International Journal of Thermal Sciencesvafai.engr.ucr.edu/Publications/2016a/Iman Zeynali Famileh.pdf · Effect of nanoparticles on condensation of humid air in vertical channels

lable at ScienceDirect

International Journal of Thermal Sciences xxx (2016) 1e14

Contents lists avai

International Journal of Thermal Sciences

journal homepage: www.elsevier .com/locate/ i j ts

Effect of nanoparticles on condensation of humid air in verticalchannels

Iman Zeynali Famileh a, b, Javad Abolfazli Esfahani a, Kambiz Vafai b, *

a Center of Excellence on Modeling and Control Systems, (CEMCS) & Department of Mechanical Engineering, Faculty of Eng., Ferdowsi University ofMashhad, Iranb Mechanical Engineering Department, University of California, Riverside, CA, USA

a r t i c l e i n f o

Article history:Received 22 February 2016Received in revised form8 May 2016Accepted 8 May 2016Available online xxx

Keywords:Filmwise condensationNon-condensable gasNano-particlesHumid airHeat and mass transfer

* Corresponding author.E-mail address: [email protected] (K. Vafai).

http://dx.doi.org/10.1016/j.ijthermalsci.2016.05.0111290-0729/ 2016 Elsevier Masson SAS. All rights res

Please cite this article in press as: I.Z. FamilJournal of Thermal Sciences (2016), http://d

a b s t r a c t

In this paper, the effect of uniform surface injection of nanoparticles on humid air condensation, as amain type of vapor condensation in the presence of non-condensable gas (NCG), is numerically inves-tigated. Various inlet conditions (velocity and relative humidity) of vertical CONAN type classical testsection were modeled. Two mass concentrations of different nanoparticles were examined and thebehavior of filmwise condensation was studied under different parameters of heat and mass transfer,such as: Reynolds number and mean Nusselt number of the condensed film, and local and mean Sher-wood number. Finally, by using response surface methodology, the statistical interpretation (objectivefunction) of the numerical results are provided for other inlet conditions. As shown in the results, anincrease in the nanoparticles mass concentration has direct influence on condensate Reynolds numberand Sherwood number of the humid air. At higher relative humidities (u), using nanoparticles has moreimpact and the maximum improvement of the condensate Reynolds number (at the outlet), meanNusselt number of the condensed film and mean Sherwood number are 11.4, 4.5 and 6%, respectively. It isobserved that, under best conditions (u 100%, Uin 3 m/s), 0.5% of nanoparticles mass concentrationimproves the total heat flux by more than 10.4%.

2016 Elsevier Masson SAS. All rights reserved.

1. Introduction

The humid air condensation, as an example of condensation inthe presence of NCG, is one of the most applicable methods ofphase change which is observed in different industrial equipmentsuch as Heating, Ventilating and Air Conditioning (HVAC) orcoolant systems. For this purpose, various studies focused onfilmwise condensation enhancement with multifarious passive oractive methods. Undeniably, transformation to the era of nano-technology has a strong potential for improvement of phase changeperformance. Therefore, using nano-material, as an additive to themain fluid, is considered and several investigators have tried toevaluate the effect of nano-materials on heat and mass transferenhancement in heat exchangers [1e3]. Accordingly, a better un-derstanding of the nano-particles/nano-fluids effects on heat andmass transfer, especially in the presence of phase change, and itsinfluence on the mechanism of condensation/evaporation is

erved.

eh, et al., Effect of nanoparticx.doi.org/10.1016/j.ijthermals

needed as a key factor for more efficient equipment design.

1.1. Condensation of humid air

There are comprehensive studies in the area of filmwisecondensation for pure vapor and air/vapor mixture, with severalcorrelations for heat and mass transfer parameters for variousgeometrical conditions [4e6]. Desrayaud and Lauriat [7] demon-strated a new analogy of heat andmass transfer for condensation ofhumid air under laminar natural convection flow. Based on the thinfilm assumption, they reported new correlations for Sherwoodnumber, latent and sensible Nusselt numbers. Rao et al. [8] per-formed an analytical model for laminar film condensation of vaporin the presence of air as a high concentration of NCG in a verticaltube. With the help of heat and mass balance equations at theinterface, they estimated the gas-liquid interface temperature andreported the condensate Nusselt number, condensate Reynoldsnumber and pressure drop for different inlet conditