider any temperature equation

Liu et al [19] on the other hand utilized CFD toexamine a critical issue of hospital Operating Room (OR)They numerically simulated a horizontal airflow to controlairborne particles inside a hospital OR The investigationwas performed on different horizontal airflow patterns andair quality inside an OR model of dimension 300 cm times

296 cm times 240 cm They realized the urgency of a properventilation system inside a hospital OR and so carriedon some onsite tests and CFD simulations to estimate theeffectiveness of latitudinal unidirectional airflow in orderto bring down infectious airborne particles The suggestedventilation supplying ultraclean air from a horizontal planeavoided obstacles like medical lights from upstream flowand also lateral flow perpendicular to the airflow of thermalplume around surgeons and patient can avoid opposingeffect between the two airflows in downward airflow systemHowever the application of airflow in horizontal directionhad not been properly examined in their paper

All the above examples verified the capability and effec-tiveness of LBM over traditional CFD but the experimentswere done either considering a natural fluid flow or forced

fluid flow whereas in reality the presence of both flows canbe seen simultaneously In purely natural convection flowthe only driving force is the density gradient and for forcedconvection the force is inflow condition or pressure-gradientSince there is temperature difference between all objectsliving beings and the environment in the presence of agravitational field temperature gradients tend to induce den-sity gradients that ultimately drives the fluid flow Watzingerand Johnson [20] took the first initiative to investigate heattransfer in a turbulent mixed convective water flow bothfor opposing and supporting flow conditions Later Prasadand Koseff [21] investigated the combined natural and forcedconvection heat transfer in a deep lid-driven cavity flowHongtau Xu et al [22] numerically studied double diffusivemixed convection around a heated cylinder in an enclosureand Al-Sanea et al [23] analyzed the effect of input Reynoldsnumber and room aspect ratio on turbulent flow and ceilingtransfer coefficient for mixed convection using CFDmethodZhao et al [24] used traditional CFD method to investigatethree-dimensional (3D) nonlinear multiple steady fluid flowsin a slot-ventilated enclosure Khanafer and Chamkha [25]applied finite volume method to experiment with a fluid-saturated porous medium on mixed convection flow in alid-driven enclosure On the other hand Kefayati et al [26]applied LBM to simulate magnetohydrodynamic mixed con-vection in a lid-driven square cavity with linearly heated wallAs the present investigation is based on mixed convectioninside a hospital ward having partition in the middle thework of Lee and Awbi [27] is worth mentioning which ison the effect of room air quality with mixing ventilation dueto internal partitioning but their observation was only onstatistical analysis using traditional CFD codes They statedthat to get better room air quality the partition positionedtowards the exhaust zone having a larger height and gapunderneath was beneficial

The purpose of the present work is to focus on indoorairflow simulation by LBM in a hospital ward with six bedsand partitions The airflow inside the ward is consideredto be mixed convection flow and different cases have beenconsidered as well The room temperature has been keptlower than patientsrsquo temperature as each patient on bed hasbeen considered to release heat continuously in the proposedmodel Before going through further simulation code valida-tion has been presentedThis paper is organized in the follow-ing way in Section 2 physical geometry of the problem hasbeen discussed followed by the mathematical formulation inSection 3 In Section 5 the results have been discussed indetail and then conclusion has been added to Section 7

2 Physical Geometry

The present investigation has been applied for the mixedconvection in a general ward of hospital as shown in Figure 1In Figure 1(a) it is just a ward without any bed or partition inFigure 1(b) a general ward with six model beds is shown andin Figure 1(c) that ward with six beds along with a partitionis depicted Here ℎ is the height and 119897 = 2ℎ is the horizontallength of each block and the height and width of the partition

Journal of Computational Engineering 3

Inlet Outlet

TC TC

TH

TC

Gy

L = 8H

(a)

Inlet Outlet

h

H = 5hl = 2h d = 4h

(b)

Inlet Outletb = h2

a = 4h

(c)

OutletInlet b = h2b = h2

a = 4h a = 4h

(d)

Figure 1 Schematic diagram of the geometry of hospital ward showing (a) principles applied building themodel (b) Case I without partition(c) Case II with one partition and (d) Case III with two partitions

are 119886 = 4ℎ and 119887 = ℎ2 respectively The height of the wardis119867 = 5ℎ and 119871 = 8119867 is the length of the wardThe length ofthe inlet and outlet is (ℎ + 119887)2

3 Mathematical Formulation

The LBM was originated from Ludwig Boltzmannrsquos kinetictheory of gasesThe basic theory of this equation is that gasesor fluids can be imagined as consisting of a large number oftiny particles moving with random motion The exchange ofmomentum and energy is found through particle streamingand collision between particles So this process can bedemonstrated by the Boltzmann transport equation [28 29]

120597119891

120597119905+ 119906 sdot nabla119891 = Ω (119891 119891

eq) (1)

where 119891eq is the equilibrium distribution function respec-tively 119906 is the particle velocity andΩ is the collision operatorHere119891 represents119891(119909 119890

119894 119905)which is the probability to locate

a particle at position 119909 with velocity vector 119890119894at time 119905

31 Lattice Boltzmann Method The LBM simplifies Boltz-mannrsquos original idea of gas dynamics by reducing the numberof particles and circumscribing them to the nodes of a latticeFor a two-dimensionalmodel a particle is preferred to streamin a possible of 9 directions including the one staying atrest For this type of modeling the most popular one is11986321198769 model which has been considered in this work Thisis the standard model for two-dimensional structure for bothflow and temperature conditions The velocities for theseconditions are known as macroscopic velocities

4 Journal of Computational Engineering

The discretized Lattice Boltzmann (LB) equations forboth flow and temperature field can bewritten as follows [29]

119891119894(119909 + 120575119890

119894 119905 + 120575119905) minus 119891

119894 (119909 119905)

= minus1

120591][119891119894 (119909 119905) minus 119891

(eq)119894

(119909 119905)] + 120575119905 sdot 119865119894

119892119894(119909 + 120575119890

119894 119905 + 120575119905) minus 119892

119894 (119909 119905)

= minus1

120591120572

[119892119894 (119909 119905) minus 119892

(eq)119894

(119909 119905)]

(2)

Here 120591] = 3] + 05 and 120591120572

= 3120572 + 05 are thesingle-relaxation times that control the rate of approach toequilibrium 119891

119894(119909 119905) and 119892

119894(119909 119905) are the density distribution

functions for velocity and temperature respectively along thedirection 119890

119894at (119909 119905) ] is the kinematic viscosity and 120572 is the

thermal diffusivityTheparticle speed is 119890119894and120588 is the density

To calculate the equilibrium distribution functions forthe velocity 119891eq

119894(119909 119905) and for the temperature 119892eq

119894(119909 119905) the

general expressions have been considered [29ndash31]

119891eq119894= 119908119894120588[1 +

3 (119890119894sdot 119906)

1198882+9 (119890119894sdot 119906)2

21198884minus3 (119906 sdot 119906)

21198882]

119892eq119894= 119908119894119879[1 +

3 (119890119894sdot 119906)

1198882+9 (119890119894sdot 119906)2

21198884minus3 (119906 sdot 119906)

21198882]

(3)

where 119906 = (119906 V) is the fluid velocity and 119888 = Δ119909Δ119905 = 1 is thelattice speed The weighting factors 119908

119894for 11986321198769 are given as

[29]

119908119894=

4

9 119894 = 0

1

9 119894 = 1 2 3 4

1

36 119894 = 5 6 7 8

(4)

The macroscopic fluid density 120588 and velocity 119906 areobtained from the moments of the distribution function asfollows [28]

120588 (119909 119905) =

8

sum

119894=0

119891119894 (119909 119905)

119906 (119909 119905) =1

120588

8

sum

119894=0

119890119894119891119894 (119909 119905)

(5)

and the temperature 119879 is obtained as [32]

119879 =

8

sum

119894=0

119892119894 (119909 119905) (6)

32 Boundary Conditions Boundary conditions (BCs) arevery important part for both the stability and the accuracy of

any kind of numerical solution For LBmodeling the discretedistribution functions on the boundary need to be taken careof to reflect the macroscopic BCs of the fluid In this work atthe wall the bounce-back condition has been applied

Bounce-back BCs are usually used to implement no-slipconditions on the boundary By the bounce-back conditionit is meant that when a particle of a certain fluid for discretedistribution function reaches a boundary node the particlewill scatter back to the fluid alongwith its incoming directionBounce-back condition can be of various types but on-gridbounce-back condition has been used in this paper

321 Boundary Condition for Velocity Four possible direc-tions in two-dimensional structuremdasheast west north andsouthmdashhave been considered in the proposedmodel and no-slip or bounce-back boundary condition is used at the wallswhich has been shown in Figure 1

At east (right) west (left) and south (bottom) walls thebounce-back condition has been applied and the resultingrelations are given below in order

1198913= 1198911

1198917= 1198915

1198916= 1198918

1198911= 1198913

1198915= 1198917

1198918= 1198916

1198912= 1198914

1198915= 1198917

1198916= 1198918

(7)

On the other hand at the north (top) wall three differentboundary conditions have been applied At the inlet Zou andHe boundary conditions have been applied as shown in thefollowing [33]

120588119873=(1198910+ 1198911+ 1198913+ 2 (119891

2+ 1198916+ 1198915))

(1 + 119880)

1198914= 1198912minus2

3120588119873119880

1198918= 1198916minus1

6120588119873119880

1198917= 1198915minus1

6120588119873119880

(8)

where 119880 is the bulk velocity based on the Reynolds numberRe def

= 119880119867] At the outlet the following boundary conditionsare used

1198914119873

= 1198914119873minus1

1198918119873

= 1198918119873minus1

1198917119873

= 1198917119873minus1

(9)

Journal of Computational Engineering 5

and bounce-back condition is used for the rest of the topwalls At the top surface and at each side of a block andpartition the following bounce-back conditions have beenused

Top surface

1198912119909119894

= 1198914119909119894

1198915119909119894

= 1198917119909119894

1198916119909119894

= 1198918119909119894

(10)

Left side

1198911119909119894

= 1198913119909119894

1198915119909119894

= 1198917119909119894

1198918119909119894

= 1198916119909119894

(11)

Right side

1198913119909119894

= 1198911119909119894

1198916119909119894

= 1198918119909119894

1198917119909119894

= 1198915119909119894

(12)

322 Boundary Condition for Temperature Cold and hottemperature conditions are applied at the walls (see Figure 1)

At east (right) wall the cold temperature condition is 1198923=

minus1198921 1198927= minus1198925 and 119892

6= minus1198928

At west (left) wall the cold temperature condition is 1198921=

minus1198923 1198925= minus1198927 and 119892

8= minus1198926

At south (bottom) wall the cold temperature condition is1198922= minus1198924 1198925= minus1198927 and 119892

6= minus1198928

At the north (top) wall in the outlet a zero gradientboundary condition is applied as follows

1198924119873

= 1198924119873minus1

1198928119873

= 1198926119873minus1

1198927119873

= 1198925119873minus1

(13)

And the rest of the top wall is kept cold by using theconditions 119892

4= minus1198922 1198928= minus1198926 and 119892

7= minus1198925

At the top surface of each block the hot temperaturecondition is used as follows

11989221199102

= 119879119908(1199082+ 1199084) minus 11989241199102

11989251199102

= 119879119908(1199085+ 1199087) minus 11989271199102

11989261199102

= 119879119908(1199086+ 1199088) minus 11989281199102

(14)

where 1199102indicates the top surface of the blocks and 119879

119908is the

wall temperature

33 Nondimensional Number and Mixed Convection Param-eter The important nondimensional number Grashof (Gr)and Prandtl (Pr) numbers are defined as [32]

Gr =1205731198661199101198673(119879119867minus 119879119862)

]2

Pr = ]120572

(15)

In the mixed convection the Richardson number Ri def=

GrRe2 controls the flow phenomena In this simulation theforce term is defined as follows [34]

119865 = 3119908119894Ri (119879 minus 119879

119898) 119890119910 (16)

where 119879119898= (119879119867+ 119879119862)2 is the mean temperature In this

paper the fluid velocity 119906 is nondimensionalized by the con-stant inlet velocity119880 and the nondimensional temperature is120579 = (119879 minus 119879

119888)(119879119908minus 119879119888)

In the present work theMach number (Ma) for Re = 100is 005 for Re = 250 is 002 and for Re = 350 is 0014 Allthese values are less than 03 which satisfy the condition ofincompressible fluid flow [32] In buoyant flowMach numberand thermal diffusivity (120572) can be defined by the followingequations after fixing the values of viscosity Prandtl numberand Reynolds number

Ma = ]radicGr119873119888

120572 =]Pr

(17)

4 Convergence Criteria

Standard LBM being explicit time-marching in naturerequires a long time to attain steady state convergenceHowever convergence of solution is one of the highlightsof the procedure of recovering the Navier-Stokes equationsfrom LBM In this single-relaxation-time LBM the iterativeprocedure is terminated when the velocity and temperaturefield satisfy the following convergence criteria

sum10038161003816100381610038161003816120601(119899+1)

minus 120601(119899)10038161003816100381610038161003816

sum1003816100381610038161003816120601(119899+1)1003816100381610038161003816

lt 10minus9 (18)

where 120601 is the velocity 119906 or temperature 119879 and 119899 is theiteration index and the sum is over the whole domain

5 Results and Discussions

This section has been divided into four subsections At firstcode validation has been performed for different values of Reand has been compared in tabular format In the consequentthree subsections three case studies have been consideredinside the hospital ward In all three cases one inlet oneoutlet and six beds have been considered Simulations havebeen carried out by placing one partition and later twopartitions in the room while observing the indoor airflow

6 Journal of Computational Engineering

Table 1 Comparison of average Nusselt numbers of present work with other investigations for Gr = 100 and Pr = 071

Re Ri Present [35] [25] [36] [37] [38] [39] [26]100 001 1917965 194 201 202 1985 210 203116 209400 000062 3789101 384 391 401 38785 385 40246 4080821000 00001 6339137 633 633 642 6345 633 648423 654687

1

05

00 2 4 6 8

xH

yH

minus014 004 021 038 056 073 090 108

(a)

0 2 4 6 8

xH

1

05

0

yH

minus021 000 021 042 063 084 105 126

(b)1

05

0

yH

0 2 4 6 8

xH

minus024 minus002 020 042 064 086 108 130

(c)

Figure 2 Streamline patterns of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

pattern and the field of temperature in the three situationsThis section is ended with the discussion and comparison ofthe average rate of change of heat transfers achieved for eachcase study In these cases Re = 100 250 and 350 Pr = 071and Ri = 1 have been kept for all simulations except the codevalidation case Different values of 120591] generated for differentRe are as follows for Re = 100 it is 0575 for Re = 250 it is0530 and for Re = 350 it is 0521 Likewise different valuesof 120591120572are as follows for Re = 350 it is 053 for Re = 250 it is

0542 and for Re = 100 it is 0605

51 Code Validation For code validation process one testcase is the mixed convection in a lid-driven square cavityflow for Re = 100 400 and 100 and Gr = 100 has beenconsideredThepresent results in terms of the averageNusseltnumber have been compared quantitatively with the availableresults published in different articles that are demonstrated inTable 1 The comparison reveals a very good agreement Theresults were compared with the works of Iwatsu et al [35]Tiwari and Das [38] Kefayati et al [26] Khanafer et al [36]Abdelkhalek [37] Khanafer and Chamkha [25] andWaheed[39]

52 Case Study I Six Beds without Partition in the WardIn the first case study six beds without partition havebeen considered Each bed is of the same dimension How-ever beds are represented as blocks in Figure 1 For thewhole computational domain a lattice size of (400 times 50) sim(119909 times 119910) has been taken in all simulations Each block of

(20times10) sim (119909times119910) lattice size is used in the wardThe beds areuniformly distributed in one row Inlet and outlet have beenplaced vertically on the ceiling on the left and right cornersrespectively The width of both the inlet and the outlet hasbeen kept from 0 to 15 lattices and from 385 to 400 latticesrespectively

Figures 2(a)ndash2(c) show the streamlines appended on 119906119880velocity contour of the airflow that enters the ward throughthe inlet and flows out through the outlet for Re = 100 250and 350 respectively In case of Re = 100 small recirculationsare seen between the blocks and also near the walls in theeast andwest sides of the ward due to bounce-back conditionA comparatively large recirculation is formed in immediateright to the inlet that is near the top wall For increasing Rethe length of the recirculation zones increases As shown inFigure 2 the highest value of 119906119880 is 108 and the lowest valueis minus014 for Re = 100 In case of Re = 250 and 350 themaximum values increase to 126 and 130 respectively AsRe increases the inertia force of air increases which makes iteasier to flow around in the ward and hence more heat willbe transferred out through the outlet

Figure 3 represents the isotherms of the room As can beseen from the simulation result only the top surface of eachblock is kept heated while the gaps between the blocks arecold The heated portion of the blocks represents patients onbeds who are releasing heat continuously

Different velocity patterns have been shown in Figures4(a)ndash4(n) demonstrating the 119906119880 velocity profiles at differentpositions of 119909119867 for the three different Re This figure

Journal of Computational Engineering 7

1

05

00 2 4 6 8

xH

yH

minus000 014 029 044 058 073 088 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 039 055 070 086 096 100

(b)

1

05

00 2 4 6 8

xH

yH

008 024 040 056 072 088 098 100

(c)

Figure 3 Isotherms of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

0 1

yH

uU

Re = 100

Re = 250

Re = 350

(a)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(b)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(c)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(d)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(e)

0 10

02040608

1

yHuU

Re = 100

Re = 250

Re = 350

(f)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(g)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(h)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(i)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(j)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(k)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(l)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

0 1uU

Re = 100

Re = 250

Re = 350

(n)

Figure 4 119906119880 velocity profiles in Case I for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

outlines the speed at which the air is flowing inside the wardDue to the recirculation near the inlet the velocity profiles arealso seen to increase resulting in a bent-shaped plot in Figures4(b) and 4(c) After 119909119867 = 35 onwards the graphs are almostthe same as there the flow characteristics are almost similarexcept for Figure 4(n)which is slightly bent at the top forming

because at this point the air is preparing to go through theoutlet

53 Case Study II Six Beds with One Partition In thisinvestigation the previousmodel has been updated by addinga partition in the middle of the general ward while all other

8 Journal of Computational Engineering

1

05

00 2 4 6 8

xH

yH

minus034 002 037 073 108 144 179 215

(a)

1

05

00 2 4 6 8

xH

yH

minus076 minus032 012 056 100 145 189 233

(b)1

05

00 2 4 6 8

xH

yH

minus093 minus046 002 049 096 143 191 238

(c)

Figure 5 Streamline patterns of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

1

05

00 2 4 6 8

xH

yH

100086072057043029014000

(a)

0 2 4 6 8

xH

1

05

0

yH

100092077069054039023008

(b)

0 2 4 6 8

xH

1

05

0

yH

100099087072056040024009

(c)

Figure 6 Isotherms of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

schematic measurements have been kept the same as shownin Figure 1The lattice size of partition is (5times40) sim (119909times119910) andit is placed just after the first three blocks (beds) Simulationshave been carried out for the same three Reynolds numbersAfter placing a partition just like in Figure 5 recirculationis seen in Figure 5 and it shows much better result thanthe previous simulations The airflow pattern is clearer thistime which shows that air moves inward smoothly passes thepartition naturally without overlapping it and nicely flowsout through the outlet creating its usual recirculation nearthe inlet between the blocks and near the outlet Unlikeearlier the recirculations now are larger and more frequentparticularly after crossing the partition For Re = 100 alarge air circulation can be noticed between blocks 4 and 5and in case of Re = 250 an even larger recirculation has

appeared between blocks 5 and 6 along with a newly emergedone just beside the outlet As for Re = 350 with the increasein convective air current more chaotic flow dynamics can benoticed before the partition appears The airflow pattern inthis region indicates that in case of mixed convection forRe = 350 the air stays in transitional state which showsboth the laminar characteristics of natural convection and theturbulent nature of forced convection thereby representingforced convection Moreover after placing the partition thepeak values of the contour have risen to 215 from 108 233from 126 and 238 from 130 for Re = 100 Re = 250 andRe = 350 respectively

Figure 6 presents the isotherms for this situation Like inprevious case here also the top surfaces of the blocks are keptheated to represent patients on beds and the spaces between

Journal of Computational Engineering 9

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(c)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(d)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 7 119906119880 velocity profiles in Case II for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

the blocks alongwith the partition are kept coldThe presenceof the partition does affect the airflow characteristics as wellas heat transfer phenomenon which has been discussed indetail in the heat transfer part Pr remains the same

In Figure 7 the119880 velocity profiles at different locations of119909 are discussed for the same three Re This time the resultsshow more curvy lines throughout the whole experimentdue to the obstacle caused because of the partition One ofthe obvious differences worth mentioning is in Figure 7(g)when the air faces the partition At this point a long verticalline with a narrow parabolic curve at the top is shownrepresenting the height of the partition whereas the curvedpart illustrates that the air is crossing the partition Evenin Figure 7(h) the graph still maintains its parabolic shapeand continues this pattern throughout till the end Anothernoticeable change can be seen in Figures 7(j) 7(k) and 7(l)at 119909 = 55 119909 = 6 and 119909 = 65 respectively where the bentsare more irregular than the previous case This is because atthese locations large recirculations have formed due to thepartition as shown in Figure 5

According to the 119880 and 119881 centerline velocity distribu-tion plots in Figures 8(a) and 8(b) respectively there isa constriction in the middle of graph This represents thepartition that actually works like a wall where the velocityplots cease just like the vertical walls in the extreme leftand right sides One possible advantage of this partition isthat the airflow can be controlled if the air enters with ahigh speed through the inlet Also it is noticeable in Figures

8(a) and 8(b) that unlike the previous case the partitionhelps to maintain the air velocity at a constant level untilit exits out through the outlet The 119881 velocity still drops tonegative range from zero at the beginning due to downwardfall of air through the inlet and ascends to zero again where itmaintains its constant velocity The graphs are more chaoticafter crossing the partition due to the recirculations shown inthe contour map The temperature plot in Figure 8(c) startsjust like that of the previous situation but this time insteadof becoming constant after a certain level the graph climbsup the partition crosses it and then drops again eventuallydecreasing to zero at 119909 = 8 The rise of airflow against thepartition also results in the increase in temperature at thispoint therefore the steep in the figure

54 Case Study III One Inlet and One Outlet with TwoPartitions This case study has been investigated by furthermodifying the proposed model adding another partition inthe ward It was done to keep patients from being exposedinto more air Each partition is placed every after two blocks(beds) Both the partitions are of the same dimension that is(5 times 40) sim (119909 times 119910) lattice size and all other measurementsare kept the same as previous situations Simulations andanalysis of this case have also been carried out for the samethree Re values Streamlines pattern of Figure 9 obtained afteradding another partition shows that the size and the numberof recirculations increase more than the last observationUnlike Case II now two large recirculations have formed

10 Journal of Computational Engineering

0 2 4 6 8

012 Partition

xH

Re = 100

Re = 250

Re = 350

uH

(a)

0 2 4 6 8

0

1 Partition

xH

Re = 100

Re = 250

Re = 350

H

(b)

0 2 4 6 80

05

1 Partition

xH

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 8 In Case II for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

1

05

00 2 4 6 8

xH

yH

237198159119080041002minus038

(a)

0 2 4 6 8

xH

1

05

0

yH

247198149100051002minus047minus096

(b)

0 2 4 6 8

xH

1

05

0

yH

252199146092039minus014minus068minus121

(c)

Figure 9 Streamline patterns of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

for the corresponding experiments with each Re Even themaximum and minimum legend values have become widerthan the previous situation for example for Re = 100 the215 value has increased to 237 For Re = 250 and Re = 350

the uppermost values have risen to 247 and 252 from 233and 238 respectively Due to bounce-back condition theair is now forming more recirculations against the walls andbetween the blocksThis augmentation of values and recircu-lations due to buoyancy effect is visible for every incrementof Re values and addition of obstacles such as partition

The generated results of isotherms in Figure 10 give avisual idea how the heat is transferred from the blocks and

passes through the outlet Like the other cases only thesurfaces of the blocks are heated to be considered as patientswho are continuously releasing heat Everything remains thesame like previous cases

Figure 11 provides the 119880 velocity profiles for differentpositions of 119909 According to this the graph characteristicfor a partition can be seen in Figure 11(e) at 119909 = 3 andFigure 11(j) at 119909 = 55 indicating the presence of partitionsat these two locations Apart from this at 119909 = 5 and 75 inFigures 11(i) and 11(n) respectively the parabolic shapes aremore curvy than the profiles at other positions caused dueto recirculations in vector plots of Re = 250 and Re = 350

Journal of Computational Engineering 11

1

05

00

2 4 6 8

xH

yH

000 015 029 043 058 072 086 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 038 054 069 077 092 100

(b)

0 2 4 6 8

xH

1

05

0

yH

008 024 040 056 071 087 095 100

(c)

Figure 10 Isotherms of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(c)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(d)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y HuU

minus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 11 119906119880 velocity profiles in Case III for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

Figures 12(a) and 12(b) illustrate119880 and119881 velocity distributioncurves in mid-119910 and Figure 12(c) shows the temperatureprofile at mid-119910 All of these three plots have one thing incommon that is also different than the previous case In theseplots there are two constrictions instead of one where the

velocities or the temperature curve ceasesThis is the locationwhere the two partitions are present But after crossing theseobstacles the respective graphs continue until 119909 = 8 Thetemperature plot in Figure 12(c) has now two steep regionsdue to the partitions

12 Journal of Computational Engineering

0 2 4 6 8

2

1

0

minus1

uH

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(a)

0 2 4 6 8

1

0

minus1

H

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(b)

0 2 4 6 8

1

05

0

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 12 In Case III for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

55 Calculation of Rate of Heat Transfer In heat transferat a boundary (surface) within a fluid the Nusselt number(Nu) is the ratio of convective to conductive heat transferacross (normal to) the boundary Here convection includesboth advection and diffusion procedures The convectionand conduction heat flows are parallel to each other andto the surface normal of the boundary surface and are allperpendicular to the mean fluid flow in the simple case Thisis denoted as [32]

Nu119871=ℎ119905119871

119896 (19)

where ℎ119905is the convective heat transfer coefficient of the

flow 119871 is the characteristic length and 119896 is the thermalconductivity of the fluid

However this section discusses the average rate of changeof heat transfer obtained for different Re This rate isexpressed as average Nusselt number Nu for each case studyin Tables 2 3 and 4 The tables also show generated localNusselt number Nu that follows the expression below

Nu (119909) = minus 120597120579

120597119910

10038161003816100381610038161003816100381610038161003816119910=1199102

(20)

where 1199102is the upper surface of each block

Average Nu is calculated by integrating the above rela-tion over the entire range of interest and thus the resultingequation becomes

Nu = 1

1199092minus 1199091

int

1199092

1199091

Nu (119909) 119889119909 (21)

Here (1199092minus 1199091) is the length of each block

For the first investigation both the individual and averageNu obtained in Table 2 show a rising trend for each increasingRe Since block 1 is the nearest to the inlet it always has thehighest rate of heat transfer while block 6 has the lowest valueas it is located farthest from the inlet

After placing the partition in the middle the rate of heattransfer shown in Table 3 changes dramatically Like Table 2the patient at block 1 is releasing most heat for all three Reand it keeps reducing until block 5 At block 5 the values ofboth individual Nu and total Nu increase for Re = 250 andRe = 350 but for Re = 100 this type of airflow pattern isseen at block 4 The large recirculations were seen earlier inFigure 5 For Re = 100 recirculation is more over block 4 andthat is the reason why at block 4 individual Nu and total Nuhave greater values than those of Re = 250 and Re = 350 Nuis 15341 at block 4 and for the same block these values are13628 and 14032 respectively for Re = 250 and Re = 350On the other hand if Nu at block 5 are observed Re = 250

and Re = 350 lead the race As per Table 3 Nu are 2011121598 and 27535 for three Re The spike in the values ofRe = 250 and Re = 350 was due to chaotic flows over block5 in Figure 5 If changes in total Nu are observed the valuesincrease rapidly for an increase in Re

For Case Study III the shape of recirculation gets biggerdue to increased Re Above block 1 the recirculation zonecomes into view and due to that reason Nu has the biggestedge in this situation But as the air has tendency to passthe first partition it moves slightly upward and that is whypatient at block 2 is getting less airflowThe heat transfer ratealso falls After passing the first partition the airflow gets itsspace and leads to recirculation near block 3 for Re = 100Meanwhile for Re = 250 and Re = 350 patients on block 4get most air More air means more heat transfer and that is

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

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2 Journal of Computational Engineering

LBM to study incompressible thermal flows Lee et al[8] researched the incompressible lattice Bhatnagar-Gross-Krook (BGK) model to simulate axisymmetric geometrySidik [9] calculated the temperature field and velocity fieldutilizing two different distribution functions for each fieldand developed an incompressible 2D and 3D thermohydro-dynamics for the LBM The main aim of Mondal and Lirsquos[10] investigation was to observe the effect that volumetricradiation has on the natural convection in a square cavitycontaining an absorbing emitting and scattering mediumSzucki and Suchy [11] studied a method concerning localviscosity changes in single-relaxation time (SRT) LBMMoreover LBM was successful in various fluid dynamicalproblems including flows in porous media [12] magnetohy-drodynamics [13] immiscible fluids [14] and turbulence [15]LBM can also be applied to investigate indoor airflow In 2002Crouse et al [16] were the first and probably the only ones toimplement LBM in indoor convective airflow analysis

An investigation was carried out by Zhang et al [17] whostudied the airflow inside an airliner ward performing exper-imental mathematics and numerical simulations The wardwas assumed to be half occupied with 28 seats and twin-aisleThe authors used the Reynolds averaged Navier-Stokes equa-tions based on theRNG 119896minus120598model to solve the air velocity airtemperature and gas contaminant concentration and applieda Lagrangian technique to model the particle transport Thenumerical results showed good agreement quantitativelywiththeir experimental data However they confessed that it isvery challenging and difficult to achieve a complete andaccurate validation for the complex flow in a ward LaterZhang and Lin [18] used LBM to analyze indoor airflowsThey worked on low Reynolds number indoor airflow fieldsin amodel room building a partition and their computationalresults of LBM were found to be in agreement with theexperimental data in terms of airflow velocitiesThey appliedLBM in a relatively more complex environment that is amodel ward with 10 beds Although their works were solelyon fluid flow they did not consider any temperature equation

Liu et al [19] on the other hand utilized CFD toexamine a critical issue of hospital Operating Room (OR)They numerically simulated a horizontal airflow to controlairborne particles inside a hospital OR The investigationwas performed on different horizontal airflow patterns andair quality inside an OR model of dimension 300 cm times

296 cm times 240 cm They realized the urgency of a properventilation system inside a hospital OR and so carriedon some onsite tests and CFD simulations to estimate theeffectiveness of latitudinal unidirectional airflow in orderto bring down infectious airborne particles The suggestedventilation supplying ultraclean air from a horizontal planeavoided obstacles like medical lights from upstream flowand also lateral flow perpendicular to the airflow of thermalplume around surgeons and patient can avoid opposingeffect between the two airflows in downward airflow systemHowever the application of airflow in horizontal directionhad not been properly examined in their paper

All the above examples verified the capability and effec-tiveness of LBM over traditional CFD but the experimentswere done either considering a natural fluid flow or forced

fluid flow whereas in reality the presence of both flows canbe seen simultaneously In purely natural convection flowthe only driving force is the density gradient and for forcedconvection the force is inflow condition or pressure-gradientSince there is temperature difference between all objectsliving beings and the environment in the presence of agravitational field temperature gradients tend to induce den-sity gradients that ultimately drives the fluid flow Watzingerand Johnson [20] took the first initiative to investigate heattransfer in a turbulent mixed convective water flow bothfor opposing and supporting flow conditions Later Prasadand Koseff [21] investigated the combined natural and forcedconvection heat transfer in a deep lid-driven cavity flowHongtau Xu et al [22] numerically studied double diffusivemixed convection around a heated cylinder in an enclosureand Al-Sanea et al [23] analyzed the effect of input Reynoldsnumber and room aspect ratio on turbulent flow and ceilingtransfer coefficient for mixed convection using CFDmethodZhao et al [24] used traditional CFD method to investigatethree-dimensional (3D) nonlinear multiple steady fluid flowsin a slot-ventilated enclosure Khanafer and Chamkha [25]applied finite volume method to experiment with a fluid-saturated porous medium on mixed convection flow in alid-driven enclosure On the other hand Kefayati et al [26]applied LBM to simulate magnetohydrodynamic mixed con-vection in a lid-driven square cavity with linearly heated wallAs the present investigation is based on mixed convectioninside a hospital ward having partition in the middle thework of Lee and Awbi [27] is worth mentioning which ison the effect of room air quality with mixing ventilation dueto internal partitioning but their observation was only onstatistical analysis using traditional CFD codes They statedthat to get better room air quality the partition positionedtowards the exhaust zone having a larger height and gapunderneath was beneficial

The purpose of the present work is to focus on indoorairflow simulation by LBM in a hospital ward with six bedsand partitions The airflow inside the ward is consideredto be mixed convection flow and different cases have beenconsidered as well The room temperature has been keptlower than patientsrsquo temperature as each patient on bed hasbeen considered to release heat continuously in the proposedmodel Before going through further simulation code valida-tion has been presentedThis paper is organized in the follow-ing way in Section 2 physical geometry of the problem hasbeen discussed followed by the mathematical formulation inSection 3 In Section 5 the results have been discussed indetail and then conclusion has been added to Section 7

2 Physical Geometry

The present investigation has been applied for the mixedconvection in a general ward of hospital as shown in Figure 1In Figure 1(a) it is just a ward without any bed or partition inFigure 1(b) a general ward with six model beds is shown andin Figure 1(c) that ward with six beds along with a partitionis depicted Here ℎ is the height and 119897 = 2ℎ is the horizontallength of each block and the height and width of the partition

Journal of Computational Engineering 3

Inlet Outlet

TC TC

TH

TC

Gy

L = 8H

(a)

Inlet Outlet

h

H = 5hl = 2h d = 4h

(b)

Inlet Outletb = h2

a = 4h

(c)

OutletInlet b = h2b = h2

a = 4h a = 4h

(d)

Figure 1 Schematic diagram of the geometry of hospital ward showing (a) principles applied building themodel (b) Case I without partition(c) Case II with one partition and (d) Case III with two partitions

are 119886 = 4ℎ and 119887 = ℎ2 respectively The height of the wardis119867 = 5ℎ and 119871 = 8119867 is the length of the wardThe length ofthe inlet and outlet is (ℎ + 119887)2

3 Mathematical Formulation

The LBM was originated from Ludwig Boltzmannrsquos kinetictheory of gasesThe basic theory of this equation is that gasesor fluids can be imagined as consisting of a large number oftiny particles moving with random motion The exchange ofmomentum and energy is found through particle streamingand collision between particles So this process can bedemonstrated by the Boltzmann transport equation [28 29]

120597119891

120597119905+ 119906 sdot nabla119891 = Ω (119891 119891

eq) (1)

where 119891eq is the equilibrium distribution function respec-tively 119906 is the particle velocity andΩ is the collision operatorHere119891 represents119891(119909 119890

119894 119905)which is the probability to locate

a particle at position 119909 with velocity vector 119890119894at time 119905

31 Lattice Boltzmann Method The LBM simplifies Boltz-mannrsquos original idea of gas dynamics by reducing the numberof particles and circumscribing them to the nodes of a latticeFor a two-dimensionalmodel a particle is preferred to streamin a possible of 9 directions including the one staying atrest For this type of modeling the most popular one is11986321198769 model which has been considered in this work Thisis the standard model for two-dimensional structure for bothflow and temperature conditions The velocities for theseconditions are known as macroscopic velocities

4 Journal of Computational Engineering

The discretized Lattice Boltzmann (LB) equations forboth flow and temperature field can bewritten as follows [29]

119891119894(119909 + 120575119890

119894 119905 + 120575119905) minus 119891

119894 (119909 119905)

= minus1

120591][119891119894 (119909 119905) minus 119891

(eq)119894

(119909 119905)] + 120575119905 sdot 119865119894

119892119894(119909 + 120575119890

119894 119905 + 120575119905) minus 119892

119894 (119909 119905)

= minus1

120591120572

[119892119894 (119909 119905) minus 119892

(eq)119894

(119909 119905)]

(2)

Here 120591] = 3] + 05 and 120591120572

= 3120572 + 05 are thesingle-relaxation times that control the rate of approach toequilibrium 119891

119894(119909 119905) and 119892

119894(119909 119905) are the density distribution

functions for velocity and temperature respectively along thedirection 119890

119894at (119909 119905) ] is the kinematic viscosity and 120572 is the

thermal diffusivityTheparticle speed is 119890119894and120588 is the density

To calculate the equilibrium distribution functions forthe velocity 119891eq

119894(119909 119905) and for the temperature 119892eq

119894(119909 119905) the

general expressions have been considered [29ndash31]

119891eq119894= 119908119894120588[1 +

3 (119890119894sdot 119906)

1198882+9 (119890119894sdot 119906)2

21198884minus3 (119906 sdot 119906)

21198882]

119892eq119894= 119908119894119879[1 +

3 (119890119894sdot 119906)

1198882+9 (119890119894sdot 119906)2

21198884minus3 (119906 sdot 119906)

21198882]

(3)

where 119906 = (119906 V) is the fluid velocity and 119888 = Δ119909Δ119905 = 1 is thelattice speed The weighting factors 119908

119894for 11986321198769 are given as

[29]

119908119894=

4

9 119894 = 0

1

9 119894 = 1 2 3 4

1

36 119894 = 5 6 7 8

(4)

The macroscopic fluid density 120588 and velocity 119906 areobtained from the moments of the distribution function asfollows [28]

120588 (119909 119905) =

8

sum

119894=0

119891119894 (119909 119905)

119906 (119909 119905) =1

120588

8

sum

119894=0

119890119894119891119894 (119909 119905)

(5)

and the temperature 119879 is obtained as [32]

119879 =

8

sum

119894=0

119892119894 (119909 119905) (6)

32 Boundary Conditions Boundary conditions (BCs) arevery important part for both the stability and the accuracy of

any kind of numerical solution For LBmodeling the discretedistribution functions on the boundary need to be taken careof to reflect the macroscopic BCs of the fluid In this work atthe wall the bounce-back condition has been applied

Bounce-back BCs are usually used to implement no-slipconditions on the boundary By the bounce-back conditionit is meant that when a particle of a certain fluid for discretedistribution function reaches a boundary node the particlewill scatter back to the fluid alongwith its incoming directionBounce-back condition can be of various types but on-gridbounce-back condition has been used in this paper

321 Boundary Condition for Velocity Four possible direc-tions in two-dimensional structuremdasheast west north andsouthmdashhave been considered in the proposedmodel and no-slip or bounce-back boundary condition is used at the wallswhich has been shown in Figure 1

At east (right) west (left) and south (bottom) walls thebounce-back condition has been applied and the resultingrelations are given below in order

1198913= 1198911

1198917= 1198915

1198916= 1198918

1198911= 1198913

1198915= 1198917

1198918= 1198916

1198912= 1198914

1198915= 1198917

1198916= 1198918

(7)

On the other hand at the north (top) wall three differentboundary conditions have been applied At the inlet Zou andHe boundary conditions have been applied as shown in thefollowing [33]

120588119873=(1198910+ 1198911+ 1198913+ 2 (119891

2+ 1198916+ 1198915))

(1 + 119880)

1198914= 1198912minus2

3120588119873119880

1198918= 1198916minus1

6120588119873119880

1198917= 1198915minus1

6120588119873119880

(8)

where 119880 is the bulk velocity based on the Reynolds numberRe def

= 119880119867] At the outlet the following boundary conditionsare used

1198914119873

= 1198914119873minus1

1198918119873

= 1198918119873minus1

1198917119873

= 1198917119873minus1

(9)

Journal of Computational Engineering 5

and bounce-back condition is used for the rest of the topwalls At the top surface and at each side of a block andpartition the following bounce-back conditions have beenused

Top surface

1198912119909119894

= 1198914119909119894

1198915119909119894

= 1198917119909119894

1198916119909119894

= 1198918119909119894

(10)

Left side

1198911119909119894

= 1198913119909119894

1198915119909119894

= 1198917119909119894

1198918119909119894

= 1198916119909119894

(11)

Right side

1198913119909119894

= 1198911119909119894

1198916119909119894

= 1198918119909119894

1198917119909119894

= 1198915119909119894

(12)

322 Boundary Condition for Temperature Cold and hottemperature conditions are applied at the walls (see Figure 1)

At east (right) wall the cold temperature condition is 1198923=

minus1198921 1198927= minus1198925 and 119892

6= minus1198928

At west (left) wall the cold temperature condition is 1198921=

minus1198923 1198925= minus1198927 and 119892

8= minus1198926

At south (bottom) wall the cold temperature condition is1198922= minus1198924 1198925= minus1198927 and 119892

6= minus1198928

At the north (top) wall in the outlet a zero gradientboundary condition is applied as follows

1198924119873

= 1198924119873minus1

1198928119873

= 1198926119873minus1

1198927119873

= 1198925119873minus1

(13)

And the rest of the top wall is kept cold by using theconditions 119892

4= minus1198922 1198928= minus1198926 and 119892

7= minus1198925

At the top surface of each block the hot temperaturecondition is used as follows

11989221199102

= 119879119908(1199082+ 1199084) minus 11989241199102

11989251199102

= 119879119908(1199085+ 1199087) minus 11989271199102

11989261199102

= 119879119908(1199086+ 1199088) minus 11989281199102

(14)

where 1199102indicates the top surface of the blocks and 119879

119908is the

wall temperature

33 Nondimensional Number and Mixed Convection Param-eter The important nondimensional number Grashof (Gr)and Prandtl (Pr) numbers are defined as [32]

Gr =1205731198661199101198673(119879119867minus 119879119862)

]2

Pr = ]120572

(15)

In the mixed convection the Richardson number Ri def=

GrRe2 controls the flow phenomena In this simulation theforce term is defined as follows [34]

119865 = 3119908119894Ri (119879 minus 119879

119898) 119890119910 (16)

where 119879119898= (119879119867+ 119879119862)2 is the mean temperature In this

paper the fluid velocity 119906 is nondimensionalized by the con-stant inlet velocity119880 and the nondimensional temperature is120579 = (119879 minus 119879

119888)(119879119908minus 119879119888)

In the present work theMach number (Ma) for Re = 100is 005 for Re = 250 is 002 and for Re = 350 is 0014 Allthese values are less than 03 which satisfy the condition ofincompressible fluid flow [32] In buoyant flowMach numberand thermal diffusivity (120572) can be defined by the followingequations after fixing the values of viscosity Prandtl numberand Reynolds number

Ma = ]radicGr119873119888

120572 =]Pr

(17)

4 Convergence Criteria

Standard LBM being explicit time-marching in naturerequires a long time to attain steady state convergenceHowever convergence of solution is one of the highlightsof the procedure of recovering the Navier-Stokes equationsfrom LBM In this single-relaxation-time LBM the iterativeprocedure is terminated when the velocity and temperaturefield satisfy the following convergence criteria

sum10038161003816100381610038161003816120601(119899+1)

minus 120601(119899)10038161003816100381610038161003816

sum1003816100381610038161003816120601(119899+1)1003816100381610038161003816

lt 10minus9 (18)

where 120601 is the velocity 119906 or temperature 119879 and 119899 is theiteration index and the sum is over the whole domain

5 Results and Discussions

This section has been divided into four subsections At firstcode validation has been performed for different values of Reand has been compared in tabular format In the consequentthree subsections three case studies have been consideredinside the hospital ward In all three cases one inlet oneoutlet and six beds have been considered Simulations havebeen carried out by placing one partition and later twopartitions in the room while observing the indoor airflow

6 Journal of Computational Engineering

Table 1 Comparison of average Nusselt numbers of present work with other investigations for Gr = 100 and Pr = 071

Re Ri Present [35] [25] [36] [37] [38] [39] [26]100 001 1917965 194 201 202 1985 210 203116 209400 000062 3789101 384 391 401 38785 385 40246 4080821000 00001 6339137 633 633 642 6345 633 648423 654687

1

05

00 2 4 6 8

xH

yH

minus014 004 021 038 056 073 090 108

(a)

0 2 4 6 8

xH

1

05

0

yH

minus021 000 021 042 063 084 105 126

(b)1

05

0

yH

0 2 4 6 8

xH

minus024 minus002 020 042 064 086 108 130

(c)

Figure 2 Streamline patterns of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

pattern and the field of temperature in the three situationsThis section is ended with the discussion and comparison ofthe average rate of change of heat transfers achieved for eachcase study In these cases Re = 100 250 and 350 Pr = 071and Ri = 1 have been kept for all simulations except the codevalidation case Different values of 120591] generated for differentRe are as follows for Re = 100 it is 0575 for Re = 250 it is0530 and for Re = 350 it is 0521 Likewise different valuesof 120591120572are as follows for Re = 350 it is 053 for Re = 250 it is

0542 and for Re = 100 it is 0605

51 Code Validation For code validation process one testcase is the mixed convection in a lid-driven square cavityflow for Re = 100 400 and 100 and Gr = 100 has beenconsideredThepresent results in terms of the averageNusseltnumber have been compared quantitatively with the availableresults published in different articles that are demonstrated inTable 1 The comparison reveals a very good agreement Theresults were compared with the works of Iwatsu et al [35]Tiwari and Das [38] Kefayati et al [26] Khanafer et al [36]Abdelkhalek [37] Khanafer and Chamkha [25] andWaheed[39]

52 Case Study I Six Beds without Partition in the WardIn the first case study six beds without partition havebeen considered Each bed is of the same dimension How-ever beds are represented as blocks in Figure 1 For thewhole computational domain a lattice size of (400 times 50) sim(119909 times 119910) has been taken in all simulations Each block of

(20times10) sim (119909times119910) lattice size is used in the wardThe beds areuniformly distributed in one row Inlet and outlet have beenplaced vertically on the ceiling on the left and right cornersrespectively The width of both the inlet and the outlet hasbeen kept from 0 to 15 lattices and from 385 to 400 latticesrespectively

Figures 2(a)ndash2(c) show the streamlines appended on 119906119880velocity contour of the airflow that enters the ward throughthe inlet and flows out through the outlet for Re = 100 250and 350 respectively In case of Re = 100 small recirculationsare seen between the blocks and also near the walls in theeast andwest sides of the ward due to bounce-back conditionA comparatively large recirculation is formed in immediateright to the inlet that is near the top wall For increasing Rethe length of the recirculation zones increases As shown inFigure 2 the highest value of 119906119880 is 108 and the lowest valueis minus014 for Re = 100 In case of Re = 250 and 350 themaximum values increase to 126 and 130 respectively AsRe increases the inertia force of air increases which makes iteasier to flow around in the ward and hence more heat willbe transferred out through the outlet

Figure 3 represents the isotherms of the room As can beseen from the simulation result only the top surface of eachblock is kept heated while the gaps between the blocks arecold The heated portion of the blocks represents patients onbeds who are releasing heat continuously

Different velocity patterns have been shown in Figures4(a)ndash4(n) demonstrating the 119906119880 velocity profiles at differentpositions of 119909119867 for the three different Re This figure

Journal of Computational Engineering 7

1

05

00 2 4 6 8

xH

yH

minus000 014 029 044 058 073 088 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 039 055 070 086 096 100

(b)

1

05

00 2 4 6 8

xH

yH

008 024 040 056 072 088 098 100

(c)

Figure 3 Isotherms of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

0 1

yH

uU

Re = 100

Re = 250

Re = 350

(a)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(b)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(c)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(d)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(e)

0 10

02040608

1

yHuU

Re = 100

Re = 250

Re = 350

(f)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(g)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(h)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(i)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(j)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(k)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(l)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

0 1uU

Re = 100

Re = 250

Re = 350

(n)

Figure 4 119906119880 velocity profiles in Case I for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

outlines the speed at which the air is flowing inside the wardDue to the recirculation near the inlet the velocity profiles arealso seen to increase resulting in a bent-shaped plot in Figures4(b) and 4(c) After 119909119867 = 35 onwards the graphs are almostthe same as there the flow characteristics are almost similarexcept for Figure 4(n)which is slightly bent at the top forming

because at this point the air is preparing to go through theoutlet

53 Case Study II Six Beds with One Partition In thisinvestigation the previousmodel has been updated by addinga partition in the middle of the general ward while all other

8 Journal of Computational Engineering

1

05

00 2 4 6 8

xH

yH

minus034 002 037 073 108 144 179 215

(a)

1

05

00 2 4 6 8

xH

yH

minus076 minus032 012 056 100 145 189 233

(b)1

05

00 2 4 6 8

xH

yH

minus093 minus046 002 049 096 143 191 238

(c)

Figure 5 Streamline patterns of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

1

05

00 2 4 6 8

xH

yH

100086072057043029014000

(a)

0 2 4 6 8

xH

1

05

0

yH

100092077069054039023008

(b)

0 2 4 6 8

xH

1

05

0

yH

100099087072056040024009

(c)

Figure 6 Isotherms of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

schematic measurements have been kept the same as shownin Figure 1The lattice size of partition is (5times40) sim (119909times119910) andit is placed just after the first three blocks (beds) Simulationshave been carried out for the same three Reynolds numbersAfter placing a partition just like in Figure 5 recirculationis seen in Figure 5 and it shows much better result thanthe previous simulations The airflow pattern is clearer thistime which shows that air moves inward smoothly passes thepartition naturally without overlapping it and nicely flowsout through the outlet creating its usual recirculation nearthe inlet between the blocks and near the outlet Unlikeearlier the recirculations now are larger and more frequentparticularly after crossing the partition For Re = 100 alarge air circulation can be noticed between blocks 4 and 5and in case of Re = 250 an even larger recirculation has

appeared between blocks 5 and 6 along with a newly emergedone just beside the outlet As for Re = 350 with the increasein convective air current more chaotic flow dynamics can benoticed before the partition appears The airflow pattern inthis region indicates that in case of mixed convection forRe = 350 the air stays in transitional state which showsboth the laminar characteristics of natural convection and theturbulent nature of forced convection thereby representingforced convection Moreover after placing the partition thepeak values of the contour have risen to 215 from 108 233from 126 and 238 from 130 for Re = 100 Re = 250 andRe = 350 respectively

Figure 6 presents the isotherms for this situation Like inprevious case here also the top surfaces of the blocks are keptheated to represent patients on beds and the spaces between

Journal of Computational Engineering 9

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(c)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(d)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 7 119906119880 velocity profiles in Case II for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

the blocks alongwith the partition are kept coldThe presenceof the partition does affect the airflow characteristics as wellas heat transfer phenomenon which has been discussed indetail in the heat transfer part Pr remains the same

In Figure 7 the119880 velocity profiles at different locations of119909 are discussed for the same three Re This time the resultsshow more curvy lines throughout the whole experimentdue to the obstacle caused because of the partition One ofthe obvious differences worth mentioning is in Figure 7(g)when the air faces the partition At this point a long verticalline with a narrow parabolic curve at the top is shownrepresenting the height of the partition whereas the curvedpart illustrates that the air is crossing the partition Evenin Figure 7(h) the graph still maintains its parabolic shapeand continues this pattern throughout till the end Anothernoticeable change can be seen in Figures 7(j) 7(k) and 7(l)at 119909 = 55 119909 = 6 and 119909 = 65 respectively where the bentsare more irregular than the previous case This is because atthese locations large recirculations have formed due to thepartition as shown in Figure 5

According to the 119880 and 119881 centerline velocity distribu-tion plots in Figures 8(a) and 8(b) respectively there isa constriction in the middle of graph This represents thepartition that actually works like a wall where the velocityplots cease just like the vertical walls in the extreme leftand right sides One possible advantage of this partition isthat the airflow can be controlled if the air enters with ahigh speed through the inlet Also it is noticeable in Figures

8(a) and 8(b) that unlike the previous case the partitionhelps to maintain the air velocity at a constant level untilit exits out through the outlet The 119881 velocity still drops tonegative range from zero at the beginning due to downwardfall of air through the inlet and ascends to zero again where itmaintains its constant velocity The graphs are more chaoticafter crossing the partition due to the recirculations shown inthe contour map The temperature plot in Figure 8(c) startsjust like that of the previous situation but this time insteadof becoming constant after a certain level the graph climbsup the partition crosses it and then drops again eventuallydecreasing to zero at 119909 = 8 The rise of airflow against thepartition also results in the increase in temperature at thispoint therefore the steep in the figure

54 Case Study III One Inlet and One Outlet with TwoPartitions This case study has been investigated by furthermodifying the proposed model adding another partition inthe ward It was done to keep patients from being exposedinto more air Each partition is placed every after two blocks(beds) Both the partitions are of the same dimension that is(5 times 40) sim (119909 times 119910) lattice size and all other measurementsare kept the same as previous situations Simulations andanalysis of this case have also been carried out for the samethree Re values Streamlines pattern of Figure 9 obtained afteradding another partition shows that the size and the numberof recirculations increase more than the last observationUnlike Case II now two large recirculations have formed

10 Journal of Computational Engineering

0 2 4 6 8

012 Partition

xH

Re = 100

Re = 250

Re = 350

uH

(a)

0 2 4 6 8

0

1 Partition

xH

Re = 100

Re = 250

Re = 350

H

(b)

0 2 4 6 80

05

1 Partition

xH

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 8 In Case II for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

1

05

00 2 4 6 8

xH

yH

237198159119080041002minus038

(a)

0 2 4 6 8

xH

1

05

0

yH

247198149100051002minus047minus096

(b)

0 2 4 6 8

xH

1

05

0

yH

252199146092039minus014minus068minus121

(c)

Figure 9 Streamline patterns of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

for the corresponding experiments with each Re Even themaximum and minimum legend values have become widerthan the previous situation for example for Re = 100 the215 value has increased to 237 For Re = 250 and Re = 350

the uppermost values have risen to 247 and 252 from 233and 238 respectively Due to bounce-back condition theair is now forming more recirculations against the walls andbetween the blocksThis augmentation of values and recircu-lations due to buoyancy effect is visible for every incrementof Re values and addition of obstacles such as partition

The generated results of isotherms in Figure 10 give avisual idea how the heat is transferred from the blocks and

passes through the outlet Like the other cases only thesurfaces of the blocks are heated to be considered as patientswho are continuously releasing heat Everything remains thesame like previous cases

Figure 11 provides the 119880 velocity profiles for differentpositions of 119909 According to this the graph characteristicfor a partition can be seen in Figure 11(e) at 119909 = 3 andFigure 11(j) at 119909 = 55 indicating the presence of partitionsat these two locations Apart from this at 119909 = 5 and 75 inFigures 11(i) and 11(n) respectively the parabolic shapes aremore curvy than the profiles at other positions caused dueto recirculations in vector plots of Re = 250 and Re = 350

Journal of Computational Engineering 11

1

05

00

2 4 6 8

xH

yH

000 015 029 043 058 072 086 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 038 054 069 077 092 100

(b)

0 2 4 6 8

xH

1

05

0

yH

008 024 040 056 071 087 095 100

(c)

Figure 10 Isotherms of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(c)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(d)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y HuU

minus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 11 119906119880 velocity profiles in Case III for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

Figures 12(a) and 12(b) illustrate119880 and119881 velocity distributioncurves in mid-119910 and Figure 12(c) shows the temperatureprofile at mid-119910 All of these three plots have one thing incommon that is also different than the previous case In theseplots there are two constrictions instead of one where the

velocities or the temperature curve ceasesThis is the locationwhere the two partitions are present But after crossing theseobstacles the respective graphs continue until 119909 = 8 Thetemperature plot in Figure 12(c) has now two steep regionsdue to the partitions

12 Journal of Computational Engineering

0 2 4 6 8

2

1

0

minus1

uH

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(a)

0 2 4 6 8

1

0

minus1

H

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(b)

0 2 4 6 8

1

05

0

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 12 In Case III for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

55 Calculation of Rate of Heat Transfer In heat transferat a boundary (surface) within a fluid the Nusselt number(Nu) is the ratio of convective to conductive heat transferacross (normal to) the boundary Here convection includesboth advection and diffusion procedures The convectionand conduction heat flows are parallel to each other andto the surface normal of the boundary surface and are allperpendicular to the mean fluid flow in the simple case Thisis denoted as [32]

Nu119871=ℎ119905119871

119896 (19)

where ℎ119905is the convective heat transfer coefficient of the

flow 119871 is the characteristic length and 119896 is the thermalconductivity of the fluid

However this section discusses the average rate of changeof heat transfer obtained for different Re This rate isexpressed as average Nusselt number Nu for each case studyin Tables 2 3 and 4 The tables also show generated localNusselt number Nu that follows the expression below

Nu (119909) = minus 120597120579

120597119910

10038161003816100381610038161003816100381610038161003816119910=1199102

(20)

where 1199102is the upper surface of each block

Average Nu is calculated by integrating the above rela-tion over the entire range of interest and thus the resultingequation becomes

Nu = 1

1199092minus 1199091

int

1199092

1199091

Nu (119909) 119889119909 (21)

Here (1199092minus 1199091) is the length of each block

For the first investigation both the individual and averageNu obtained in Table 2 show a rising trend for each increasingRe Since block 1 is the nearest to the inlet it always has thehighest rate of heat transfer while block 6 has the lowest valueas it is located farthest from the inlet

After placing the partition in the middle the rate of heattransfer shown in Table 3 changes dramatically Like Table 2the patient at block 1 is releasing most heat for all three Reand it keeps reducing until block 5 At block 5 the values ofboth individual Nu and total Nu increase for Re = 250 andRe = 350 but for Re = 100 this type of airflow pattern isseen at block 4 The large recirculations were seen earlier inFigure 5 For Re = 100 recirculation is more over block 4 andthat is the reason why at block 4 individual Nu and total Nuhave greater values than those of Re = 250 and Re = 350 Nuis 15341 at block 4 and for the same block these values are13628 and 14032 respectively for Re = 250 and Re = 350On the other hand if Nu at block 5 are observed Re = 250

and Re = 350 lead the race As per Table 3 Nu are 2011121598 and 27535 for three Re The spike in the values ofRe = 250 and Re = 350 was due to chaotic flows over block5 in Figure 5 If changes in total Nu are observed the valuesincrease rapidly for an increase in Re

For Case Study III the shape of recirculation gets biggerdue to increased Re Above block 1 the recirculation zonecomes into view and due to that reason Nu has the biggestedge in this situation But as the air has tendency to passthe first partition it moves slightly upward and that is whypatient at block 2 is getting less airflowThe heat transfer ratealso falls After passing the first partition the airflow gets itsspace and leads to recirculation near block 3 for Re = 100Meanwhile for Re = 250 and Re = 350 patients on block 4get most air More air means more heat transfer and that is

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

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International Journal of

Journal of Computational Engineering 3

Inlet Outlet

TC TC

TH

TC

Gy

L = 8H

(a)

Inlet Outlet

h

H = 5hl = 2h d = 4h

(b)

Inlet Outletb = h2

a = 4h

(c)

OutletInlet b = h2b = h2

a = 4h a = 4h

(d)

Figure 1 Schematic diagram of the geometry of hospital ward showing (a) principles applied building themodel (b) Case I without partition(c) Case II with one partition and (d) Case III with two partitions

are 119886 = 4ℎ and 119887 = ℎ2 respectively The height of the wardis119867 = 5ℎ and 119871 = 8119867 is the length of the wardThe length ofthe inlet and outlet is (ℎ + 119887)2

3 Mathematical Formulation

The LBM was originated from Ludwig Boltzmannrsquos kinetictheory of gasesThe basic theory of this equation is that gasesor fluids can be imagined as consisting of a large number oftiny particles moving with random motion The exchange ofmomentum and energy is found through particle streamingand collision between particles So this process can bedemonstrated by the Boltzmann transport equation [28 29]

120597119891

120597119905+ 119906 sdot nabla119891 = Ω (119891 119891

eq) (1)

where 119891eq is the equilibrium distribution function respec-tively 119906 is the particle velocity andΩ is the collision operatorHere119891 represents119891(119909 119890

119894 119905)which is the probability to locate

a particle at position 119909 with velocity vector 119890119894at time 119905

31 Lattice Boltzmann Method The LBM simplifies Boltz-mannrsquos original idea of gas dynamics by reducing the numberof particles and circumscribing them to the nodes of a latticeFor a two-dimensionalmodel a particle is preferred to streamin a possible of 9 directions including the one staying atrest For this type of modeling the most popular one is11986321198769 model which has been considered in this work Thisis the standard model for two-dimensional structure for bothflow and temperature conditions The velocities for theseconditions are known as macroscopic velocities

4 Journal of Computational Engineering

The discretized Lattice Boltzmann (LB) equations forboth flow and temperature field can bewritten as follows [29]

119891119894(119909 + 120575119890

119894 119905 + 120575119905) minus 119891

119894 (119909 119905)

= minus1

120591][119891119894 (119909 119905) minus 119891

(eq)119894

(119909 119905)] + 120575119905 sdot 119865119894

119892119894(119909 + 120575119890

119894 119905 + 120575119905) minus 119892

119894 (119909 119905)

= minus1

120591120572

[119892119894 (119909 119905) minus 119892

(eq)119894

(119909 119905)]

(2)

Here 120591] = 3] + 05 and 120591120572

= 3120572 + 05 are thesingle-relaxation times that control the rate of approach toequilibrium 119891

119894(119909 119905) and 119892

119894(119909 119905) are the density distribution

functions for velocity and temperature respectively along thedirection 119890

119894at (119909 119905) ] is the kinematic viscosity and 120572 is the

thermal diffusivityTheparticle speed is 119890119894and120588 is the density

To calculate the equilibrium distribution functions forthe velocity 119891eq

119894(119909 119905) and for the temperature 119892eq

119894(119909 119905) the

general expressions have been considered [29ndash31]

119891eq119894= 119908119894120588[1 +

3 (119890119894sdot 119906)

1198882+9 (119890119894sdot 119906)2

21198884minus3 (119906 sdot 119906)

21198882]

119892eq119894= 119908119894119879[1 +

3 (119890119894sdot 119906)

1198882+9 (119890119894sdot 119906)2

21198884minus3 (119906 sdot 119906)

21198882]

(3)

where 119906 = (119906 V) is the fluid velocity and 119888 = Δ119909Δ119905 = 1 is thelattice speed The weighting factors 119908

119894for 11986321198769 are given as

[29]

119908119894=

4

9 119894 = 0

1

9 119894 = 1 2 3 4

1

36 119894 = 5 6 7 8

(4)

The macroscopic fluid density 120588 and velocity 119906 areobtained from the moments of the distribution function asfollows [28]

120588 (119909 119905) =

8

sum

119894=0

119891119894 (119909 119905)

119906 (119909 119905) =1

120588

8

sum

119894=0

119890119894119891119894 (119909 119905)

(5)

and the temperature 119879 is obtained as [32]

119879 =

8

sum

119894=0

119892119894 (119909 119905) (6)

32 Boundary Conditions Boundary conditions (BCs) arevery important part for both the stability and the accuracy of

any kind of numerical solution For LBmodeling the discretedistribution functions on the boundary need to be taken careof to reflect the macroscopic BCs of the fluid In this work atthe wall the bounce-back condition has been applied

Bounce-back BCs are usually used to implement no-slipconditions on the boundary By the bounce-back conditionit is meant that when a particle of a certain fluid for discretedistribution function reaches a boundary node the particlewill scatter back to the fluid alongwith its incoming directionBounce-back condition can be of various types but on-gridbounce-back condition has been used in this paper

321 Boundary Condition for Velocity Four possible direc-tions in two-dimensional structuremdasheast west north andsouthmdashhave been considered in the proposedmodel and no-slip or bounce-back boundary condition is used at the wallswhich has been shown in Figure 1

At east (right) west (left) and south (bottom) walls thebounce-back condition has been applied and the resultingrelations are given below in order

1198913= 1198911

1198917= 1198915

1198916= 1198918

1198911= 1198913

1198915= 1198917

1198918= 1198916

1198912= 1198914

1198915= 1198917

1198916= 1198918

(7)

On the other hand at the north (top) wall three differentboundary conditions have been applied At the inlet Zou andHe boundary conditions have been applied as shown in thefollowing [33]

120588119873=(1198910+ 1198911+ 1198913+ 2 (119891

2+ 1198916+ 1198915))

(1 + 119880)

1198914= 1198912minus2

3120588119873119880

1198918= 1198916minus1

6120588119873119880

1198917= 1198915minus1

6120588119873119880

(8)

where 119880 is the bulk velocity based on the Reynolds numberRe def

= 119880119867] At the outlet the following boundary conditionsare used

1198914119873

= 1198914119873minus1

1198918119873

= 1198918119873minus1

1198917119873

= 1198917119873minus1

(9)

Journal of Computational Engineering 5

and bounce-back condition is used for the rest of the topwalls At the top surface and at each side of a block andpartition the following bounce-back conditions have beenused

Top surface

1198912119909119894

= 1198914119909119894

1198915119909119894

= 1198917119909119894

1198916119909119894

= 1198918119909119894

(10)

Left side

1198911119909119894

= 1198913119909119894

1198915119909119894

= 1198917119909119894

1198918119909119894

= 1198916119909119894

(11)

Right side

1198913119909119894

= 1198911119909119894

1198916119909119894

= 1198918119909119894

1198917119909119894

= 1198915119909119894

(12)

322 Boundary Condition for Temperature Cold and hottemperature conditions are applied at the walls (see Figure 1)

At east (right) wall the cold temperature condition is 1198923=

minus1198921 1198927= minus1198925 and 119892

6= minus1198928

At west (left) wall the cold temperature condition is 1198921=

minus1198923 1198925= minus1198927 and 119892

8= minus1198926

At south (bottom) wall the cold temperature condition is1198922= minus1198924 1198925= minus1198927 and 119892

6= minus1198928

At the north (top) wall in the outlet a zero gradientboundary condition is applied as follows

1198924119873

= 1198924119873minus1

1198928119873

= 1198926119873minus1

1198927119873

= 1198925119873minus1

(13)

And the rest of the top wall is kept cold by using theconditions 119892

4= minus1198922 1198928= minus1198926 and 119892

7= minus1198925

At the top surface of each block the hot temperaturecondition is used as follows

11989221199102

= 119879119908(1199082+ 1199084) minus 11989241199102

11989251199102

= 119879119908(1199085+ 1199087) minus 11989271199102

11989261199102

= 119879119908(1199086+ 1199088) minus 11989281199102

(14)

where 1199102indicates the top surface of the blocks and 119879

119908is the

wall temperature

33 Nondimensional Number and Mixed Convection Param-eter The important nondimensional number Grashof (Gr)and Prandtl (Pr) numbers are defined as [32]

Gr =1205731198661199101198673(119879119867minus 119879119862)

]2

Pr = ]120572

(15)

In the mixed convection the Richardson number Ri def=

GrRe2 controls the flow phenomena In this simulation theforce term is defined as follows [34]

119865 = 3119908119894Ri (119879 minus 119879

119898) 119890119910 (16)

where 119879119898= (119879119867+ 119879119862)2 is the mean temperature In this

paper the fluid velocity 119906 is nondimensionalized by the con-stant inlet velocity119880 and the nondimensional temperature is120579 = (119879 minus 119879

119888)(119879119908minus 119879119888)

In the present work theMach number (Ma) for Re = 100is 005 for Re = 250 is 002 and for Re = 350 is 0014 Allthese values are less than 03 which satisfy the condition ofincompressible fluid flow [32] In buoyant flowMach numberand thermal diffusivity (120572) can be defined by the followingequations after fixing the values of viscosity Prandtl numberand Reynolds number

Ma = ]radicGr119873119888

120572 =]Pr

(17)

4 Convergence Criteria

Standard LBM being explicit time-marching in naturerequires a long time to attain steady state convergenceHowever convergence of solution is one of the highlightsof the procedure of recovering the Navier-Stokes equationsfrom LBM In this single-relaxation-time LBM the iterativeprocedure is terminated when the velocity and temperaturefield satisfy the following convergence criteria

sum10038161003816100381610038161003816120601(119899+1)

minus 120601(119899)10038161003816100381610038161003816

sum1003816100381610038161003816120601(119899+1)1003816100381610038161003816

lt 10minus9 (18)

where 120601 is the velocity 119906 or temperature 119879 and 119899 is theiteration index and the sum is over the whole domain

5 Results and Discussions

This section has been divided into four subsections At firstcode validation has been performed for different values of Reand has been compared in tabular format In the consequentthree subsections three case studies have been consideredinside the hospital ward In all three cases one inlet oneoutlet and six beds have been considered Simulations havebeen carried out by placing one partition and later twopartitions in the room while observing the indoor airflow

6 Journal of Computational Engineering

Table 1 Comparison of average Nusselt numbers of present work with other investigations for Gr = 100 and Pr = 071

Re Ri Present [35] [25] [36] [37] [38] [39] [26]100 001 1917965 194 201 202 1985 210 203116 209400 000062 3789101 384 391 401 38785 385 40246 4080821000 00001 6339137 633 633 642 6345 633 648423 654687

1

05

00 2 4 6 8

xH

yH

minus014 004 021 038 056 073 090 108

(a)

0 2 4 6 8

xH

1

05

0

yH

minus021 000 021 042 063 084 105 126

(b)1

05

0

yH

0 2 4 6 8

xH

minus024 minus002 020 042 064 086 108 130

(c)

Figure 2 Streamline patterns of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

pattern and the field of temperature in the three situationsThis section is ended with the discussion and comparison ofthe average rate of change of heat transfers achieved for eachcase study In these cases Re = 100 250 and 350 Pr = 071and Ri = 1 have been kept for all simulations except the codevalidation case Different values of 120591] generated for differentRe are as follows for Re = 100 it is 0575 for Re = 250 it is0530 and for Re = 350 it is 0521 Likewise different valuesof 120591120572are as follows for Re = 350 it is 053 for Re = 250 it is

0542 and for Re = 100 it is 0605

51 Code Validation For code validation process one testcase is the mixed convection in a lid-driven square cavityflow for Re = 100 400 and 100 and Gr = 100 has beenconsideredThepresent results in terms of the averageNusseltnumber have been compared quantitatively with the availableresults published in different articles that are demonstrated inTable 1 The comparison reveals a very good agreement Theresults were compared with the works of Iwatsu et al [35]Tiwari and Das [38] Kefayati et al [26] Khanafer et al [36]Abdelkhalek [37] Khanafer and Chamkha [25] andWaheed[39]

52 Case Study I Six Beds without Partition in the WardIn the first case study six beds without partition havebeen considered Each bed is of the same dimension How-ever beds are represented as blocks in Figure 1 For thewhole computational domain a lattice size of (400 times 50) sim(119909 times 119910) has been taken in all simulations Each block of

(20times10) sim (119909times119910) lattice size is used in the wardThe beds areuniformly distributed in one row Inlet and outlet have beenplaced vertically on the ceiling on the left and right cornersrespectively The width of both the inlet and the outlet hasbeen kept from 0 to 15 lattices and from 385 to 400 latticesrespectively

Figures 2(a)ndash2(c) show the streamlines appended on 119906119880velocity contour of the airflow that enters the ward throughthe inlet and flows out through the outlet for Re = 100 250and 350 respectively In case of Re = 100 small recirculationsare seen between the blocks and also near the walls in theeast andwest sides of the ward due to bounce-back conditionA comparatively large recirculation is formed in immediateright to the inlet that is near the top wall For increasing Rethe length of the recirculation zones increases As shown inFigure 2 the highest value of 119906119880 is 108 and the lowest valueis minus014 for Re = 100 In case of Re = 250 and 350 themaximum values increase to 126 and 130 respectively AsRe increases the inertia force of air increases which makes iteasier to flow around in the ward and hence more heat willbe transferred out through the outlet

Figure 3 represents the isotherms of the room As can beseen from the simulation result only the top surface of eachblock is kept heated while the gaps between the blocks arecold The heated portion of the blocks represents patients onbeds who are releasing heat continuously

Different velocity patterns have been shown in Figures4(a)ndash4(n) demonstrating the 119906119880 velocity profiles at differentpositions of 119909119867 for the three different Re This figure

Journal of Computational Engineering 7

1

05

00 2 4 6 8

xH

yH

minus000 014 029 044 058 073 088 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 039 055 070 086 096 100

(b)

1

05

00 2 4 6 8

xH

yH

008 024 040 056 072 088 098 100

(c)

Figure 3 Isotherms of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

0 1

yH

uU

Re = 100

Re = 250

Re = 350

(a)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(b)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(c)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(d)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(e)

0 10

02040608

1

yHuU

Re = 100

Re = 250

Re = 350

(f)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(g)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(h)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(i)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(j)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(k)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(l)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

0 1uU

Re = 100

Re = 250

Re = 350

(n)

Figure 4 119906119880 velocity profiles in Case I for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

outlines the speed at which the air is flowing inside the wardDue to the recirculation near the inlet the velocity profiles arealso seen to increase resulting in a bent-shaped plot in Figures4(b) and 4(c) After 119909119867 = 35 onwards the graphs are almostthe same as there the flow characteristics are almost similarexcept for Figure 4(n)which is slightly bent at the top forming

because at this point the air is preparing to go through theoutlet

53 Case Study II Six Beds with One Partition In thisinvestigation the previousmodel has been updated by addinga partition in the middle of the general ward while all other

8 Journal of Computational Engineering

1

05

00 2 4 6 8

xH

yH

minus034 002 037 073 108 144 179 215

(a)

1

05

00 2 4 6 8

xH

yH

minus076 minus032 012 056 100 145 189 233

(b)1

05

00 2 4 6 8

xH

yH

minus093 minus046 002 049 096 143 191 238

(c)

Figure 5 Streamline patterns of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

1

05

00 2 4 6 8

xH

yH

100086072057043029014000

(a)

0 2 4 6 8

xH

1

05

0

yH

100092077069054039023008

(b)

0 2 4 6 8

xH

1

05

0

yH

100099087072056040024009

(c)

Figure 6 Isotherms of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

schematic measurements have been kept the same as shownin Figure 1The lattice size of partition is (5times40) sim (119909times119910) andit is placed just after the first three blocks (beds) Simulationshave been carried out for the same three Reynolds numbersAfter placing a partition just like in Figure 5 recirculationis seen in Figure 5 and it shows much better result thanthe previous simulations The airflow pattern is clearer thistime which shows that air moves inward smoothly passes thepartition naturally without overlapping it and nicely flowsout through the outlet creating its usual recirculation nearthe inlet between the blocks and near the outlet Unlikeearlier the recirculations now are larger and more frequentparticularly after crossing the partition For Re = 100 alarge air circulation can be noticed between blocks 4 and 5and in case of Re = 250 an even larger recirculation has

appeared between blocks 5 and 6 along with a newly emergedone just beside the outlet As for Re = 350 with the increasein convective air current more chaotic flow dynamics can benoticed before the partition appears The airflow pattern inthis region indicates that in case of mixed convection forRe = 350 the air stays in transitional state which showsboth the laminar characteristics of natural convection and theturbulent nature of forced convection thereby representingforced convection Moreover after placing the partition thepeak values of the contour have risen to 215 from 108 233from 126 and 238 from 130 for Re = 100 Re = 250 andRe = 350 respectively

Figure 6 presents the isotherms for this situation Like inprevious case here also the top surfaces of the blocks are keptheated to represent patients on beds and the spaces between

Journal of Computational Engineering 9

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(c)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(d)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 7 119906119880 velocity profiles in Case II for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

the blocks alongwith the partition are kept coldThe presenceof the partition does affect the airflow characteristics as wellas heat transfer phenomenon which has been discussed indetail in the heat transfer part Pr remains the same

In Figure 7 the119880 velocity profiles at different locations of119909 are discussed for the same three Re This time the resultsshow more curvy lines throughout the whole experimentdue to the obstacle caused because of the partition One ofthe obvious differences worth mentioning is in Figure 7(g)when the air faces the partition At this point a long verticalline with a narrow parabolic curve at the top is shownrepresenting the height of the partition whereas the curvedpart illustrates that the air is crossing the partition Evenin Figure 7(h) the graph still maintains its parabolic shapeand continues this pattern throughout till the end Anothernoticeable change can be seen in Figures 7(j) 7(k) and 7(l)at 119909 = 55 119909 = 6 and 119909 = 65 respectively where the bentsare more irregular than the previous case This is because atthese locations large recirculations have formed due to thepartition as shown in Figure 5

According to the 119880 and 119881 centerline velocity distribu-tion plots in Figures 8(a) and 8(b) respectively there isa constriction in the middle of graph This represents thepartition that actually works like a wall where the velocityplots cease just like the vertical walls in the extreme leftand right sides One possible advantage of this partition isthat the airflow can be controlled if the air enters with ahigh speed through the inlet Also it is noticeable in Figures

8(a) and 8(b) that unlike the previous case the partitionhelps to maintain the air velocity at a constant level untilit exits out through the outlet The 119881 velocity still drops tonegative range from zero at the beginning due to downwardfall of air through the inlet and ascends to zero again where itmaintains its constant velocity The graphs are more chaoticafter crossing the partition due to the recirculations shown inthe contour map The temperature plot in Figure 8(c) startsjust like that of the previous situation but this time insteadof becoming constant after a certain level the graph climbsup the partition crosses it and then drops again eventuallydecreasing to zero at 119909 = 8 The rise of airflow against thepartition also results in the increase in temperature at thispoint therefore the steep in the figure

54 Case Study III One Inlet and One Outlet with TwoPartitions This case study has been investigated by furthermodifying the proposed model adding another partition inthe ward It was done to keep patients from being exposedinto more air Each partition is placed every after two blocks(beds) Both the partitions are of the same dimension that is(5 times 40) sim (119909 times 119910) lattice size and all other measurementsare kept the same as previous situations Simulations andanalysis of this case have also been carried out for the samethree Re values Streamlines pattern of Figure 9 obtained afteradding another partition shows that the size and the numberof recirculations increase more than the last observationUnlike Case II now two large recirculations have formed

10 Journal of Computational Engineering

0 2 4 6 8

012 Partition

xH

Re = 100

Re = 250

Re = 350

uH

(a)

0 2 4 6 8

0

1 Partition

xH

Re = 100

Re = 250

Re = 350

H

(b)

0 2 4 6 80

05

1 Partition

xH

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 8 In Case II for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

1

05

00 2 4 6 8

xH

yH

237198159119080041002minus038

(a)

0 2 4 6 8

xH

1

05

0

yH

247198149100051002minus047minus096

(b)

0 2 4 6 8

xH

1

05

0

yH

252199146092039minus014minus068minus121

(c)

Figure 9 Streamline patterns of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

for the corresponding experiments with each Re Even themaximum and minimum legend values have become widerthan the previous situation for example for Re = 100 the215 value has increased to 237 For Re = 250 and Re = 350

the uppermost values have risen to 247 and 252 from 233and 238 respectively Due to bounce-back condition theair is now forming more recirculations against the walls andbetween the blocksThis augmentation of values and recircu-lations due to buoyancy effect is visible for every incrementof Re values and addition of obstacles such as partition

The generated results of isotherms in Figure 10 give avisual idea how the heat is transferred from the blocks and

passes through the outlet Like the other cases only thesurfaces of the blocks are heated to be considered as patientswho are continuously releasing heat Everything remains thesame like previous cases

Figure 11 provides the 119880 velocity profiles for differentpositions of 119909 According to this the graph characteristicfor a partition can be seen in Figure 11(e) at 119909 = 3 andFigure 11(j) at 119909 = 55 indicating the presence of partitionsat these two locations Apart from this at 119909 = 5 and 75 inFigures 11(i) and 11(n) respectively the parabolic shapes aremore curvy than the profiles at other positions caused dueto recirculations in vector plots of Re = 250 and Re = 350

Journal of Computational Engineering 11

1

05

00

2 4 6 8

xH

yH

000 015 029 043 058 072 086 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 038 054 069 077 092 100

(b)

0 2 4 6 8

xH

1

05

0

yH

008 024 040 056 071 087 095 100

(c)

Figure 10 Isotherms of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(c)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(d)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y HuU

minus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 11 119906119880 velocity profiles in Case III for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

Figures 12(a) and 12(b) illustrate119880 and119881 velocity distributioncurves in mid-119910 and Figure 12(c) shows the temperatureprofile at mid-119910 All of these three plots have one thing incommon that is also different than the previous case In theseplots there are two constrictions instead of one where the

velocities or the temperature curve ceasesThis is the locationwhere the two partitions are present But after crossing theseobstacles the respective graphs continue until 119909 = 8 Thetemperature plot in Figure 12(c) has now two steep regionsdue to the partitions

12 Journal of Computational Engineering

0 2 4 6 8

2

1

0

minus1

uH

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(a)

0 2 4 6 8

1

0

minus1

H

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(b)

0 2 4 6 8

1

05

0

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 12 In Case III for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

55 Calculation of Rate of Heat Transfer In heat transferat a boundary (surface) within a fluid the Nusselt number(Nu) is the ratio of convective to conductive heat transferacross (normal to) the boundary Here convection includesboth advection and diffusion procedures The convectionand conduction heat flows are parallel to each other andto the surface normal of the boundary surface and are allperpendicular to the mean fluid flow in the simple case Thisis denoted as [32]

Nu119871=ℎ119905119871

119896 (19)

where ℎ119905is the convective heat transfer coefficient of the

flow 119871 is the characteristic length and 119896 is the thermalconductivity of the fluid

However this section discusses the average rate of changeof heat transfer obtained for different Re This rate isexpressed as average Nusselt number Nu for each case studyin Tables 2 3 and 4 The tables also show generated localNusselt number Nu that follows the expression below

Nu (119909) = minus 120597120579

120597119910

10038161003816100381610038161003816100381610038161003816119910=1199102

(20)

where 1199102is the upper surface of each block

Average Nu is calculated by integrating the above rela-tion over the entire range of interest and thus the resultingequation becomes

Nu = 1

1199092minus 1199091

int

1199092

1199091

Nu (119909) 119889119909 (21)

Here (1199092minus 1199091) is the length of each block

For the first investigation both the individual and averageNu obtained in Table 2 show a rising trend for each increasingRe Since block 1 is the nearest to the inlet it always has thehighest rate of heat transfer while block 6 has the lowest valueas it is located farthest from the inlet

After placing the partition in the middle the rate of heattransfer shown in Table 3 changes dramatically Like Table 2the patient at block 1 is releasing most heat for all three Reand it keeps reducing until block 5 At block 5 the values ofboth individual Nu and total Nu increase for Re = 250 andRe = 350 but for Re = 100 this type of airflow pattern isseen at block 4 The large recirculations were seen earlier inFigure 5 For Re = 100 recirculation is more over block 4 andthat is the reason why at block 4 individual Nu and total Nuhave greater values than those of Re = 250 and Re = 350 Nuis 15341 at block 4 and for the same block these values are13628 and 14032 respectively for Re = 250 and Re = 350On the other hand if Nu at block 5 are observed Re = 250

and Re = 350 lead the race As per Table 3 Nu are 2011121598 and 27535 for three Re The spike in the values ofRe = 250 and Re = 350 was due to chaotic flows over block5 in Figure 5 If changes in total Nu are observed the valuesincrease rapidly for an increase in Re

For Case Study III the shape of recirculation gets biggerdue to increased Re Above block 1 the recirculation zonecomes into view and due to that reason Nu has the biggestedge in this situation But as the air has tendency to passthe first partition it moves slightly upward and that is whypatient at block 2 is getting less airflowThe heat transfer ratealso falls After passing the first partition the airflow gets itsspace and leads to recirculation near block 3 for Re = 100Meanwhile for Re = 250 and Re = 350 patients on block 4get most air More air means more heat transfer and that is

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

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International Journal of

4 Journal of Computational Engineering

The discretized Lattice Boltzmann (LB) equations forboth flow and temperature field can bewritten as follows [29]

119891119894(119909 + 120575119890

119894 119905 + 120575119905) minus 119891

119894 (119909 119905)

= minus1

120591][119891119894 (119909 119905) minus 119891

(eq)119894

(119909 119905)] + 120575119905 sdot 119865119894

119892119894(119909 + 120575119890

119894 119905 + 120575119905) minus 119892

119894 (119909 119905)

= minus1

120591120572

[119892119894 (119909 119905) minus 119892

(eq)119894

(119909 119905)]

(2)

Here 120591] = 3] + 05 and 120591120572

= 3120572 + 05 are thesingle-relaxation times that control the rate of approach toequilibrium 119891

119894(119909 119905) and 119892

119894(119909 119905) are the density distribution

functions for velocity and temperature respectively along thedirection 119890

119894at (119909 119905) ] is the kinematic viscosity and 120572 is the

thermal diffusivityTheparticle speed is 119890119894and120588 is the density

To calculate the equilibrium distribution functions forthe velocity 119891eq

119894(119909 119905) and for the temperature 119892eq

119894(119909 119905) the

general expressions have been considered [29ndash31]

119891eq119894= 119908119894120588[1 +

3 (119890119894sdot 119906)

1198882+9 (119890119894sdot 119906)2

21198884minus3 (119906 sdot 119906)

21198882]

119892eq119894= 119908119894119879[1 +

3 (119890119894sdot 119906)

1198882+9 (119890119894sdot 119906)2

21198884minus3 (119906 sdot 119906)

21198882]

(3)

where 119906 = (119906 V) is the fluid velocity and 119888 = Δ119909Δ119905 = 1 is thelattice speed The weighting factors 119908

119894for 11986321198769 are given as

[29]

119908119894=

4

9 119894 = 0

1

9 119894 = 1 2 3 4

1

36 119894 = 5 6 7 8

(4)

The macroscopic fluid density 120588 and velocity 119906 areobtained from the moments of the distribution function asfollows [28]

120588 (119909 119905) =

8

sum

119894=0

119891119894 (119909 119905)

119906 (119909 119905) =1

120588

8

sum

119894=0

119890119894119891119894 (119909 119905)

(5)

and the temperature 119879 is obtained as [32]

119879 =

8

sum

119894=0

119892119894 (119909 119905) (6)

32 Boundary Conditions Boundary conditions (BCs) arevery important part for both the stability and the accuracy of

any kind of numerical solution For LBmodeling the discretedistribution functions on the boundary need to be taken careof to reflect the macroscopic BCs of the fluid In this work atthe wall the bounce-back condition has been applied

Bounce-back BCs are usually used to implement no-slipconditions on the boundary By the bounce-back conditionit is meant that when a particle of a certain fluid for discretedistribution function reaches a boundary node the particlewill scatter back to the fluid alongwith its incoming directionBounce-back condition can be of various types but on-gridbounce-back condition has been used in this paper

321 Boundary Condition for Velocity Four possible direc-tions in two-dimensional structuremdasheast west north andsouthmdashhave been considered in the proposedmodel and no-slip or bounce-back boundary condition is used at the wallswhich has been shown in Figure 1

At east (right) west (left) and south (bottom) walls thebounce-back condition has been applied and the resultingrelations are given below in order

1198913= 1198911

1198917= 1198915

1198916= 1198918

1198911= 1198913

1198915= 1198917

1198918= 1198916

1198912= 1198914

1198915= 1198917

1198916= 1198918

(7)

On the other hand at the north (top) wall three differentboundary conditions have been applied At the inlet Zou andHe boundary conditions have been applied as shown in thefollowing [33]

120588119873=(1198910+ 1198911+ 1198913+ 2 (119891

2+ 1198916+ 1198915))

(1 + 119880)

1198914= 1198912minus2

3120588119873119880

1198918= 1198916minus1

6120588119873119880

1198917= 1198915minus1

6120588119873119880

(8)

where 119880 is the bulk velocity based on the Reynolds numberRe def

= 119880119867] At the outlet the following boundary conditionsare used

1198914119873

= 1198914119873minus1

1198918119873

= 1198918119873minus1

1198917119873

= 1198917119873minus1

(9)

Journal of Computational Engineering 5

and bounce-back condition is used for the rest of the topwalls At the top surface and at each side of a block andpartition the following bounce-back conditions have beenused

Top surface

1198912119909119894

= 1198914119909119894

1198915119909119894

= 1198917119909119894

1198916119909119894

= 1198918119909119894

(10)

Left side

1198911119909119894

= 1198913119909119894

1198915119909119894

= 1198917119909119894

1198918119909119894

= 1198916119909119894

(11)

Right side

1198913119909119894

= 1198911119909119894

1198916119909119894

= 1198918119909119894

1198917119909119894

= 1198915119909119894

(12)

322 Boundary Condition for Temperature Cold and hottemperature conditions are applied at the walls (see Figure 1)

At east (right) wall the cold temperature condition is 1198923=

minus1198921 1198927= minus1198925 and 119892

6= minus1198928

At west (left) wall the cold temperature condition is 1198921=

minus1198923 1198925= minus1198927 and 119892

8= minus1198926

At south (bottom) wall the cold temperature condition is1198922= minus1198924 1198925= minus1198927 and 119892

6= minus1198928

At the north (top) wall in the outlet a zero gradientboundary condition is applied as follows

1198924119873

= 1198924119873minus1

1198928119873

= 1198926119873minus1

1198927119873

= 1198925119873minus1

(13)

And the rest of the top wall is kept cold by using theconditions 119892

4= minus1198922 1198928= minus1198926 and 119892

7= minus1198925

At the top surface of each block the hot temperaturecondition is used as follows

11989221199102

= 119879119908(1199082+ 1199084) minus 11989241199102

11989251199102

= 119879119908(1199085+ 1199087) minus 11989271199102

11989261199102

= 119879119908(1199086+ 1199088) minus 11989281199102

(14)

where 1199102indicates the top surface of the blocks and 119879

119908is the

wall temperature

33 Nondimensional Number and Mixed Convection Param-eter The important nondimensional number Grashof (Gr)and Prandtl (Pr) numbers are defined as [32]

Gr =1205731198661199101198673(119879119867minus 119879119862)

]2

Pr = ]120572

(15)

In the mixed convection the Richardson number Ri def=

GrRe2 controls the flow phenomena In this simulation theforce term is defined as follows [34]

119865 = 3119908119894Ri (119879 minus 119879

119898) 119890119910 (16)

where 119879119898= (119879119867+ 119879119862)2 is the mean temperature In this

paper the fluid velocity 119906 is nondimensionalized by the con-stant inlet velocity119880 and the nondimensional temperature is120579 = (119879 minus 119879

119888)(119879119908minus 119879119888)

In the present work theMach number (Ma) for Re = 100is 005 for Re = 250 is 002 and for Re = 350 is 0014 Allthese values are less than 03 which satisfy the condition ofincompressible fluid flow [32] In buoyant flowMach numberand thermal diffusivity (120572) can be defined by the followingequations after fixing the values of viscosity Prandtl numberand Reynolds number

Ma = ]radicGr119873119888

120572 =]Pr

(17)

4 Convergence Criteria

Standard LBM being explicit time-marching in naturerequires a long time to attain steady state convergenceHowever convergence of solution is one of the highlightsof the procedure of recovering the Navier-Stokes equationsfrom LBM In this single-relaxation-time LBM the iterativeprocedure is terminated when the velocity and temperaturefield satisfy the following convergence criteria

sum10038161003816100381610038161003816120601(119899+1)

minus 120601(119899)10038161003816100381610038161003816

sum1003816100381610038161003816120601(119899+1)1003816100381610038161003816

lt 10minus9 (18)

where 120601 is the velocity 119906 or temperature 119879 and 119899 is theiteration index and the sum is over the whole domain

5 Results and Discussions

This section has been divided into four subsections At firstcode validation has been performed for different values of Reand has been compared in tabular format In the consequentthree subsections three case studies have been consideredinside the hospital ward In all three cases one inlet oneoutlet and six beds have been considered Simulations havebeen carried out by placing one partition and later twopartitions in the room while observing the indoor airflow

6 Journal of Computational Engineering

Table 1 Comparison of average Nusselt numbers of present work with other investigations for Gr = 100 and Pr = 071

Re Ri Present [35] [25] [36] [37] [38] [39] [26]100 001 1917965 194 201 202 1985 210 203116 209400 000062 3789101 384 391 401 38785 385 40246 4080821000 00001 6339137 633 633 642 6345 633 648423 654687

1

05

00 2 4 6 8

xH

yH

minus014 004 021 038 056 073 090 108

(a)

0 2 4 6 8

xH

1

05

0

yH

minus021 000 021 042 063 084 105 126

(b)1

05

0

yH

0 2 4 6 8

xH

minus024 minus002 020 042 064 086 108 130

(c)

Figure 2 Streamline patterns of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

pattern and the field of temperature in the three situationsThis section is ended with the discussion and comparison ofthe average rate of change of heat transfers achieved for eachcase study In these cases Re = 100 250 and 350 Pr = 071and Ri = 1 have been kept for all simulations except the codevalidation case Different values of 120591] generated for differentRe are as follows for Re = 100 it is 0575 for Re = 250 it is0530 and for Re = 350 it is 0521 Likewise different valuesof 120591120572are as follows for Re = 350 it is 053 for Re = 250 it is

0542 and for Re = 100 it is 0605

51 Code Validation For code validation process one testcase is the mixed convection in a lid-driven square cavityflow for Re = 100 400 and 100 and Gr = 100 has beenconsideredThepresent results in terms of the averageNusseltnumber have been compared quantitatively with the availableresults published in different articles that are demonstrated inTable 1 The comparison reveals a very good agreement Theresults were compared with the works of Iwatsu et al [35]Tiwari and Das [38] Kefayati et al [26] Khanafer et al [36]Abdelkhalek [37] Khanafer and Chamkha [25] andWaheed[39]

52 Case Study I Six Beds without Partition in the WardIn the first case study six beds without partition havebeen considered Each bed is of the same dimension How-ever beds are represented as blocks in Figure 1 For thewhole computational domain a lattice size of (400 times 50) sim(119909 times 119910) has been taken in all simulations Each block of

(20times10) sim (119909times119910) lattice size is used in the wardThe beds areuniformly distributed in one row Inlet and outlet have beenplaced vertically on the ceiling on the left and right cornersrespectively The width of both the inlet and the outlet hasbeen kept from 0 to 15 lattices and from 385 to 400 latticesrespectively

Figures 2(a)ndash2(c) show the streamlines appended on 119906119880velocity contour of the airflow that enters the ward throughthe inlet and flows out through the outlet for Re = 100 250and 350 respectively In case of Re = 100 small recirculationsare seen between the blocks and also near the walls in theeast andwest sides of the ward due to bounce-back conditionA comparatively large recirculation is formed in immediateright to the inlet that is near the top wall For increasing Rethe length of the recirculation zones increases As shown inFigure 2 the highest value of 119906119880 is 108 and the lowest valueis minus014 for Re = 100 In case of Re = 250 and 350 themaximum values increase to 126 and 130 respectively AsRe increases the inertia force of air increases which makes iteasier to flow around in the ward and hence more heat willbe transferred out through the outlet

Figure 3 represents the isotherms of the room As can beseen from the simulation result only the top surface of eachblock is kept heated while the gaps between the blocks arecold The heated portion of the blocks represents patients onbeds who are releasing heat continuously

Different velocity patterns have been shown in Figures4(a)ndash4(n) demonstrating the 119906119880 velocity profiles at differentpositions of 119909119867 for the three different Re This figure

Journal of Computational Engineering 7

1

05

00 2 4 6 8

xH

yH

minus000 014 029 044 058 073 088 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 039 055 070 086 096 100

(b)

1

05

00 2 4 6 8

xH

yH

008 024 040 056 072 088 098 100

(c)

Figure 3 Isotherms of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

0 1

yH

uU

Re = 100

Re = 250

Re = 350

(a)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(b)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(c)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(d)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(e)

0 10

02040608

1

yHuU

Re = 100

Re = 250

Re = 350

(f)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(g)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(h)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(i)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(j)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(k)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(l)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

0 1uU

Re = 100

Re = 250

Re = 350

(n)

Figure 4 119906119880 velocity profiles in Case I for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

outlines the speed at which the air is flowing inside the wardDue to the recirculation near the inlet the velocity profiles arealso seen to increase resulting in a bent-shaped plot in Figures4(b) and 4(c) After 119909119867 = 35 onwards the graphs are almostthe same as there the flow characteristics are almost similarexcept for Figure 4(n)which is slightly bent at the top forming

because at this point the air is preparing to go through theoutlet

53 Case Study II Six Beds with One Partition In thisinvestigation the previousmodel has been updated by addinga partition in the middle of the general ward while all other

8 Journal of Computational Engineering

1

05

00 2 4 6 8

xH

yH

minus034 002 037 073 108 144 179 215

(a)

1

05

00 2 4 6 8

xH

yH

minus076 minus032 012 056 100 145 189 233

(b)1

05

00 2 4 6 8

xH

yH

minus093 minus046 002 049 096 143 191 238

(c)

Figure 5 Streamline patterns of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

1

05

00 2 4 6 8

xH

yH

100086072057043029014000

(a)

0 2 4 6 8

xH

1

05

0

yH

100092077069054039023008

(b)

0 2 4 6 8

xH

1

05

0

yH

100099087072056040024009

(c)

Figure 6 Isotherms of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

schematic measurements have been kept the same as shownin Figure 1The lattice size of partition is (5times40) sim (119909times119910) andit is placed just after the first three blocks (beds) Simulationshave been carried out for the same three Reynolds numbersAfter placing a partition just like in Figure 5 recirculationis seen in Figure 5 and it shows much better result thanthe previous simulations The airflow pattern is clearer thistime which shows that air moves inward smoothly passes thepartition naturally without overlapping it and nicely flowsout through the outlet creating its usual recirculation nearthe inlet between the blocks and near the outlet Unlikeearlier the recirculations now are larger and more frequentparticularly after crossing the partition For Re = 100 alarge air circulation can be noticed between blocks 4 and 5and in case of Re = 250 an even larger recirculation has

appeared between blocks 5 and 6 along with a newly emergedone just beside the outlet As for Re = 350 with the increasein convective air current more chaotic flow dynamics can benoticed before the partition appears The airflow pattern inthis region indicates that in case of mixed convection forRe = 350 the air stays in transitional state which showsboth the laminar characteristics of natural convection and theturbulent nature of forced convection thereby representingforced convection Moreover after placing the partition thepeak values of the contour have risen to 215 from 108 233from 126 and 238 from 130 for Re = 100 Re = 250 andRe = 350 respectively

Figure 6 presents the isotherms for this situation Like inprevious case here also the top surfaces of the blocks are keptheated to represent patients on beds and the spaces between

Journal of Computational Engineering 9

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(c)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(d)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 7 119906119880 velocity profiles in Case II for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

the blocks alongwith the partition are kept coldThe presenceof the partition does affect the airflow characteristics as wellas heat transfer phenomenon which has been discussed indetail in the heat transfer part Pr remains the same

In Figure 7 the119880 velocity profiles at different locations of119909 are discussed for the same three Re This time the resultsshow more curvy lines throughout the whole experimentdue to the obstacle caused because of the partition One ofthe obvious differences worth mentioning is in Figure 7(g)when the air faces the partition At this point a long verticalline with a narrow parabolic curve at the top is shownrepresenting the height of the partition whereas the curvedpart illustrates that the air is crossing the partition Evenin Figure 7(h) the graph still maintains its parabolic shapeand continues this pattern throughout till the end Anothernoticeable change can be seen in Figures 7(j) 7(k) and 7(l)at 119909 = 55 119909 = 6 and 119909 = 65 respectively where the bentsare more irregular than the previous case This is because atthese locations large recirculations have formed due to thepartition as shown in Figure 5

According to the 119880 and 119881 centerline velocity distribu-tion plots in Figures 8(a) and 8(b) respectively there isa constriction in the middle of graph This represents thepartition that actually works like a wall where the velocityplots cease just like the vertical walls in the extreme leftand right sides One possible advantage of this partition isthat the airflow can be controlled if the air enters with ahigh speed through the inlet Also it is noticeable in Figures

8(a) and 8(b) that unlike the previous case the partitionhelps to maintain the air velocity at a constant level untilit exits out through the outlet The 119881 velocity still drops tonegative range from zero at the beginning due to downwardfall of air through the inlet and ascends to zero again where itmaintains its constant velocity The graphs are more chaoticafter crossing the partition due to the recirculations shown inthe contour map The temperature plot in Figure 8(c) startsjust like that of the previous situation but this time insteadof becoming constant after a certain level the graph climbsup the partition crosses it and then drops again eventuallydecreasing to zero at 119909 = 8 The rise of airflow against thepartition also results in the increase in temperature at thispoint therefore the steep in the figure

54 Case Study III One Inlet and One Outlet with TwoPartitions This case study has been investigated by furthermodifying the proposed model adding another partition inthe ward It was done to keep patients from being exposedinto more air Each partition is placed every after two blocks(beds) Both the partitions are of the same dimension that is(5 times 40) sim (119909 times 119910) lattice size and all other measurementsare kept the same as previous situations Simulations andanalysis of this case have also been carried out for the samethree Re values Streamlines pattern of Figure 9 obtained afteradding another partition shows that the size and the numberof recirculations increase more than the last observationUnlike Case II now two large recirculations have formed

10 Journal of Computational Engineering

0 2 4 6 8

012 Partition

xH

Re = 100

Re = 250

Re = 350

uH

(a)

0 2 4 6 8

0

1 Partition

xH

Re = 100

Re = 250

Re = 350

H

(b)

0 2 4 6 80

05

1 Partition

xH

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 8 In Case II for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

1

05

00 2 4 6 8

xH

yH

237198159119080041002minus038

(a)

0 2 4 6 8

xH

1

05

0

yH

247198149100051002minus047minus096

(b)

0 2 4 6 8

xH

1

05

0

yH

252199146092039minus014minus068minus121

(c)

Figure 9 Streamline patterns of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

for the corresponding experiments with each Re Even themaximum and minimum legend values have become widerthan the previous situation for example for Re = 100 the215 value has increased to 237 For Re = 250 and Re = 350

the uppermost values have risen to 247 and 252 from 233and 238 respectively Due to bounce-back condition theair is now forming more recirculations against the walls andbetween the blocksThis augmentation of values and recircu-lations due to buoyancy effect is visible for every incrementof Re values and addition of obstacles such as partition

The generated results of isotherms in Figure 10 give avisual idea how the heat is transferred from the blocks and

passes through the outlet Like the other cases only thesurfaces of the blocks are heated to be considered as patientswho are continuously releasing heat Everything remains thesame like previous cases

Figure 11 provides the 119880 velocity profiles for differentpositions of 119909 According to this the graph characteristicfor a partition can be seen in Figure 11(e) at 119909 = 3 andFigure 11(j) at 119909 = 55 indicating the presence of partitionsat these two locations Apart from this at 119909 = 5 and 75 inFigures 11(i) and 11(n) respectively the parabolic shapes aremore curvy than the profiles at other positions caused dueto recirculations in vector plots of Re = 250 and Re = 350

Journal of Computational Engineering 11

1

05

00

2 4 6 8

xH

yH

000 015 029 043 058 072 086 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 038 054 069 077 092 100

(b)

0 2 4 6 8

xH

1

05

0

yH

008 024 040 056 071 087 095 100

(c)

Figure 10 Isotherms of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(c)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(d)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y HuU

minus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 11 119906119880 velocity profiles in Case III for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

Figures 12(a) and 12(b) illustrate119880 and119881 velocity distributioncurves in mid-119910 and Figure 12(c) shows the temperatureprofile at mid-119910 All of these three plots have one thing incommon that is also different than the previous case In theseplots there are two constrictions instead of one where the

velocities or the temperature curve ceasesThis is the locationwhere the two partitions are present But after crossing theseobstacles the respective graphs continue until 119909 = 8 Thetemperature plot in Figure 12(c) has now two steep regionsdue to the partitions

12 Journal of Computational Engineering

0 2 4 6 8

2

1

0

minus1

uH

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(a)

0 2 4 6 8

1

0

minus1

H

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(b)

0 2 4 6 8

1

05

0

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 12 In Case III for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

55 Calculation of Rate of Heat Transfer In heat transferat a boundary (surface) within a fluid the Nusselt number(Nu) is the ratio of convective to conductive heat transferacross (normal to) the boundary Here convection includesboth advection and diffusion procedures The convectionand conduction heat flows are parallel to each other andto the surface normal of the boundary surface and are allperpendicular to the mean fluid flow in the simple case Thisis denoted as [32]

Nu119871=ℎ119905119871

119896 (19)

where ℎ119905is the convective heat transfer coefficient of the

flow 119871 is the characteristic length and 119896 is the thermalconductivity of the fluid

However this section discusses the average rate of changeof heat transfer obtained for different Re This rate isexpressed as average Nusselt number Nu for each case studyin Tables 2 3 and 4 The tables also show generated localNusselt number Nu that follows the expression below

Nu (119909) = minus 120597120579

120597119910

10038161003816100381610038161003816100381610038161003816119910=1199102

(20)

where 1199102is the upper surface of each block

Average Nu is calculated by integrating the above rela-tion over the entire range of interest and thus the resultingequation becomes

Nu = 1

1199092minus 1199091

int

1199092

1199091

Nu (119909) 119889119909 (21)

Here (1199092minus 1199091) is the length of each block

For the first investigation both the individual and averageNu obtained in Table 2 show a rising trend for each increasingRe Since block 1 is the nearest to the inlet it always has thehighest rate of heat transfer while block 6 has the lowest valueas it is located farthest from the inlet

After placing the partition in the middle the rate of heattransfer shown in Table 3 changes dramatically Like Table 2the patient at block 1 is releasing most heat for all three Reand it keeps reducing until block 5 At block 5 the values ofboth individual Nu and total Nu increase for Re = 250 andRe = 350 but for Re = 100 this type of airflow pattern isseen at block 4 The large recirculations were seen earlier inFigure 5 For Re = 100 recirculation is more over block 4 andthat is the reason why at block 4 individual Nu and total Nuhave greater values than those of Re = 250 and Re = 350 Nuis 15341 at block 4 and for the same block these values are13628 and 14032 respectively for Re = 250 and Re = 350On the other hand if Nu at block 5 are observed Re = 250

and Re = 350 lead the race As per Table 3 Nu are 2011121598 and 27535 for three Re The spike in the values ofRe = 250 and Re = 350 was due to chaotic flows over block5 in Figure 5 If changes in total Nu are observed the valuesincrease rapidly for an increase in Re

For Case Study III the shape of recirculation gets biggerdue to increased Re Above block 1 the recirculation zonecomes into view and due to that reason Nu has the biggestedge in this situation But as the air has tendency to passthe first partition it moves slightly upward and that is whypatient at block 2 is getting less airflowThe heat transfer ratealso falls After passing the first partition the airflow gets itsspace and leads to recirculation near block 3 for Re = 100Meanwhile for Re = 250 and Re = 350 patients on block 4get most air More air means more heat transfer and that is

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

International Journal of

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International Journal of

Journal of Computational Engineering 5

and bounce-back condition is used for the rest of the topwalls At the top surface and at each side of a block andpartition the following bounce-back conditions have beenused

Top surface

1198912119909119894

= 1198914119909119894

1198915119909119894

= 1198917119909119894

1198916119909119894

= 1198918119909119894

(10)

Left side

1198911119909119894

= 1198913119909119894

1198915119909119894

= 1198917119909119894

1198918119909119894

= 1198916119909119894

(11)

Right side

1198913119909119894

= 1198911119909119894

1198916119909119894

= 1198918119909119894

1198917119909119894

= 1198915119909119894

(12)

322 Boundary Condition for Temperature Cold and hottemperature conditions are applied at the walls (see Figure 1)

At east (right) wall the cold temperature condition is 1198923=

minus1198921 1198927= minus1198925 and 119892

6= minus1198928

At west (left) wall the cold temperature condition is 1198921=

minus1198923 1198925= minus1198927 and 119892

8= minus1198926

At south (bottom) wall the cold temperature condition is1198922= minus1198924 1198925= minus1198927 and 119892

6= minus1198928

At the north (top) wall in the outlet a zero gradientboundary condition is applied as follows

1198924119873

= 1198924119873minus1

1198928119873

= 1198926119873minus1

1198927119873

= 1198925119873minus1

(13)

And the rest of the top wall is kept cold by using theconditions 119892

4= minus1198922 1198928= minus1198926 and 119892

7= minus1198925

At the top surface of each block the hot temperaturecondition is used as follows

11989221199102

= 119879119908(1199082+ 1199084) minus 11989241199102

11989251199102

= 119879119908(1199085+ 1199087) minus 11989271199102

11989261199102

= 119879119908(1199086+ 1199088) minus 11989281199102

(14)

where 1199102indicates the top surface of the blocks and 119879

119908is the

wall temperature

33 Nondimensional Number and Mixed Convection Param-eter The important nondimensional number Grashof (Gr)and Prandtl (Pr) numbers are defined as [32]

Gr =1205731198661199101198673(119879119867minus 119879119862)

]2

Pr = ]120572

(15)

In the mixed convection the Richardson number Ri def=

GrRe2 controls the flow phenomena In this simulation theforce term is defined as follows [34]

119865 = 3119908119894Ri (119879 minus 119879

119898) 119890119910 (16)

where 119879119898= (119879119867+ 119879119862)2 is the mean temperature In this

paper the fluid velocity 119906 is nondimensionalized by the con-stant inlet velocity119880 and the nondimensional temperature is120579 = (119879 minus 119879

119888)(119879119908minus 119879119888)

In the present work theMach number (Ma) for Re = 100is 005 for Re = 250 is 002 and for Re = 350 is 0014 Allthese values are less than 03 which satisfy the condition ofincompressible fluid flow [32] In buoyant flowMach numberand thermal diffusivity (120572) can be defined by the followingequations after fixing the values of viscosity Prandtl numberand Reynolds number

Ma = ]radicGr119873119888

120572 =]Pr

(17)

4 Convergence Criteria

Standard LBM being explicit time-marching in naturerequires a long time to attain steady state convergenceHowever convergence of solution is one of the highlightsof the procedure of recovering the Navier-Stokes equationsfrom LBM In this single-relaxation-time LBM the iterativeprocedure is terminated when the velocity and temperaturefield satisfy the following convergence criteria

sum10038161003816100381610038161003816120601(119899+1)

minus 120601(119899)10038161003816100381610038161003816

sum1003816100381610038161003816120601(119899+1)1003816100381610038161003816

lt 10minus9 (18)

where 120601 is the velocity 119906 or temperature 119879 and 119899 is theiteration index and the sum is over the whole domain

5 Results and Discussions

This section has been divided into four subsections At firstcode validation has been performed for different values of Reand has been compared in tabular format In the consequentthree subsections three case studies have been consideredinside the hospital ward In all three cases one inlet oneoutlet and six beds have been considered Simulations havebeen carried out by placing one partition and later twopartitions in the room while observing the indoor airflow

6 Journal of Computational Engineering

Table 1 Comparison of average Nusselt numbers of present work with other investigations for Gr = 100 and Pr = 071

Re Ri Present [35] [25] [36] [37] [38] [39] [26]100 001 1917965 194 201 202 1985 210 203116 209400 000062 3789101 384 391 401 38785 385 40246 4080821000 00001 6339137 633 633 642 6345 633 648423 654687

1

05

00 2 4 6 8

xH

yH

minus014 004 021 038 056 073 090 108

(a)

0 2 4 6 8

xH

1

05

0

yH

minus021 000 021 042 063 084 105 126

(b)1

05

0

yH

0 2 4 6 8

xH

minus024 minus002 020 042 064 086 108 130

(c)

Figure 2 Streamline patterns of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

pattern and the field of temperature in the three situationsThis section is ended with the discussion and comparison ofthe average rate of change of heat transfers achieved for eachcase study In these cases Re = 100 250 and 350 Pr = 071and Ri = 1 have been kept for all simulations except the codevalidation case Different values of 120591] generated for differentRe are as follows for Re = 100 it is 0575 for Re = 250 it is0530 and for Re = 350 it is 0521 Likewise different valuesof 120591120572are as follows for Re = 350 it is 053 for Re = 250 it is

0542 and for Re = 100 it is 0605

51 Code Validation For code validation process one testcase is the mixed convection in a lid-driven square cavityflow for Re = 100 400 and 100 and Gr = 100 has beenconsideredThepresent results in terms of the averageNusseltnumber have been compared quantitatively with the availableresults published in different articles that are demonstrated inTable 1 The comparison reveals a very good agreement Theresults were compared with the works of Iwatsu et al [35]Tiwari and Das [38] Kefayati et al [26] Khanafer et al [36]Abdelkhalek [37] Khanafer and Chamkha [25] andWaheed[39]

52 Case Study I Six Beds without Partition in the WardIn the first case study six beds without partition havebeen considered Each bed is of the same dimension How-ever beds are represented as blocks in Figure 1 For thewhole computational domain a lattice size of (400 times 50) sim(119909 times 119910) has been taken in all simulations Each block of

(20times10) sim (119909times119910) lattice size is used in the wardThe beds areuniformly distributed in one row Inlet and outlet have beenplaced vertically on the ceiling on the left and right cornersrespectively The width of both the inlet and the outlet hasbeen kept from 0 to 15 lattices and from 385 to 400 latticesrespectively

Figures 2(a)ndash2(c) show the streamlines appended on 119906119880velocity contour of the airflow that enters the ward throughthe inlet and flows out through the outlet for Re = 100 250and 350 respectively In case of Re = 100 small recirculationsare seen between the blocks and also near the walls in theeast andwest sides of the ward due to bounce-back conditionA comparatively large recirculation is formed in immediateright to the inlet that is near the top wall For increasing Rethe length of the recirculation zones increases As shown inFigure 2 the highest value of 119906119880 is 108 and the lowest valueis minus014 for Re = 100 In case of Re = 250 and 350 themaximum values increase to 126 and 130 respectively AsRe increases the inertia force of air increases which makes iteasier to flow around in the ward and hence more heat willbe transferred out through the outlet

Figure 3 represents the isotherms of the room As can beseen from the simulation result only the top surface of eachblock is kept heated while the gaps between the blocks arecold The heated portion of the blocks represents patients onbeds who are releasing heat continuously

Different velocity patterns have been shown in Figures4(a)ndash4(n) demonstrating the 119906119880 velocity profiles at differentpositions of 119909119867 for the three different Re This figure

Journal of Computational Engineering 7

1

05

00 2 4 6 8

xH

yH

minus000 014 029 044 058 073 088 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 039 055 070 086 096 100

(b)

1

05

00 2 4 6 8

xH

yH

008 024 040 056 072 088 098 100

(c)

Figure 3 Isotherms of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

0 1

yH

uU

Re = 100

Re = 250

Re = 350

(a)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(b)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(c)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(d)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(e)

0 10

02040608

1

yHuU

Re = 100

Re = 250

Re = 350

(f)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(g)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(h)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(i)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(j)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(k)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(l)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

0 1uU

Re = 100

Re = 250

Re = 350

(n)

Figure 4 119906119880 velocity profiles in Case I for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

outlines the speed at which the air is flowing inside the wardDue to the recirculation near the inlet the velocity profiles arealso seen to increase resulting in a bent-shaped plot in Figures4(b) and 4(c) After 119909119867 = 35 onwards the graphs are almostthe same as there the flow characteristics are almost similarexcept for Figure 4(n)which is slightly bent at the top forming

because at this point the air is preparing to go through theoutlet

53 Case Study II Six Beds with One Partition In thisinvestigation the previousmodel has been updated by addinga partition in the middle of the general ward while all other

8 Journal of Computational Engineering

1

05

00 2 4 6 8

xH

yH

minus034 002 037 073 108 144 179 215

(a)

1

05

00 2 4 6 8

xH

yH

minus076 minus032 012 056 100 145 189 233

(b)1

05

00 2 4 6 8

xH

yH

minus093 minus046 002 049 096 143 191 238

(c)

Figure 5 Streamline patterns of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

1

05

00 2 4 6 8

xH

yH

100086072057043029014000

(a)

0 2 4 6 8

xH

1

05

0

yH

100092077069054039023008

(b)

0 2 4 6 8

xH

1

05

0

yH

100099087072056040024009

(c)

Figure 6 Isotherms of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

schematic measurements have been kept the same as shownin Figure 1The lattice size of partition is (5times40) sim (119909times119910) andit is placed just after the first three blocks (beds) Simulationshave been carried out for the same three Reynolds numbersAfter placing a partition just like in Figure 5 recirculationis seen in Figure 5 and it shows much better result thanthe previous simulations The airflow pattern is clearer thistime which shows that air moves inward smoothly passes thepartition naturally without overlapping it and nicely flowsout through the outlet creating its usual recirculation nearthe inlet between the blocks and near the outlet Unlikeearlier the recirculations now are larger and more frequentparticularly after crossing the partition For Re = 100 alarge air circulation can be noticed between blocks 4 and 5and in case of Re = 250 an even larger recirculation has

appeared between blocks 5 and 6 along with a newly emergedone just beside the outlet As for Re = 350 with the increasein convective air current more chaotic flow dynamics can benoticed before the partition appears The airflow pattern inthis region indicates that in case of mixed convection forRe = 350 the air stays in transitional state which showsboth the laminar characteristics of natural convection and theturbulent nature of forced convection thereby representingforced convection Moreover after placing the partition thepeak values of the contour have risen to 215 from 108 233from 126 and 238 from 130 for Re = 100 Re = 250 andRe = 350 respectively

Figure 6 presents the isotherms for this situation Like inprevious case here also the top surfaces of the blocks are keptheated to represent patients on beds and the spaces between

Journal of Computational Engineering 9

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(c)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(d)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 7 119906119880 velocity profiles in Case II for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

the blocks alongwith the partition are kept coldThe presenceof the partition does affect the airflow characteristics as wellas heat transfer phenomenon which has been discussed indetail in the heat transfer part Pr remains the same

In Figure 7 the119880 velocity profiles at different locations of119909 are discussed for the same three Re This time the resultsshow more curvy lines throughout the whole experimentdue to the obstacle caused because of the partition One ofthe obvious differences worth mentioning is in Figure 7(g)when the air faces the partition At this point a long verticalline with a narrow parabolic curve at the top is shownrepresenting the height of the partition whereas the curvedpart illustrates that the air is crossing the partition Evenin Figure 7(h) the graph still maintains its parabolic shapeand continues this pattern throughout till the end Anothernoticeable change can be seen in Figures 7(j) 7(k) and 7(l)at 119909 = 55 119909 = 6 and 119909 = 65 respectively where the bentsare more irregular than the previous case This is because atthese locations large recirculations have formed due to thepartition as shown in Figure 5

According to the 119880 and 119881 centerline velocity distribu-tion plots in Figures 8(a) and 8(b) respectively there isa constriction in the middle of graph This represents thepartition that actually works like a wall where the velocityplots cease just like the vertical walls in the extreme leftand right sides One possible advantage of this partition isthat the airflow can be controlled if the air enters with ahigh speed through the inlet Also it is noticeable in Figures

8(a) and 8(b) that unlike the previous case the partitionhelps to maintain the air velocity at a constant level untilit exits out through the outlet The 119881 velocity still drops tonegative range from zero at the beginning due to downwardfall of air through the inlet and ascends to zero again where itmaintains its constant velocity The graphs are more chaoticafter crossing the partition due to the recirculations shown inthe contour map The temperature plot in Figure 8(c) startsjust like that of the previous situation but this time insteadof becoming constant after a certain level the graph climbsup the partition crosses it and then drops again eventuallydecreasing to zero at 119909 = 8 The rise of airflow against thepartition also results in the increase in temperature at thispoint therefore the steep in the figure

54 Case Study III One Inlet and One Outlet with TwoPartitions This case study has been investigated by furthermodifying the proposed model adding another partition inthe ward It was done to keep patients from being exposedinto more air Each partition is placed every after two blocks(beds) Both the partitions are of the same dimension that is(5 times 40) sim (119909 times 119910) lattice size and all other measurementsare kept the same as previous situations Simulations andanalysis of this case have also been carried out for the samethree Re values Streamlines pattern of Figure 9 obtained afteradding another partition shows that the size and the numberof recirculations increase more than the last observationUnlike Case II now two large recirculations have formed

10 Journal of Computational Engineering

0 2 4 6 8

012 Partition

xH

Re = 100

Re = 250

Re = 350

uH

(a)

0 2 4 6 8

0

1 Partition

xH

Re = 100

Re = 250

Re = 350

H

(b)

0 2 4 6 80

05

1 Partition

xH

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 8 In Case II for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

1

05

00 2 4 6 8

xH

yH

237198159119080041002minus038

(a)

0 2 4 6 8

xH

1

05

0

yH

247198149100051002minus047minus096

(b)

0 2 4 6 8

xH

1

05

0

yH

252199146092039minus014minus068minus121

(c)

Figure 9 Streamline patterns of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

for the corresponding experiments with each Re Even themaximum and minimum legend values have become widerthan the previous situation for example for Re = 100 the215 value has increased to 237 For Re = 250 and Re = 350

the uppermost values have risen to 247 and 252 from 233and 238 respectively Due to bounce-back condition theair is now forming more recirculations against the walls andbetween the blocksThis augmentation of values and recircu-lations due to buoyancy effect is visible for every incrementof Re values and addition of obstacles such as partition

The generated results of isotherms in Figure 10 give avisual idea how the heat is transferred from the blocks and

passes through the outlet Like the other cases only thesurfaces of the blocks are heated to be considered as patientswho are continuously releasing heat Everything remains thesame like previous cases

Figure 11 provides the 119880 velocity profiles for differentpositions of 119909 According to this the graph characteristicfor a partition can be seen in Figure 11(e) at 119909 = 3 andFigure 11(j) at 119909 = 55 indicating the presence of partitionsat these two locations Apart from this at 119909 = 5 and 75 inFigures 11(i) and 11(n) respectively the parabolic shapes aremore curvy than the profiles at other positions caused dueto recirculations in vector plots of Re = 250 and Re = 350

Journal of Computational Engineering 11

1

05

00

2 4 6 8

xH

yH

000 015 029 043 058 072 086 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 038 054 069 077 092 100

(b)

0 2 4 6 8

xH

1

05

0

yH

008 024 040 056 071 087 095 100

(c)

Figure 10 Isotherms of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(c)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(d)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y HuU

minus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 11 119906119880 velocity profiles in Case III for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

Figures 12(a) and 12(b) illustrate119880 and119881 velocity distributioncurves in mid-119910 and Figure 12(c) shows the temperatureprofile at mid-119910 All of these three plots have one thing incommon that is also different than the previous case In theseplots there are two constrictions instead of one where the

velocities or the temperature curve ceasesThis is the locationwhere the two partitions are present But after crossing theseobstacles the respective graphs continue until 119909 = 8 Thetemperature plot in Figure 12(c) has now two steep regionsdue to the partitions

12 Journal of Computational Engineering

0 2 4 6 8

2

1

0

minus1

uH

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(a)

0 2 4 6 8

1

0

minus1

H

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(b)

0 2 4 6 8

1

05

0

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 12 In Case III for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

55 Calculation of Rate of Heat Transfer In heat transferat a boundary (surface) within a fluid the Nusselt number(Nu) is the ratio of convective to conductive heat transferacross (normal to) the boundary Here convection includesboth advection and diffusion procedures The convectionand conduction heat flows are parallel to each other andto the surface normal of the boundary surface and are allperpendicular to the mean fluid flow in the simple case Thisis denoted as [32]

Nu119871=ℎ119905119871

119896 (19)

where ℎ119905is the convective heat transfer coefficient of the

flow 119871 is the characteristic length and 119896 is the thermalconductivity of the fluid

However this section discusses the average rate of changeof heat transfer obtained for different Re This rate isexpressed as average Nusselt number Nu for each case studyin Tables 2 3 and 4 The tables also show generated localNusselt number Nu that follows the expression below

Nu (119909) = minus 120597120579

120597119910

10038161003816100381610038161003816100381610038161003816119910=1199102

(20)

where 1199102is the upper surface of each block

Average Nu is calculated by integrating the above rela-tion over the entire range of interest and thus the resultingequation becomes

Nu = 1

1199092minus 1199091

int

1199092

1199091

Nu (119909) 119889119909 (21)

Here (1199092minus 1199091) is the length of each block

For the first investigation both the individual and averageNu obtained in Table 2 show a rising trend for each increasingRe Since block 1 is the nearest to the inlet it always has thehighest rate of heat transfer while block 6 has the lowest valueas it is located farthest from the inlet

After placing the partition in the middle the rate of heattransfer shown in Table 3 changes dramatically Like Table 2the patient at block 1 is releasing most heat for all three Reand it keeps reducing until block 5 At block 5 the values ofboth individual Nu and total Nu increase for Re = 250 andRe = 350 but for Re = 100 this type of airflow pattern isseen at block 4 The large recirculations were seen earlier inFigure 5 For Re = 100 recirculation is more over block 4 andthat is the reason why at block 4 individual Nu and total Nuhave greater values than those of Re = 250 and Re = 350 Nuis 15341 at block 4 and for the same block these values are13628 and 14032 respectively for Re = 250 and Re = 350On the other hand if Nu at block 5 are observed Re = 250

and Re = 350 lead the race As per Table 3 Nu are 2011121598 and 27535 for three Re The spike in the values ofRe = 250 and Re = 350 was due to chaotic flows over block5 in Figure 5 If changes in total Nu are observed the valuesincrease rapidly for an increase in Re

For Case Study III the shape of recirculation gets biggerdue to increased Re Above block 1 the recirculation zonecomes into view and due to that reason Nu has the biggestedge in this situation But as the air has tendency to passthe first partition it moves slightly upward and that is whypatient at block 2 is getting less airflowThe heat transfer ratealso falls After passing the first partition the airflow gets itsspace and leads to recirculation near block 3 for Re = 100Meanwhile for Re = 250 and Re = 350 patients on block 4get most air More air means more heat transfer and that is

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

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6 Journal of Computational Engineering

Table 1 Comparison of average Nusselt numbers of present work with other investigations for Gr = 100 and Pr = 071

Re Ri Present [35] [25] [36] [37] [38] [39] [26]100 001 1917965 194 201 202 1985 210 203116 209400 000062 3789101 384 391 401 38785 385 40246 4080821000 00001 6339137 633 633 642 6345 633 648423 654687

1

05

00 2 4 6 8

xH

yH

minus014 004 021 038 056 073 090 108

(a)

0 2 4 6 8

xH

1

05

0

yH

minus021 000 021 042 063 084 105 126

(b)1

05

0

yH

0 2 4 6 8

xH

minus024 minus002 020 042 064 086 108 130

(c)

Figure 2 Streamline patterns of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

pattern and the field of temperature in the three situationsThis section is ended with the discussion and comparison ofthe average rate of change of heat transfers achieved for eachcase study In these cases Re = 100 250 and 350 Pr = 071and Ri = 1 have been kept for all simulations except the codevalidation case Different values of 120591] generated for differentRe are as follows for Re = 100 it is 0575 for Re = 250 it is0530 and for Re = 350 it is 0521 Likewise different valuesof 120591120572are as follows for Re = 350 it is 053 for Re = 250 it is

0542 and for Re = 100 it is 0605

51 Code Validation For code validation process one testcase is the mixed convection in a lid-driven square cavityflow for Re = 100 400 and 100 and Gr = 100 has beenconsideredThepresent results in terms of the averageNusseltnumber have been compared quantitatively with the availableresults published in different articles that are demonstrated inTable 1 The comparison reveals a very good agreement Theresults were compared with the works of Iwatsu et al [35]Tiwari and Das [38] Kefayati et al [26] Khanafer et al [36]Abdelkhalek [37] Khanafer and Chamkha [25] andWaheed[39]

52 Case Study I Six Beds without Partition in the WardIn the first case study six beds without partition havebeen considered Each bed is of the same dimension How-ever beds are represented as blocks in Figure 1 For thewhole computational domain a lattice size of (400 times 50) sim(119909 times 119910) has been taken in all simulations Each block of

(20times10) sim (119909times119910) lattice size is used in the wardThe beds areuniformly distributed in one row Inlet and outlet have beenplaced vertically on the ceiling on the left and right cornersrespectively The width of both the inlet and the outlet hasbeen kept from 0 to 15 lattices and from 385 to 400 latticesrespectively

Figures 2(a)ndash2(c) show the streamlines appended on 119906119880velocity contour of the airflow that enters the ward throughthe inlet and flows out through the outlet for Re = 100 250and 350 respectively In case of Re = 100 small recirculationsare seen between the blocks and also near the walls in theeast andwest sides of the ward due to bounce-back conditionA comparatively large recirculation is formed in immediateright to the inlet that is near the top wall For increasing Rethe length of the recirculation zones increases As shown inFigure 2 the highest value of 119906119880 is 108 and the lowest valueis minus014 for Re = 100 In case of Re = 250 and 350 themaximum values increase to 126 and 130 respectively AsRe increases the inertia force of air increases which makes iteasier to flow around in the ward and hence more heat willbe transferred out through the outlet

Figure 3 represents the isotherms of the room As can beseen from the simulation result only the top surface of eachblock is kept heated while the gaps between the blocks arecold The heated portion of the blocks represents patients onbeds who are releasing heat continuously

Different velocity patterns have been shown in Figures4(a)ndash4(n) demonstrating the 119906119880 velocity profiles at differentpositions of 119909119867 for the three different Re This figure

Journal of Computational Engineering 7

1

05

00 2 4 6 8

xH

yH

minus000 014 029 044 058 073 088 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 039 055 070 086 096 100

(b)

1

05

00 2 4 6 8

xH

yH

008 024 040 056 072 088 098 100

(c)

Figure 3 Isotherms of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

0 1

yH

uU

Re = 100

Re = 250

Re = 350

(a)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(b)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(c)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(d)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(e)

0 10

02040608

1

yHuU

Re = 100

Re = 250

Re = 350

(f)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(g)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(h)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(i)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(j)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(k)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(l)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

0 1uU

Re = 100

Re = 250

Re = 350

(n)

Figure 4 119906119880 velocity profiles in Case I for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

outlines the speed at which the air is flowing inside the wardDue to the recirculation near the inlet the velocity profiles arealso seen to increase resulting in a bent-shaped plot in Figures4(b) and 4(c) After 119909119867 = 35 onwards the graphs are almostthe same as there the flow characteristics are almost similarexcept for Figure 4(n)which is slightly bent at the top forming

because at this point the air is preparing to go through theoutlet

53 Case Study II Six Beds with One Partition In thisinvestigation the previousmodel has been updated by addinga partition in the middle of the general ward while all other

8 Journal of Computational Engineering

1

05

00 2 4 6 8

xH

yH

minus034 002 037 073 108 144 179 215

(a)

1

05

00 2 4 6 8

xH

yH

minus076 minus032 012 056 100 145 189 233

(b)1

05

00 2 4 6 8

xH

yH

minus093 minus046 002 049 096 143 191 238

(c)

Figure 5 Streamline patterns of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

1

05

00 2 4 6 8

xH

yH

100086072057043029014000

(a)

0 2 4 6 8

xH

1

05

0

yH

100092077069054039023008

(b)

0 2 4 6 8

xH

1

05

0

yH

100099087072056040024009

(c)

Figure 6 Isotherms of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

schematic measurements have been kept the same as shownin Figure 1The lattice size of partition is (5times40) sim (119909times119910) andit is placed just after the first three blocks (beds) Simulationshave been carried out for the same three Reynolds numbersAfter placing a partition just like in Figure 5 recirculationis seen in Figure 5 and it shows much better result thanthe previous simulations The airflow pattern is clearer thistime which shows that air moves inward smoothly passes thepartition naturally without overlapping it and nicely flowsout through the outlet creating its usual recirculation nearthe inlet between the blocks and near the outlet Unlikeearlier the recirculations now are larger and more frequentparticularly after crossing the partition For Re = 100 alarge air circulation can be noticed between blocks 4 and 5and in case of Re = 250 an even larger recirculation has

appeared between blocks 5 and 6 along with a newly emergedone just beside the outlet As for Re = 350 with the increasein convective air current more chaotic flow dynamics can benoticed before the partition appears The airflow pattern inthis region indicates that in case of mixed convection forRe = 350 the air stays in transitional state which showsboth the laminar characteristics of natural convection and theturbulent nature of forced convection thereby representingforced convection Moreover after placing the partition thepeak values of the contour have risen to 215 from 108 233from 126 and 238 from 130 for Re = 100 Re = 250 andRe = 350 respectively

Figure 6 presents the isotherms for this situation Like inprevious case here also the top surfaces of the blocks are keptheated to represent patients on beds and the spaces between

Journal of Computational Engineering 9

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(c)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(d)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 7 119906119880 velocity profiles in Case II for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

the blocks alongwith the partition are kept coldThe presenceof the partition does affect the airflow characteristics as wellas heat transfer phenomenon which has been discussed indetail in the heat transfer part Pr remains the same

In Figure 7 the119880 velocity profiles at different locations of119909 are discussed for the same three Re This time the resultsshow more curvy lines throughout the whole experimentdue to the obstacle caused because of the partition One ofthe obvious differences worth mentioning is in Figure 7(g)when the air faces the partition At this point a long verticalline with a narrow parabolic curve at the top is shownrepresenting the height of the partition whereas the curvedpart illustrates that the air is crossing the partition Evenin Figure 7(h) the graph still maintains its parabolic shapeand continues this pattern throughout till the end Anothernoticeable change can be seen in Figures 7(j) 7(k) and 7(l)at 119909 = 55 119909 = 6 and 119909 = 65 respectively where the bentsare more irregular than the previous case This is because atthese locations large recirculations have formed due to thepartition as shown in Figure 5

According to the 119880 and 119881 centerline velocity distribu-tion plots in Figures 8(a) and 8(b) respectively there isa constriction in the middle of graph This represents thepartition that actually works like a wall where the velocityplots cease just like the vertical walls in the extreme leftand right sides One possible advantage of this partition isthat the airflow can be controlled if the air enters with ahigh speed through the inlet Also it is noticeable in Figures

8(a) and 8(b) that unlike the previous case the partitionhelps to maintain the air velocity at a constant level untilit exits out through the outlet The 119881 velocity still drops tonegative range from zero at the beginning due to downwardfall of air through the inlet and ascends to zero again where itmaintains its constant velocity The graphs are more chaoticafter crossing the partition due to the recirculations shown inthe contour map The temperature plot in Figure 8(c) startsjust like that of the previous situation but this time insteadof becoming constant after a certain level the graph climbsup the partition crosses it and then drops again eventuallydecreasing to zero at 119909 = 8 The rise of airflow against thepartition also results in the increase in temperature at thispoint therefore the steep in the figure

54 Case Study III One Inlet and One Outlet with TwoPartitions This case study has been investigated by furthermodifying the proposed model adding another partition inthe ward It was done to keep patients from being exposedinto more air Each partition is placed every after two blocks(beds) Both the partitions are of the same dimension that is(5 times 40) sim (119909 times 119910) lattice size and all other measurementsare kept the same as previous situations Simulations andanalysis of this case have also been carried out for the samethree Re values Streamlines pattern of Figure 9 obtained afteradding another partition shows that the size and the numberof recirculations increase more than the last observationUnlike Case II now two large recirculations have formed

10 Journal of Computational Engineering

0 2 4 6 8

012 Partition

xH

Re = 100

Re = 250

Re = 350

uH

(a)

0 2 4 6 8

0

1 Partition

xH

Re = 100

Re = 250

Re = 350

H

(b)

0 2 4 6 80

05

1 Partition

xH

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 8 In Case II for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

1

05

00 2 4 6 8

xH

yH

237198159119080041002minus038

(a)

0 2 4 6 8

xH

1

05

0

yH

247198149100051002minus047minus096

(b)

0 2 4 6 8

xH

1

05

0

yH

252199146092039minus014minus068minus121

(c)

Figure 9 Streamline patterns of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

for the corresponding experiments with each Re Even themaximum and minimum legend values have become widerthan the previous situation for example for Re = 100 the215 value has increased to 237 For Re = 250 and Re = 350

the uppermost values have risen to 247 and 252 from 233and 238 respectively Due to bounce-back condition theair is now forming more recirculations against the walls andbetween the blocksThis augmentation of values and recircu-lations due to buoyancy effect is visible for every incrementof Re values and addition of obstacles such as partition

The generated results of isotherms in Figure 10 give avisual idea how the heat is transferred from the blocks and

passes through the outlet Like the other cases only thesurfaces of the blocks are heated to be considered as patientswho are continuously releasing heat Everything remains thesame like previous cases

Figure 11 provides the 119880 velocity profiles for differentpositions of 119909 According to this the graph characteristicfor a partition can be seen in Figure 11(e) at 119909 = 3 andFigure 11(j) at 119909 = 55 indicating the presence of partitionsat these two locations Apart from this at 119909 = 5 and 75 inFigures 11(i) and 11(n) respectively the parabolic shapes aremore curvy than the profiles at other positions caused dueto recirculations in vector plots of Re = 250 and Re = 350

Journal of Computational Engineering 11

1

05

00

2 4 6 8

xH

yH

000 015 029 043 058 072 086 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 038 054 069 077 092 100

(b)

0 2 4 6 8

xH

1

05

0

yH

008 024 040 056 071 087 095 100

(c)

Figure 10 Isotherms of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(c)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(d)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y HuU

minus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 11 119906119880 velocity profiles in Case III for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

Figures 12(a) and 12(b) illustrate119880 and119881 velocity distributioncurves in mid-119910 and Figure 12(c) shows the temperatureprofile at mid-119910 All of these three plots have one thing incommon that is also different than the previous case In theseplots there are two constrictions instead of one where the

velocities or the temperature curve ceasesThis is the locationwhere the two partitions are present But after crossing theseobstacles the respective graphs continue until 119909 = 8 Thetemperature plot in Figure 12(c) has now two steep regionsdue to the partitions

12 Journal of Computational Engineering

0 2 4 6 8

2

1

0

minus1

uH

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(a)

0 2 4 6 8

1

0

minus1

H

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(b)

0 2 4 6 8

1

05

0

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 12 In Case III for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

55 Calculation of Rate of Heat Transfer In heat transferat a boundary (surface) within a fluid the Nusselt number(Nu) is the ratio of convective to conductive heat transferacross (normal to) the boundary Here convection includesboth advection and diffusion procedures The convectionand conduction heat flows are parallel to each other andto the surface normal of the boundary surface and are allperpendicular to the mean fluid flow in the simple case Thisis denoted as [32]

Nu119871=ℎ119905119871

119896 (19)

where ℎ119905is the convective heat transfer coefficient of the

flow 119871 is the characteristic length and 119896 is the thermalconductivity of the fluid

However this section discusses the average rate of changeof heat transfer obtained for different Re This rate isexpressed as average Nusselt number Nu for each case studyin Tables 2 3 and 4 The tables also show generated localNusselt number Nu that follows the expression below

Nu (119909) = minus 120597120579

120597119910

10038161003816100381610038161003816100381610038161003816119910=1199102

(20)

where 1199102is the upper surface of each block

Average Nu is calculated by integrating the above rela-tion over the entire range of interest and thus the resultingequation becomes

Nu = 1

1199092minus 1199091

int

1199092

1199091

Nu (119909) 119889119909 (21)

Here (1199092minus 1199091) is the length of each block

For the first investigation both the individual and averageNu obtained in Table 2 show a rising trend for each increasingRe Since block 1 is the nearest to the inlet it always has thehighest rate of heat transfer while block 6 has the lowest valueas it is located farthest from the inlet

After placing the partition in the middle the rate of heattransfer shown in Table 3 changes dramatically Like Table 2the patient at block 1 is releasing most heat for all three Reand it keeps reducing until block 5 At block 5 the values ofboth individual Nu and total Nu increase for Re = 250 andRe = 350 but for Re = 100 this type of airflow pattern isseen at block 4 The large recirculations were seen earlier inFigure 5 For Re = 100 recirculation is more over block 4 andthat is the reason why at block 4 individual Nu and total Nuhave greater values than those of Re = 250 and Re = 350 Nuis 15341 at block 4 and for the same block these values are13628 and 14032 respectively for Re = 250 and Re = 350On the other hand if Nu at block 5 are observed Re = 250

and Re = 350 lead the race As per Table 3 Nu are 2011121598 and 27535 for three Re The spike in the values ofRe = 250 and Re = 350 was due to chaotic flows over block5 in Figure 5 If changes in total Nu are observed the valuesincrease rapidly for an increase in Re

For Case Study III the shape of recirculation gets biggerdue to increased Re Above block 1 the recirculation zonecomes into view and due to that reason Nu has the biggestedge in this situation But as the air has tendency to passthe first partition it moves slightly upward and that is whypatient at block 2 is getting less airflowThe heat transfer ratealso falls After passing the first partition the airflow gets itsspace and leads to recirculation near block 3 for Re = 100Meanwhile for Re = 250 and Re = 350 patients on block 4get most air More air means more heat transfer and that is

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

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DistributedSensor Networks

International Journal of

Journal of Computational Engineering 7

1

05

00 2 4 6 8

xH

yH

minus000 014 029 044 058 073 088 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 039 055 070 086 096 100

(b)

1

05

00 2 4 6 8

xH

yH

008 024 040 056 072 088 098 100

(c)

Figure 3 Isotherms of Case I for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

0 1

yH

uU

Re = 100

Re = 250

Re = 350

(a)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(b)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(c)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(d)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(e)

0 10

02040608

1

yHuU

Re = 100

Re = 250

Re = 350

(f)

0 10

02040608

1

yH

uU

Re = 100

Re = 250

Re = 350

(g)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(h)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(i)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(j)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(k)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(l)

002040608

1

yH

0 1uU

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

0 1uU

Re = 100

Re = 250

Re = 350

(n)

Figure 4 119906119880 velocity profiles in Case I for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

outlines the speed at which the air is flowing inside the wardDue to the recirculation near the inlet the velocity profiles arealso seen to increase resulting in a bent-shaped plot in Figures4(b) and 4(c) After 119909119867 = 35 onwards the graphs are almostthe same as there the flow characteristics are almost similarexcept for Figure 4(n)which is slightly bent at the top forming

because at this point the air is preparing to go through theoutlet

53 Case Study II Six Beds with One Partition In thisinvestigation the previousmodel has been updated by addinga partition in the middle of the general ward while all other

8 Journal of Computational Engineering

1

05

00 2 4 6 8

xH

yH

minus034 002 037 073 108 144 179 215

(a)

1

05

00 2 4 6 8

xH

yH

minus076 minus032 012 056 100 145 189 233

(b)1

05

00 2 4 6 8

xH

yH

minus093 minus046 002 049 096 143 191 238

(c)

Figure 5 Streamline patterns of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

1

05

00 2 4 6 8

xH

yH

100086072057043029014000

(a)

0 2 4 6 8

xH

1

05

0

yH

100092077069054039023008

(b)

0 2 4 6 8

xH

1

05

0

yH

100099087072056040024009

(c)

Figure 6 Isotherms of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

schematic measurements have been kept the same as shownin Figure 1The lattice size of partition is (5times40) sim (119909times119910) andit is placed just after the first three blocks (beds) Simulationshave been carried out for the same three Reynolds numbersAfter placing a partition just like in Figure 5 recirculationis seen in Figure 5 and it shows much better result thanthe previous simulations The airflow pattern is clearer thistime which shows that air moves inward smoothly passes thepartition naturally without overlapping it and nicely flowsout through the outlet creating its usual recirculation nearthe inlet between the blocks and near the outlet Unlikeearlier the recirculations now are larger and more frequentparticularly after crossing the partition For Re = 100 alarge air circulation can be noticed between blocks 4 and 5and in case of Re = 250 an even larger recirculation has

appeared between blocks 5 and 6 along with a newly emergedone just beside the outlet As for Re = 350 with the increasein convective air current more chaotic flow dynamics can benoticed before the partition appears The airflow pattern inthis region indicates that in case of mixed convection forRe = 350 the air stays in transitional state which showsboth the laminar characteristics of natural convection and theturbulent nature of forced convection thereby representingforced convection Moreover after placing the partition thepeak values of the contour have risen to 215 from 108 233from 126 and 238 from 130 for Re = 100 Re = 250 andRe = 350 respectively

Figure 6 presents the isotherms for this situation Like inprevious case here also the top surfaces of the blocks are keptheated to represent patients on beds and the spaces between

Journal of Computational Engineering 9

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(c)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(d)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 7 119906119880 velocity profiles in Case II for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

the blocks alongwith the partition are kept coldThe presenceof the partition does affect the airflow characteristics as wellas heat transfer phenomenon which has been discussed indetail in the heat transfer part Pr remains the same

In Figure 7 the119880 velocity profiles at different locations of119909 are discussed for the same three Re This time the resultsshow more curvy lines throughout the whole experimentdue to the obstacle caused because of the partition One ofthe obvious differences worth mentioning is in Figure 7(g)when the air faces the partition At this point a long verticalline with a narrow parabolic curve at the top is shownrepresenting the height of the partition whereas the curvedpart illustrates that the air is crossing the partition Evenin Figure 7(h) the graph still maintains its parabolic shapeand continues this pattern throughout till the end Anothernoticeable change can be seen in Figures 7(j) 7(k) and 7(l)at 119909 = 55 119909 = 6 and 119909 = 65 respectively where the bentsare more irregular than the previous case This is because atthese locations large recirculations have formed due to thepartition as shown in Figure 5

According to the 119880 and 119881 centerline velocity distribu-tion plots in Figures 8(a) and 8(b) respectively there isa constriction in the middle of graph This represents thepartition that actually works like a wall where the velocityplots cease just like the vertical walls in the extreme leftand right sides One possible advantage of this partition isthat the airflow can be controlled if the air enters with ahigh speed through the inlet Also it is noticeable in Figures

8(a) and 8(b) that unlike the previous case the partitionhelps to maintain the air velocity at a constant level untilit exits out through the outlet The 119881 velocity still drops tonegative range from zero at the beginning due to downwardfall of air through the inlet and ascends to zero again where itmaintains its constant velocity The graphs are more chaoticafter crossing the partition due to the recirculations shown inthe contour map The temperature plot in Figure 8(c) startsjust like that of the previous situation but this time insteadof becoming constant after a certain level the graph climbsup the partition crosses it and then drops again eventuallydecreasing to zero at 119909 = 8 The rise of airflow against thepartition also results in the increase in temperature at thispoint therefore the steep in the figure

54 Case Study III One Inlet and One Outlet with TwoPartitions This case study has been investigated by furthermodifying the proposed model adding another partition inthe ward It was done to keep patients from being exposedinto more air Each partition is placed every after two blocks(beds) Both the partitions are of the same dimension that is(5 times 40) sim (119909 times 119910) lattice size and all other measurementsare kept the same as previous situations Simulations andanalysis of this case have also been carried out for the samethree Re values Streamlines pattern of Figure 9 obtained afteradding another partition shows that the size and the numberof recirculations increase more than the last observationUnlike Case II now two large recirculations have formed

10 Journal of Computational Engineering

0 2 4 6 8

012 Partition

xH

Re = 100

Re = 250

Re = 350

uH

(a)

0 2 4 6 8

0

1 Partition

xH

Re = 100

Re = 250

Re = 350

H

(b)

0 2 4 6 80

05

1 Partition

xH

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 8 In Case II for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

1

05

00 2 4 6 8

xH

yH

237198159119080041002minus038

(a)

0 2 4 6 8

xH

1

05

0

yH

247198149100051002minus047minus096

(b)

0 2 4 6 8

xH

1

05

0

yH

252199146092039minus014minus068minus121

(c)

Figure 9 Streamline patterns of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

for the corresponding experiments with each Re Even themaximum and minimum legend values have become widerthan the previous situation for example for Re = 100 the215 value has increased to 237 For Re = 250 and Re = 350

the uppermost values have risen to 247 and 252 from 233and 238 respectively Due to bounce-back condition theair is now forming more recirculations against the walls andbetween the blocksThis augmentation of values and recircu-lations due to buoyancy effect is visible for every incrementof Re values and addition of obstacles such as partition

The generated results of isotherms in Figure 10 give avisual idea how the heat is transferred from the blocks and

passes through the outlet Like the other cases only thesurfaces of the blocks are heated to be considered as patientswho are continuously releasing heat Everything remains thesame like previous cases

Figure 11 provides the 119880 velocity profiles for differentpositions of 119909 According to this the graph characteristicfor a partition can be seen in Figure 11(e) at 119909 = 3 andFigure 11(j) at 119909 = 55 indicating the presence of partitionsat these two locations Apart from this at 119909 = 5 and 75 inFigures 11(i) and 11(n) respectively the parabolic shapes aremore curvy than the profiles at other positions caused dueto recirculations in vector plots of Re = 250 and Re = 350

Journal of Computational Engineering 11

1

05

00

2 4 6 8

xH

yH

000 015 029 043 058 072 086 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 038 054 069 077 092 100

(b)

0 2 4 6 8

xH

1

05

0

yH

008 024 040 056 071 087 095 100

(c)

Figure 10 Isotherms of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(c)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(d)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y HuU

minus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 11 119906119880 velocity profiles in Case III for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

Figures 12(a) and 12(b) illustrate119880 and119881 velocity distributioncurves in mid-119910 and Figure 12(c) shows the temperatureprofile at mid-119910 All of these three plots have one thing incommon that is also different than the previous case In theseplots there are two constrictions instead of one where the

velocities or the temperature curve ceasesThis is the locationwhere the two partitions are present But after crossing theseobstacles the respective graphs continue until 119909 = 8 Thetemperature plot in Figure 12(c) has now two steep regionsdue to the partitions

12 Journal of Computational Engineering

0 2 4 6 8

2

1

0

minus1

uH

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(a)

0 2 4 6 8

1

0

minus1

H

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(b)

0 2 4 6 8

1

05

0

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 12 In Case III for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

55 Calculation of Rate of Heat Transfer In heat transferat a boundary (surface) within a fluid the Nusselt number(Nu) is the ratio of convective to conductive heat transferacross (normal to) the boundary Here convection includesboth advection and diffusion procedures The convectionand conduction heat flows are parallel to each other andto the surface normal of the boundary surface and are allperpendicular to the mean fluid flow in the simple case Thisis denoted as [32]

Nu119871=ℎ119905119871

119896 (19)

where ℎ119905is the convective heat transfer coefficient of the

flow 119871 is the characteristic length and 119896 is the thermalconductivity of the fluid

However this section discusses the average rate of changeof heat transfer obtained for different Re This rate isexpressed as average Nusselt number Nu for each case studyin Tables 2 3 and 4 The tables also show generated localNusselt number Nu that follows the expression below

Nu (119909) = minus 120597120579

120597119910

10038161003816100381610038161003816100381610038161003816119910=1199102

(20)

where 1199102is the upper surface of each block

Average Nu is calculated by integrating the above rela-tion over the entire range of interest and thus the resultingequation becomes

Nu = 1

1199092minus 1199091

int

1199092

1199091

Nu (119909) 119889119909 (21)

Here (1199092minus 1199091) is the length of each block

For the first investigation both the individual and averageNu obtained in Table 2 show a rising trend for each increasingRe Since block 1 is the nearest to the inlet it always has thehighest rate of heat transfer while block 6 has the lowest valueas it is located farthest from the inlet

After placing the partition in the middle the rate of heattransfer shown in Table 3 changes dramatically Like Table 2the patient at block 1 is releasing most heat for all three Reand it keeps reducing until block 5 At block 5 the values ofboth individual Nu and total Nu increase for Re = 250 andRe = 350 but for Re = 100 this type of airflow pattern isseen at block 4 The large recirculations were seen earlier inFigure 5 For Re = 100 recirculation is more over block 4 andthat is the reason why at block 4 individual Nu and total Nuhave greater values than those of Re = 250 and Re = 350 Nuis 15341 at block 4 and for the same block these values are13628 and 14032 respectively for Re = 250 and Re = 350On the other hand if Nu at block 5 are observed Re = 250

and Re = 350 lead the race As per Table 3 Nu are 2011121598 and 27535 for three Re The spike in the values ofRe = 250 and Re = 350 was due to chaotic flows over block5 in Figure 5 If changes in total Nu are observed the valuesincrease rapidly for an increase in Re

For Case Study III the shape of recirculation gets biggerdue to increased Re Above block 1 the recirculation zonecomes into view and due to that reason Nu has the biggestedge in this situation But as the air has tendency to passthe first partition it moves slightly upward and that is whypatient at block 2 is getting less airflowThe heat transfer ratealso falls After passing the first partition the airflow gets itsspace and leads to recirculation near block 3 for Re = 100Meanwhile for Re = 250 and Re = 350 patients on block 4get most air More air means more heat transfer and that is

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

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DistributedSensor Networks

International Journal of

8 Journal of Computational Engineering

1

05

00 2 4 6 8

xH

yH

minus034 002 037 073 108 144 179 215

(a)

1

05

00 2 4 6 8

xH

yH

minus076 minus032 012 056 100 145 189 233

(b)1

05

00 2 4 6 8

xH

yH

minus093 minus046 002 049 096 143 191 238

(c)

Figure 5 Streamline patterns of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

1

05

00 2 4 6 8

xH

yH

100086072057043029014000

(a)

0 2 4 6 8

xH

1

05

0

yH

100092077069054039023008

(b)

0 2 4 6 8

xH

1

05

0

yH

100099087072056040024009

(c)

Figure 6 Isotherms of Case II for (a) Re = 100 (b) Re = 250 and (c) Re = 350

schematic measurements have been kept the same as shownin Figure 1The lattice size of partition is (5times40) sim (119909times119910) andit is placed just after the first three blocks (beds) Simulationshave been carried out for the same three Reynolds numbersAfter placing a partition just like in Figure 5 recirculationis seen in Figure 5 and it shows much better result thanthe previous simulations The airflow pattern is clearer thistime which shows that air moves inward smoothly passes thepartition naturally without overlapping it and nicely flowsout through the outlet creating its usual recirculation nearthe inlet between the blocks and near the outlet Unlikeearlier the recirculations now are larger and more frequentparticularly after crossing the partition For Re = 100 alarge air circulation can be noticed between blocks 4 and 5and in case of Re = 250 an even larger recirculation has

appeared between blocks 5 and 6 along with a newly emergedone just beside the outlet As for Re = 350 with the increasein convective air current more chaotic flow dynamics can benoticed before the partition appears The airflow pattern inthis region indicates that in case of mixed convection forRe = 350 the air stays in transitional state which showsboth the laminar characteristics of natural convection and theturbulent nature of forced convection thereby representingforced convection Moreover after placing the partition thepeak values of the contour have risen to 215 from 108 233from 126 and 238 from 130 for Re = 100 Re = 250 andRe = 350 respectively

Figure 6 presents the isotherms for this situation Like inprevious case here also the top surfaces of the blocks are keptheated to represent patients on beds and the spaces between

Journal of Computational Engineering 9

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(c)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(d)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 7 119906119880 velocity profiles in Case II for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

the blocks alongwith the partition are kept coldThe presenceof the partition does affect the airflow characteristics as wellas heat transfer phenomenon which has been discussed indetail in the heat transfer part Pr remains the same

In Figure 7 the119880 velocity profiles at different locations of119909 are discussed for the same three Re This time the resultsshow more curvy lines throughout the whole experimentdue to the obstacle caused because of the partition One ofthe obvious differences worth mentioning is in Figure 7(g)when the air faces the partition At this point a long verticalline with a narrow parabolic curve at the top is shownrepresenting the height of the partition whereas the curvedpart illustrates that the air is crossing the partition Evenin Figure 7(h) the graph still maintains its parabolic shapeand continues this pattern throughout till the end Anothernoticeable change can be seen in Figures 7(j) 7(k) and 7(l)at 119909 = 55 119909 = 6 and 119909 = 65 respectively where the bentsare more irregular than the previous case This is because atthese locations large recirculations have formed due to thepartition as shown in Figure 5

According to the 119880 and 119881 centerline velocity distribu-tion plots in Figures 8(a) and 8(b) respectively there isa constriction in the middle of graph This represents thepartition that actually works like a wall where the velocityplots cease just like the vertical walls in the extreme leftand right sides One possible advantage of this partition isthat the airflow can be controlled if the air enters with ahigh speed through the inlet Also it is noticeable in Figures

8(a) and 8(b) that unlike the previous case the partitionhelps to maintain the air velocity at a constant level untilit exits out through the outlet The 119881 velocity still drops tonegative range from zero at the beginning due to downwardfall of air through the inlet and ascends to zero again where itmaintains its constant velocity The graphs are more chaoticafter crossing the partition due to the recirculations shown inthe contour map The temperature plot in Figure 8(c) startsjust like that of the previous situation but this time insteadof becoming constant after a certain level the graph climbsup the partition crosses it and then drops again eventuallydecreasing to zero at 119909 = 8 The rise of airflow against thepartition also results in the increase in temperature at thispoint therefore the steep in the figure

54 Case Study III One Inlet and One Outlet with TwoPartitions This case study has been investigated by furthermodifying the proposed model adding another partition inthe ward It was done to keep patients from being exposedinto more air Each partition is placed every after two blocks(beds) Both the partitions are of the same dimension that is(5 times 40) sim (119909 times 119910) lattice size and all other measurementsare kept the same as previous situations Simulations andanalysis of this case have also been carried out for the samethree Re values Streamlines pattern of Figure 9 obtained afteradding another partition shows that the size and the numberof recirculations increase more than the last observationUnlike Case II now two large recirculations have formed

10 Journal of Computational Engineering

0 2 4 6 8

012 Partition

xH

Re = 100

Re = 250

Re = 350

uH

(a)

0 2 4 6 8

0

1 Partition

xH

Re = 100

Re = 250

Re = 350

H

(b)

0 2 4 6 80

05

1 Partition

xH

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 8 In Case II for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

1

05

00 2 4 6 8

xH

yH

237198159119080041002minus038

(a)

0 2 4 6 8

xH

1

05

0

yH

247198149100051002minus047minus096

(b)

0 2 4 6 8

xH

1

05

0

yH

252199146092039minus014minus068minus121

(c)

Figure 9 Streamline patterns of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

for the corresponding experiments with each Re Even themaximum and minimum legend values have become widerthan the previous situation for example for Re = 100 the215 value has increased to 237 For Re = 250 and Re = 350

the uppermost values have risen to 247 and 252 from 233and 238 respectively Due to bounce-back condition theair is now forming more recirculations against the walls andbetween the blocksThis augmentation of values and recircu-lations due to buoyancy effect is visible for every incrementof Re values and addition of obstacles such as partition

The generated results of isotherms in Figure 10 give avisual idea how the heat is transferred from the blocks and

passes through the outlet Like the other cases only thesurfaces of the blocks are heated to be considered as patientswho are continuously releasing heat Everything remains thesame like previous cases

Figure 11 provides the 119880 velocity profiles for differentpositions of 119909 According to this the graph characteristicfor a partition can be seen in Figure 11(e) at 119909 = 3 andFigure 11(j) at 119909 = 55 indicating the presence of partitionsat these two locations Apart from this at 119909 = 5 and 75 inFigures 11(i) and 11(n) respectively the parabolic shapes aremore curvy than the profiles at other positions caused dueto recirculations in vector plots of Re = 250 and Re = 350

Journal of Computational Engineering 11

1

05

00

2 4 6 8

xH

yH

000 015 029 043 058 072 086 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 038 054 069 077 092 100

(b)

0 2 4 6 8

xH

1

05

0

yH

008 024 040 056 071 087 095 100

(c)

Figure 10 Isotherms of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(c)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(d)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y HuU

minus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 11 119906119880 velocity profiles in Case III for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

Figures 12(a) and 12(b) illustrate119880 and119881 velocity distributioncurves in mid-119910 and Figure 12(c) shows the temperatureprofile at mid-119910 All of these three plots have one thing incommon that is also different than the previous case In theseplots there are two constrictions instead of one where the

velocities or the temperature curve ceasesThis is the locationwhere the two partitions are present But after crossing theseobstacles the respective graphs continue until 119909 = 8 Thetemperature plot in Figure 12(c) has now two steep regionsdue to the partitions

12 Journal of Computational Engineering

0 2 4 6 8

2

1

0

minus1

uH

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(a)

0 2 4 6 8

1

0

minus1

H

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(b)

0 2 4 6 8

1

05

0

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 12 In Case III for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

55 Calculation of Rate of Heat Transfer In heat transferat a boundary (surface) within a fluid the Nusselt number(Nu) is the ratio of convective to conductive heat transferacross (normal to) the boundary Here convection includesboth advection and diffusion procedures The convectionand conduction heat flows are parallel to each other andto the surface normal of the boundary surface and are allperpendicular to the mean fluid flow in the simple case Thisis denoted as [32]

Nu119871=ℎ119905119871

119896 (19)

where ℎ119905is the convective heat transfer coefficient of the

flow 119871 is the characteristic length and 119896 is the thermalconductivity of the fluid

However this section discusses the average rate of changeof heat transfer obtained for different Re This rate isexpressed as average Nusselt number Nu for each case studyin Tables 2 3 and 4 The tables also show generated localNusselt number Nu that follows the expression below

Nu (119909) = minus 120597120579

120597119910

10038161003816100381610038161003816100381610038161003816119910=1199102

(20)

where 1199102is the upper surface of each block

Average Nu is calculated by integrating the above rela-tion over the entire range of interest and thus the resultingequation becomes

Nu = 1

1199092minus 1199091

int

1199092

1199091

Nu (119909) 119889119909 (21)

Here (1199092minus 1199091) is the length of each block

For the first investigation both the individual and averageNu obtained in Table 2 show a rising trend for each increasingRe Since block 1 is the nearest to the inlet it always has thehighest rate of heat transfer while block 6 has the lowest valueas it is located farthest from the inlet

After placing the partition in the middle the rate of heattransfer shown in Table 3 changes dramatically Like Table 2the patient at block 1 is releasing most heat for all three Reand it keeps reducing until block 5 At block 5 the values ofboth individual Nu and total Nu increase for Re = 250 andRe = 350 but for Re = 100 this type of airflow pattern isseen at block 4 The large recirculations were seen earlier inFigure 5 For Re = 100 recirculation is more over block 4 andthat is the reason why at block 4 individual Nu and total Nuhave greater values than those of Re = 250 and Re = 350 Nuis 15341 at block 4 and for the same block these values are13628 and 14032 respectively for Re = 250 and Re = 350On the other hand if Nu at block 5 are observed Re = 250

and Re = 350 lead the race As per Table 3 Nu are 2011121598 and 27535 for three Re The spike in the values ofRe = 250 and Re = 350 was due to chaotic flows over block5 in Figure 5 If changes in total Nu are observed the valuesincrease rapidly for an increase in Re

For Case Study III the shape of recirculation gets biggerdue to increased Re Above block 1 the recirculation zonecomes into view and due to that reason Nu has the biggestedge in this situation But as the air has tendency to passthe first partition it moves slightly upward and that is whypatient at block 2 is getting less airflowThe heat transfer ratealso falls After passing the first partition the airflow gets itsspace and leads to recirculation near block 3 for Re = 100Meanwhile for Re = 250 and Re = 350 patients on block 4get most air More air means more heat transfer and that is

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

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DistributedSensor Networks

International Journal of

Journal of Computational Engineering 9

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(c)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(d)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 7 119906119880 velocity profiles in Case II for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

the blocks alongwith the partition are kept coldThe presenceof the partition does affect the airflow characteristics as wellas heat transfer phenomenon which has been discussed indetail in the heat transfer part Pr remains the same

In Figure 7 the119880 velocity profiles at different locations of119909 are discussed for the same three Re This time the resultsshow more curvy lines throughout the whole experimentdue to the obstacle caused because of the partition One ofthe obvious differences worth mentioning is in Figure 7(g)when the air faces the partition At this point a long verticalline with a narrow parabolic curve at the top is shownrepresenting the height of the partition whereas the curvedpart illustrates that the air is crossing the partition Evenin Figure 7(h) the graph still maintains its parabolic shapeand continues this pattern throughout till the end Anothernoticeable change can be seen in Figures 7(j) 7(k) and 7(l)at 119909 = 55 119909 = 6 and 119909 = 65 respectively where the bentsare more irregular than the previous case This is because atthese locations large recirculations have formed due to thepartition as shown in Figure 5

According to the 119880 and 119881 centerline velocity distribu-tion plots in Figures 8(a) and 8(b) respectively there isa constriction in the middle of graph This represents thepartition that actually works like a wall where the velocityplots cease just like the vertical walls in the extreme leftand right sides One possible advantage of this partition isthat the airflow can be controlled if the air enters with ahigh speed through the inlet Also it is noticeable in Figures

8(a) and 8(b) that unlike the previous case the partitionhelps to maintain the air velocity at a constant level untilit exits out through the outlet The 119881 velocity still drops tonegative range from zero at the beginning due to downwardfall of air through the inlet and ascends to zero again where itmaintains its constant velocity The graphs are more chaoticafter crossing the partition due to the recirculations shown inthe contour map The temperature plot in Figure 8(c) startsjust like that of the previous situation but this time insteadof becoming constant after a certain level the graph climbsup the partition crosses it and then drops again eventuallydecreasing to zero at 119909 = 8 The rise of airflow against thepartition also results in the increase in temperature at thispoint therefore the steep in the figure

54 Case Study III One Inlet and One Outlet with TwoPartitions This case study has been investigated by furthermodifying the proposed model adding another partition inthe ward It was done to keep patients from being exposedinto more air Each partition is placed every after two blocks(beds) Both the partitions are of the same dimension that is(5 times 40) sim (119909 times 119910) lattice size and all other measurementsare kept the same as previous situations Simulations andanalysis of this case have also been carried out for the samethree Re values Streamlines pattern of Figure 9 obtained afteradding another partition shows that the size and the numberof recirculations increase more than the last observationUnlike Case II now two large recirculations have formed

10 Journal of Computational Engineering

0 2 4 6 8

012 Partition

xH

Re = 100

Re = 250

Re = 350

uH

(a)

0 2 4 6 8

0

1 Partition

xH

Re = 100

Re = 250

Re = 350

H

(b)

0 2 4 6 80

05

1 Partition

xH

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 8 In Case II for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

1

05

00 2 4 6 8

xH

yH

237198159119080041002minus038

(a)

0 2 4 6 8

xH

1

05

0

yH

247198149100051002minus047minus096

(b)

0 2 4 6 8

xH

1

05

0

yH

252199146092039minus014minus068minus121

(c)

Figure 9 Streamline patterns of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

for the corresponding experiments with each Re Even themaximum and minimum legend values have become widerthan the previous situation for example for Re = 100 the215 value has increased to 237 For Re = 250 and Re = 350

the uppermost values have risen to 247 and 252 from 233and 238 respectively Due to bounce-back condition theair is now forming more recirculations against the walls andbetween the blocksThis augmentation of values and recircu-lations due to buoyancy effect is visible for every incrementof Re values and addition of obstacles such as partition

The generated results of isotherms in Figure 10 give avisual idea how the heat is transferred from the blocks and

passes through the outlet Like the other cases only thesurfaces of the blocks are heated to be considered as patientswho are continuously releasing heat Everything remains thesame like previous cases

Figure 11 provides the 119880 velocity profiles for differentpositions of 119909 According to this the graph characteristicfor a partition can be seen in Figure 11(e) at 119909 = 3 andFigure 11(j) at 119909 = 55 indicating the presence of partitionsat these two locations Apart from this at 119909 = 5 and 75 inFigures 11(i) and 11(n) respectively the parabolic shapes aremore curvy than the profiles at other positions caused dueto recirculations in vector plots of Re = 250 and Re = 350

Journal of Computational Engineering 11

1

05

00

2 4 6 8

xH

yH

000 015 029 043 058 072 086 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 038 054 069 077 092 100

(b)

0 2 4 6 8

xH

1

05

0

yH

008 024 040 056 071 087 095 100

(c)

Figure 10 Isotherms of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(c)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(d)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y HuU

minus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 11 119906119880 velocity profiles in Case III for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

Figures 12(a) and 12(b) illustrate119880 and119881 velocity distributioncurves in mid-119910 and Figure 12(c) shows the temperatureprofile at mid-119910 All of these three plots have one thing incommon that is also different than the previous case In theseplots there are two constrictions instead of one where the

velocities or the temperature curve ceasesThis is the locationwhere the two partitions are present But after crossing theseobstacles the respective graphs continue until 119909 = 8 Thetemperature plot in Figure 12(c) has now two steep regionsdue to the partitions

12 Journal of Computational Engineering

0 2 4 6 8

2

1

0

minus1

uH

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(a)

0 2 4 6 8

1

0

minus1

H

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(b)

0 2 4 6 8

1

05

0

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 12 In Case III for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

55 Calculation of Rate of Heat Transfer In heat transferat a boundary (surface) within a fluid the Nusselt number(Nu) is the ratio of convective to conductive heat transferacross (normal to) the boundary Here convection includesboth advection and diffusion procedures The convectionand conduction heat flows are parallel to each other andto the surface normal of the boundary surface and are allperpendicular to the mean fluid flow in the simple case Thisis denoted as [32]

Nu119871=ℎ119905119871

119896 (19)

where ℎ119905is the convective heat transfer coefficient of the

flow 119871 is the characteristic length and 119896 is the thermalconductivity of the fluid

However this section discusses the average rate of changeof heat transfer obtained for different Re This rate isexpressed as average Nusselt number Nu for each case studyin Tables 2 3 and 4 The tables also show generated localNusselt number Nu that follows the expression below

Nu (119909) = minus 120597120579

120597119910

10038161003816100381610038161003816100381610038161003816119910=1199102

(20)

where 1199102is the upper surface of each block

Average Nu is calculated by integrating the above rela-tion over the entire range of interest and thus the resultingequation becomes

Nu = 1

1199092minus 1199091

int

1199092

1199091

Nu (119909) 119889119909 (21)

Here (1199092minus 1199091) is the length of each block

For the first investigation both the individual and averageNu obtained in Table 2 show a rising trend for each increasingRe Since block 1 is the nearest to the inlet it always has thehighest rate of heat transfer while block 6 has the lowest valueas it is located farthest from the inlet

After placing the partition in the middle the rate of heattransfer shown in Table 3 changes dramatically Like Table 2the patient at block 1 is releasing most heat for all three Reand it keeps reducing until block 5 At block 5 the values ofboth individual Nu and total Nu increase for Re = 250 andRe = 350 but for Re = 100 this type of airflow pattern isseen at block 4 The large recirculations were seen earlier inFigure 5 For Re = 100 recirculation is more over block 4 andthat is the reason why at block 4 individual Nu and total Nuhave greater values than those of Re = 250 and Re = 350 Nuis 15341 at block 4 and for the same block these values are13628 and 14032 respectively for Re = 250 and Re = 350On the other hand if Nu at block 5 are observed Re = 250

and Re = 350 lead the race As per Table 3 Nu are 2011121598 and 27535 for three Re The spike in the values ofRe = 250 and Re = 350 was due to chaotic flows over block5 in Figure 5 If changes in total Nu are observed the valuesincrease rapidly for an increase in Re

For Case Study III the shape of recirculation gets biggerdue to increased Re Above block 1 the recirculation zonecomes into view and due to that reason Nu has the biggestedge in this situation But as the air has tendency to passthe first partition it moves slightly upward and that is whypatient at block 2 is getting less airflowThe heat transfer ratealso falls After passing the first partition the airflow gets itsspace and leads to recirculation near block 3 for Re = 100Meanwhile for Re = 250 and Re = 350 patients on block 4get most air More air means more heat transfer and that is

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

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International Journal of

10 Journal of Computational Engineering

0 2 4 6 8

012 Partition

xH

Re = 100

Re = 250

Re = 350

uH

(a)

0 2 4 6 8

0

1 Partition

xH

Re = 100

Re = 250

Re = 350

H

(b)

0 2 4 6 80

05

1 Partition

xH

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 8 In Case II for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

1

05

00 2 4 6 8

xH

yH

237198159119080041002minus038

(a)

0 2 4 6 8

xH

1

05

0

yH

247198149100051002minus047minus096

(b)

0 2 4 6 8

xH

1

05

0

yH

252199146092039minus014minus068minus121

(c)

Figure 9 Streamline patterns of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

for the corresponding experiments with each Re Even themaximum and minimum legend values have become widerthan the previous situation for example for Re = 100 the215 value has increased to 237 For Re = 250 and Re = 350

the uppermost values have risen to 247 and 252 from 233and 238 respectively Due to bounce-back condition theair is now forming more recirculations against the walls andbetween the blocksThis augmentation of values and recircu-lations due to buoyancy effect is visible for every incrementof Re values and addition of obstacles such as partition

The generated results of isotherms in Figure 10 give avisual idea how the heat is transferred from the blocks and

passes through the outlet Like the other cases only thesurfaces of the blocks are heated to be considered as patientswho are continuously releasing heat Everything remains thesame like previous cases

Figure 11 provides the 119880 velocity profiles for differentpositions of 119909 According to this the graph characteristicfor a partition can be seen in Figure 11(e) at 119909 = 3 andFigure 11(j) at 119909 = 55 indicating the presence of partitionsat these two locations Apart from this at 119909 = 5 and 75 inFigures 11(i) and 11(n) respectively the parabolic shapes aremore curvy than the profiles at other positions caused dueto recirculations in vector plots of Re = 250 and Re = 350

Journal of Computational Engineering 11

1

05

00

2 4 6 8

xH

yH

000 015 029 043 058 072 086 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 038 054 069 077 092 100

(b)

0 2 4 6 8

xH

1

05

0

yH

008 024 040 056 071 087 095 100

(c)

Figure 10 Isotherms of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(c)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(d)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y HuU

minus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 11 119906119880 velocity profiles in Case III for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

Figures 12(a) and 12(b) illustrate119880 and119881 velocity distributioncurves in mid-119910 and Figure 12(c) shows the temperatureprofile at mid-119910 All of these three plots have one thing incommon that is also different than the previous case In theseplots there are two constrictions instead of one where the

velocities or the temperature curve ceasesThis is the locationwhere the two partitions are present But after crossing theseobstacles the respective graphs continue until 119909 = 8 Thetemperature plot in Figure 12(c) has now two steep regionsdue to the partitions

12 Journal of Computational Engineering

0 2 4 6 8

2

1

0

minus1

uH

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(a)

0 2 4 6 8

1

0

minus1

H

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(b)

0 2 4 6 8

1

05

0

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 12 In Case III for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

55 Calculation of Rate of Heat Transfer In heat transferat a boundary (surface) within a fluid the Nusselt number(Nu) is the ratio of convective to conductive heat transferacross (normal to) the boundary Here convection includesboth advection and diffusion procedures The convectionand conduction heat flows are parallel to each other andto the surface normal of the boundary surface and are allperpendicular to the mean fluid flow in the simple case Thisis denoted as [32]

Nu119871=ℎ119905119871

119896 (19)

where ℎ119905is the convective heat transfer coefficient of the

flow 119871 is the characteristic length and 119896 is the thermalconductivity of the fluid

However this section discusses the average rate of changeof heat transfer obtained for different Re This rate isexpressed as average Nusselt number Nu for each case studyin Tables 2 3 and 4 The tables also show generated localNusselt number Nu that follows the expression below

Nu (119909) = minus 120597120579

120597119910

10038161003816100381610038161003816100381610038161003816119910=1199102

(20)

where 1199102is the upper surface of each block

Average Nu is calculated by integrating the above rela-tion over the entire range of interest and thus the resultingequation becomes

Nu = 1

1199092minus 1199091

int

1199092

1199091

Nu (119909) 119889119909 (21)

Here (1199092minus 1199091) is the length of each block

For the first investigation both the individual and averageNu obtained in Table 2 show a rising trend for each increasingRe Since block 1 is the nearest to the inlet it always has thehighest rate of heat transfer while block 6 has the lowest valueas it is located farthest from the inlet

After placing the partition in the middle the rate of heattransfer shown in Table 3 changes dramatically Like Table 2the patient at block 1 is releasing most heat for all three Reand it keeps reducing until block 5 At block 5 the values ofboth individual Nu and total Nu increase for Re = 250 andRe = 350 but for Re = 100 this type of airflow pattern isseen at block 4 The large recirculations were seen earlier inFigure 5 For Re = 100 recirculation is more over block 4 andthat is the reason why at block 4 individual Nu and total Nuhave greater values than those of Re = 250 and Re = 350 Nuis 15341 at block 4 and for the same block these values are13628 and 14032 respectively for Re = 250 and Re = 350On the other hand if Nu at block 5 are observed Re = 250

and Re = 350 lead the race As per Table 3 Nu are 2011121598 and 27535 for three Re The spike in the values ofRe = 250 and Re = 350 was due to chaotic flows over block5 in Figure 5 If changes in total Nu are observed the valuesincrease rapidly for an increase in Re

For Case Study III the shape of recirculation gets biggerdue to increased Re Above block 1 the recirculation zonecomes into view and due to that reason Nu has the biggestedge in this situation But as the air has tendency to passthe first partition it moves slightly upward and that is whypatient at block 2 is getting less airflowThe heat transfer ratealso falls After passing the first partition the airflow gets itsspace and leads to recirculation near block 3 for Re = 100Meanwhile for Re = 250 and Re = 350 patients on block 4get most air More air means more heat transfer and that is

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

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DistributedSensor Networks

International Journal of

Journal of Computational Engineering 11

1

05

00

2 4 6 8

xH

yH

000 015 029 043 058 072 086 100

(a)

0 2 4 6 8

xH

1

05

0

yH

008 023 038 054 069 077 092 100

(b)

0 2 4 6 8

xH

1

05

0

yH

008 024 040 056 071 087 095 100

(c)

Figure 10 Isotherms of Case III for (a) Re = 100 (b) Re = 250 and (c) Re = 350

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(a)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(b)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(c)

uUminus1 0 1 2

002040608

1

y H

Re = 100

Re = 250

Re = 350

(d)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(e)

002040608

1

y HuU

minus1 0 1 2

Re = 100

Re = 250

Re = 350

(f)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(g)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(h)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(i)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(j)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(k)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(l)

002040608

1

y H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(m)

002040608

1y

H

uUminus1 0 1 2

Re = 100

Re = 250

Re = 350

(n)

Figure 11 119906119880 velocity profiles in Case III for the different Re at different positions of horizontal locations (a) 119909119867 = 05 (b) 119909119867 = 1 (c)119909119867 = 15 (d) 119909119867 = 2 (e) 119909119867 = 3 (f) 119909119867 = 35 (g) 119909119867 = 4 (h) 119909119867 = 45 (i) 119909119867 = 5 (j) 119909119867 = 55 (k) 119909119867 = 6 (l) 119909119867 = 65 (m)119909119867 = 7 and (n) 119909119867 = 75

Figures 12(a) and 12(b) illustrate119880 and119881 velocity distributioncurves in mid-119910 and Figure 12(c) shows the temperatureprofile at mid-119910 All of these three plots have one thing incommon that is also different than the previous case In theseplots there are two constrictions instead of one where the

velocities or the temperature curve ceasesThis is the locationwhere the two partitions are present But after crossing theseobstacles the respective graphs continue until 119909 = 8 Thetemperature plot in Figure 12(c) has now two steep regionsdue to the partitions

12 Journal of Computational Engineering

0 2 4 6 8

2

1

0

minus1

uH

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(a)

0 2 4 6 8

1

0

minus1

H

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(b)

0 2 4 6 8

1

05

0

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 12 In Case III for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

55 Calculation of Rate of Heat Transfer In heat transferat a boundary (surface) within a fluid the Nusselt number(Nu) is the ratio of convective to conductive heat transferacross (normal to) the boundary Here convection includesboth advection and diffusion procedures The convectionand conduction heat flows are parallel to each other andto the surface normal of the boundary surface and are allperpendicular to the mean fluid flow in the simple case Thisis denoted as [32]

Nu119871=ℎ119905119871

119896 (19)

where ℎ119905is the convective heat transfer coefficient of the

flow 119871 is the characteristic length and 119896 is the thermalconductivity of the fluid

However this section discusses the average rate of changeof heat transfer obtained for different Re This rate isexpressed as average Nusselt number Nu for each case studyin Tables 2 3 and 4 The tables also show generated localNusselt number Nu that follows the expression below

Nu (119909) = minus 120597120579

120597119910

10038161003816100381610038161003816100381610038161003816119910=1199102

(20)

where 1199102is the upper surface of each block

Average Nu is calculated by integrating the above rela-tion over the entire range of interest and thus the resultingequation becomes

Nu = 1

1199092minus 1199091

int

1199092

1199091

Nu (119909) 119889119909 (21)

Here (1199092minus 1199091) is the length of each block

For the first investigation both the individual and averageNu obtained in Table 2 show a rising trend for each increasingRe Since block 1 is the nearest to the inlet it always has thehighest rate of heat transfer while block 6 has the lowest valueas it is located farthest from the inlet

After placing the partition in the middle the rate of heattransfer shown in Table 3 changes dramatically Like Table 2the patient at block 1 is releasing most heat for all three Reand it keeps reducing until block 5 At block 5 the values ofboth individual Nu and total Nu increase for Re = 250 andRe = 350 but for Re = 100 this type of airflow pattern isseen at block 4 The large recirculations were seen earlier inFigure 5 For Re = 100 recirculation is more over block 4 andthat is the reason why at block 4 individual Nu and total Nuhave greater values than those of Re = 250 and Re = 350 Nuis 15341 at block 4 and for the same block these values are13628 and 14032 respectively for Re = 250 and Re = 350On the other hand if Nu at block 5 are observed Re = 250

and Re = 350 lead the race As per Table 3 Nu are 2011121598 and 27535 for three Re The spike in the values ofRe = 250 and Re = 350 was due to chaotic flows over block5 in Figure 5 If changes in total Nu are observed the valuesincrease rapidly for an increase in Re

For Case Study III the shape of recirculation gets biggerdue to increased Re Above block 1 the recirculation zonecomes into view and due to that reason Nu has the biggestedge in this situation But as the air has tendency to passthe first partition it moves slightly upward and that is whypatient at block 2 is getting less airflowThe heat transfer ratealso falls After passing the first partition the airflow gets itsspace and leads to recirculation near block 3 for Re = 100Meanwhile for Re = 250 and Re = 350 patients on block 4get most air More air means more heat transfer and that is

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Journal of Computational Engineering

0 2 4 6 8

2

1

0

minus1

uH

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(a)

0 2 4 6 8

1

0

minus1

H

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

(b)

0 2 4 6 8

1

05

0

xH

Partition 1 Partition 2

Re = 100

Re = 250

Re = 350

120579

(c)

Figure 12 In Case III for Re = 100 250 and Re = 350 the velocity distributions are (a) 119906119867 at mid-119910 and (b) V119867 at mid-119910 and temperaturedistribution is (c) 120579 at mid-119910

55 Calculation of Rate of Heat Transfer In heat transferat a boundary (surface) within a fluid the Nusselt number(Nu) is the ratio of convective to conductive heat transferacross (normal to) the boundary Here convection includesboth advection and diffusion procedures The convectionand conduction heat flows are parallel to each other andto the surface normal of the boundary surface and are allperpendicular to the mean fluid flow in the simple case Thisis denoted as [32]

Nu119871=ℎ119905119871

119896 (19)

where ℎ119905is the convective heat transfer coefficient of the

flow 119871 is the characteristic length and 119896 is the thermalconductivity of the fluid

However this section discusses the average rate of changeof heat transfer obtained for different Re This rate isexpressed as average Nusselt number Nu for each case studyin Tables 2 3 and 4 The tables also show generated localNusselt number Nu that follows the expression below

Nu (119909) = minus 120597120579

120597119910

10038161003816100381610038161003816100381610038161003816119910=1199102

(20)

where 1199102is the upper surface of each block

Average Nu is calculated by integrating the above rela-tion over the entire range of interest and thus the resultingequation becomes

Nu = 1

1199092minus 1199091

int

1199092

1199091

Nu (119909) 119889119909 (21)

Here (1199092minus 1199091) is the length of each block

For the first investigation both the individual and averageNu obtained in Table 2 show a rising trend for each increasingRe Since block 1 is the nearest to the inlet it always has thehighest rate of heat transfer while block 6 has the lowest valueas it is located farthest from the inlet

After placing the partition in the middle the rate of heattransfer shown in Table 3 changes dramatically Like Table 2the patient at block 1 is releasing most heat for all three Reand it keeps reducing until block 5 At block 5 the values ofboth individual Nu and total Nu increase for Re = 250 andRe = 350 but for Re = 100 this type of airflow pattern isseen at block 4 The large recirculations were seen earlier inFigure 5 For Re = 100 recirculation is more over block 4 andthat is the reason why at block 4 individual Nu and total Nuhave greater values than those of Re = 250 and Re = 350 Nuis 15341 at block 4 and for the same block these values are13628 and 14032 respectively for Re = 250 and Re = 350On the other hand if Nu at block 5 are observed Re = 250

and Re = 350 lead the race As per Table 3 Nu are 2011121598 and 27535 for three Re The spike in the values ofRe = 250 and Re = 350 was due to chaotic flows over block5 in Figure 5 If changes in total Nu are observed the valuesincrease rapidly for an increase in Re

For Case Study III the shape of recirculation gets biggerdue to increased Re Above block 1 the recirculation zonecomes into view and due to that reason Nu has the biggestedge in this situation But as the air has tendency to passthe first partition it moves slightly upward and that is whypatient at block 2 is getting less airflowThe heat transfer ratealso falls After passing the first partition the airflow gets itsspace and leads to recirculation near block 3 for Re = 100Meanwhile for Re = 250 and Re = 350 patients on block 4get most air More air means more heat transfer and that is

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Computational Engineering 13

Table 2 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwithout partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6100 30164 20366 17990 16667 15695 14486 115368250 46238 29266 22996 21784 20573 18028 158885350 54359 20344 24841 22300 21352 17329 175970

Table 3 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case ofwith partition

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32979 20344 16115 15341 20111 16124 121014250 50273 29488 17955 13628 21598 38673 171615350 58293 36676 18670 14032 27535 53320 208527

Table 4 Summary of average Nusselt numbers Nu for six blocks individually and in total for three Reynolds numbers at Pr = 071 in case oftwo partitions

Re Nu (individually) Nu (total)Block 1 Block 2 Block 3 Block 4 Block 5 Block 6

100 32791 18265 16086 18914 15810 17583 119449250 49303 22066 11352 25811 13338 24044 145915350 57620 24463 11924 29056 12632 27495 163191

why Nu are 25811 and 29056 in terms of block 4 for Re =250 350 However the change in the values of Nu repeats interms of block 5 For Re = 100 patient at block 5 getsmost airand that is also due to vorticity which is seen in Figure 9 Fortwo other Re these recirculations appear over block 6 whichalso lead to an increase in Nu as per Table 4

Comparing the results after analyzing Tables 2 3 and 4few statements can bemade Heat transfer rate is at its highestlevel when one partition is present For example when thereis not any partition total Nu is 158885 for Re = 250 andit rises to 171615 when one partition is present Howeverplacing two partitions create one extra obstacle for airflowandNudecreases to 145915 Same variations can be observedfor Re = 100 and Re = 350 as well

The finding of three case studies can be related to theneed of airflow of hospital patients For instance if a hospitalward does not have any obstacle or partition between any bedpatient who is in need of most airflow should be put on block(bed) 1 If anyone needs less air due to fever or is sufferingfrom any type of airborne disease or germs he or she shouldbe kept at block 6 or on any bed which is farthest to the inlet

Consequently if the ward has one partition in the middle(which is pretty common in hospital nowadays) both blocks(beds) 1 and 2will be just fine formore air If disease is relatedto air these two beds in particular should be avoided Formoderate airflow any bed or block after the first two shouldbe considered

Last but not least if three different zones are availablein the ward due to two partitions any bed between 3 and

6 should be okay for normal airflow Blocks (beds) 1 and2 should be kept for patients who are suffering from acutetemperature related disease By any chance if none of thosebeds are available block (bed) 4 will be a pretty goodreplacement

6 Local Reynolds Number

Local Reynolds numbers (Re119897) for all obstacles have been

computed at the mid of the gap between block and top wallfor Case II (with one partition) at Re = 100 They are 6154for block 1 3534 for block 2 2554 for block 3 3693 forpartition 1632 for block 4 2454 for block 5 and 3219 forblock 6 The above results demonstrate that as the air entersthe domain and flows far away from the inlet the inlet airvelocity also reduces and consequently the local Re

119897values

also decrease Block 1 has the highest local Re119897value since

the inlet velocity is maximum at this position After gradualdecline of the numerals block 4 has negative local Re

119897due

to the negative velocity of the recirculation zone The valuesthen increase as the air flows up towards the outlet but cannotattain the maximum value due to the distance from the inlet

7 Conclusion

In this paper the study of airflow on mixed convectionflow inside a hospital ward has been analyzed using theLattice Boltzmann Method The changes in the patterns ofairflow have been observed in three different case studiesThe

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

14 Journal of Computational Engineering

code validation has been carried out for three different Reand agreement has been shown as well In the case studiesLBM was able to capture the convective structure as theair flowed over the room and even when the partition waspresent It was found that the heat transfer process andflow characteristics depend on different Re Moreover thepresence of the partition in each case was found to havesignificance on the pattern of airflow in both streamlines andisotherms on a particular Ri and Gr Some conclusions aresummarized as follows

(a) A proper code validation with previous numericalinvestigations implies that Lattice BoltzmannMethodis indeed an appropriate method for studying mixedconvective airflow

(b) Generally the increase in Reynolds number resultedin augmentation of heat transfer The pattern ofairflow also changed

(c) As the Reynolds number increases theMach numberdecreasesTheMach number cannot bemore than 03to satisfy the condition of flow in incompressible fluid

(d) Since local Re is directly proportional to the velocityof inlet flow therefore as the air gradually flows awayfrom the inlet the flow velocity reduces for whichlocal Re also decreases

(e) Placing partition between the blocks or beds hadeffects on the airflow structure and for different casesthe results were different

(f) The most effective rate of heat transfer was foundwhen one partition was present which were due torecirculations in the contours

(g) Influence of two partitions on heat transfer was lessfor all three Reynolds numbers which indicates thatair did not get enough space to flow freely and that ledto a fall in heat transfer rate

(h) Patients who are in need of most air should be keptnear the inlet and patients who do not need to beexposed directly to air should be moved near theoutlet

Nomenclature

English Symbols

119886 Height of the partition119887 Width of the partition119888 Lattice speed119890119894 Particle velocity

119865 External forces119891 Distribution function for velocity119891eq Equilibrium distribution function for velocity

Gr Grashof number119866119910 Gravitational acceleration in 119910-direction

119892 Distribution function for temperature119892eq Equilibrium distribution function for temperature119867 Height of the hospital wardℎ Height of each block

ℎ119905 Convective heat transfer coefficient of the flow

119896 Thermal conductivity of the fluid119871 Length of the hospital ward119897 Length of each blockMa Mach number119873 Number of lattices parallel to 119910-directionNu Local Nusselt numberNu Average Nusselt number119899 Iteration indexPr Prandtl numberRe Reynolds numberRi Richardson number119879 Temperature of the fluid119879119867 119879119882 Hot wall temperature

119879119862 Cold wall temperature

119905 Time119906 Velocity vector119906 Velocity component along 119909-directionV Velocity component along 119910-direction119880 Bulk velocity119908119894 Weighted factor

119909119883 Horizontal axial coordinate119910 119884 Vertical axial coordinate

Greek Symbols

120572 Thermal diffusivity120583 Dynamic viscosity of the fluid] Kinematic viscosity120588 Density120591] Single-relaxation time based on ]120591120572 Single-relaxation time based on 120572

120579 Nondimensional temperature120601 Generic variableΩ Collision operatornabla Gradient operator

Competing Interests

The authors declare that they have no competing interests

References

[1] C K Cha and Y Jaluria ldquoRecirculating mixed convection flowfor energy extractionrdquo International Journal of Heat and MassTransfer vol 27 no 10 pp 1801ndash1812 1984

[2] F J K Ideriah ldquoPrediction of turbulent cavity flow driven bybuoyancy and shearrdquo Journal of Mechanical Engineering Sciencevol 22 no 6 pp 287ndash295 1980

[3] J Imberger and P F Hamblin ldquoDynamics of lakes reservoirsand cooling pondsrdquo Annual Review of Fluid Mechanics vol 14pp 153ndash187 1982

[4] H Huang M C Sukop and X Lu Multiphase Lattice Boltz-mann Methods Theory and Application John Wiley amp SonsNew York NY USA 2015

[5] B Hasslacher Y Pomeau and U Frisch ldquoLattice-gas automatafor the Navier-Stokes equationrdquo Physical Review Letters vol 56no 14 pp 1505ndash1508 1986

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Computational Engineering 15

[6] G Vahala P Pavlo L Vahala and N S Martys ldquoThermallattice-boltzmann models (TLBM) for compressible flowsrdquoInternational Journal ofModern Physics C vol 9 no 8 pp 1247ndash1261 1998

[7] Y Peng C Shu and Y T Chew ldquoSimplified thermal latticeBoltzmann model for incompressible thermal flowsrdquo PhysicalReview E vol 68 no 2 Article ID 026701 2003

[8] T S Lee H Huang and C Shu ldquoAn axisymmetric incompress-ible lattice BGK model for simulation of the pulsatile flow ina circular piperdquo International Journal for Numerical Methods inFluids vol 49 no 1 pp 99ndash116 2005

[9] N A C Sidik ldquoThe development of thermal lattice Boltzmannmodels in incompressible limitrdquo Malaysian Journal of Funda-mental and Applied Sciences vol 3 no 2 pp 193ndash202 2008

[10] B Mondal and X Li ldquoEffect of volumetric radiation on naturalconvection in a square cavity using lattice Boltzmann methodwith non-uniform latticesrdquo International Journal of Heat andMass Transfer vol 53 no 21-22 pp 4935ndash4948 2010

[11] M Szucki and J S Suchy ldquoA method for taking into accountlocal viscosity changes in single relaxation time the latticeBoltzmann modelrdquo Metallurgy and Foundry Engineering vol38 pp 33ndash42 2012

[12] S Chen and G D Doolen ldquoLattice Boltzmannmethod for fluidflowsrdquoAnnual Review of FluidMechanics vol 30 no 1 pp 329ndash364 1998

[13] G Breyiannis and D Valougeorgis ldquoLattice kinetic simulationsin three-dimensionalmagnetohydrodynamicsrdquoPhysical ReviewE vol 69 no 6 Article ID 065702 2004

[14] I Halliday L A Hammond C M Care K Good and AStevens ldquoLattice Boltzmann equation hydrodynamicsrdquo PhysicalReview E vol 64 no 1 I Article ID 011208 2001

[15] C S N Azwadi and T Tanahashi ldquoDevelopment of 2-Dand 3-D double-population thermal lattice boltzmannmodelsrdquoMatematika vol 24 no 1 pp 53ndash66 2008

[16] B Crouse M Krafczyk S Kuhner E Rank and C Van TreeckldquoIndoor air flow analysis based on lattice Boltzmann methodsrdquoEnergy and Buildings vol 34 no 9 pp 941ndash949 2002

[17] Z Zhang X Chen S Mazumdar T Zhang and Q ChenldquoExperimental and numerical investigation of airflow andcontaminant transport in an airliner cabin mockuprdquo Buildingand Environment vol 44 no 1 pp 85ndash94 2009

[18] S J Zhang and C X Lin ldquoApplication of lattice Boltzmannmethod in indoor airflow simulationrdquoHVACampR Research vol16 no 6 pp 825ndash841 2010

[19] J Liu H Wang and W Wen ldquoNumerical simulation on ahorizontal airflow for airborne particles control in hospitaloperating roomrdquo Building and Environment vol 44 no 11 pp2284ndash2289 2009

[20] A Watzinger and D G Johnson ldquoWarmeubertragung vonwasser an rohrwand bei senkrechter stromung im ubergangsge-biet zwischen laminarer und turbulenter stromungrdquo Forschungauf demGebiet des Ingenieurwesens A vol 10 no 4 pp 182ndash1961939

[21] A K Prasad and J R Koseff ldquoCombined forced and naturalconvection heat transfer in a deep lid-driven cavity flowrdquoInternational Journal of Heat and Fluid Flow vol 17 no 5 pp460ndash467 1996

[22] H Xu R Xiao F Karimi M Yang and Y Zhang ldquoNumericalstudy of double diffusive mixed convection around a heatedcylinder in an enclosurerdquo International Journal of ThermalSciences vol 78 pp 169ndash181 2014

[23] S A Al-Sanea M F Zedan and M B Al-Harbi ldquoEffectof supply Reynolds number and room aspect ratio on flowand ceiling heat-transfer coefficient for mixing ventilationrdquoInternational Journal of Thermal Sciences vol 54 pp 176ndash1872012

[24] F-Y Zhao D Liu and G-F Tang ldquoMultiple steady fluid flowsin a slot-ventilated enclosurerdquo International Journal of Heat andFluid Flow vol 29 no 5 pp 1295ndash1308 2008

[25] K M Khanafer and A J Chamkha ldquoMixed convection flowin a lid-driven enclosure filled with a fluid-saturated porousmediumrdquo International Journal of Heat and Mass Transfer vol42 no 13 pp 2465ndash2481 1999

[26] G H R Kefayati S F Hosseinizadeh M Gorji and H SajjadildquoLattice Boltzmann simulation of natural convection in an openenclosure subjugated to watercopper nanofluidrdquo InternationalJournal of Thermal Sciences vol 52 no 1 pp 91ndash101 2012

[27] H Lee and H B Awbi ldquoEffect of internal partitioning onroom air quality with mixing ventilation-statistical analysisrdquoRenewable Energy vol 29 no 10 pp 1721ndash1732 2004

[28] Y B Bao and J Meskas Lattice Boltzmann Method for FluidSimulations Courant Institute of Mathematical Sciences NewYork NY USA 2011

[29] H N Dixit and V Babu ldquoSimulation of high Rayleigh numbernatural convection in a square cavity using the lattice Boltz-mannmethodrdquo International Journal of Heat andMass Transfervol 49 no 3-4 pp 727ndash739 2006

[30] R Huang H Wu and P Cheng ldquoA new lattice Boltzmannmodel for solid-liquid phase changerdquo International Journal ofHeat and Mass Transfer vol 59 no 1 pp 295ndash301 2013

[31] Y Xuan and Z Yao ldquoLattice boltzmann model for nanofluidsrdquoHeat and Mass Transfer vol 41 no 3 pp 199ndash205 2005

[32] G R Kefayati M Gorji-Bandpy H Sajjadi and D D GanjildquoLattice Boltzmann simulation of MHD mixed convection ina lid-driven square cavity with linearly heated wallrdquo ScientiaIranica vol 19 no 4 pp 1053ndash1065 2012

[33] Q Zou and X He ldquoOn pressure and velocity boundaryconditions for the lattice Boltzmann BGK modelrdquo Physics ofFluids vol 9 no 6 pp 1591ndash1598 1997

[34] A A Mohamad and A Kuzmin ldquoA critical evaluation offorce term in lattice Boltzmann method natural convectionproblemrdquo International Journal of Heat and Mass Transfer vol53 no 5-6 pp 990ndash996 2010

[35] R Iwatsu J M Hyun and K Kuwahara ldquoMixed convectionin a driven cavity with a stable vertical temperature gradientrdquoInternational Journal of Heat and Mass Transfer vol 36 no 6pp 1601ndash1608 1993

[36] K M Khanafer A M Al-Amiri and I Pop ldquoNumericalsimulation of unsteady mixed convection in a driven cavityusing an externally excited sliding lidrdquo European Journal ofMechanics B Fluids vol 26 no 5 pp 669ndash687 2007

[37] M M Abdelkhalek ldquoMixed convection in a square cavity by aperturbation techniquerdquo Computational Materials Science vol42 no 2 pp 212ndash219 2008

[38] R K Tiwari and M K Das ldquoHeat transfer augmentation in atwo-sided lid-driven differentially heated square cavity utilizingnanofluidsrdquo International Journal of Heat and Mass Transfervol 50 no 9-10 pp 2002ndash2018 2007

[39] M A Waheed ldquoMixed convective heat transfer in rectangularenclosures driven by a continuously moving horizontal platerdquoInternational Journal of Heat and Mass Transfer vol 52 no 21-22 pp 5055ndash5063 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of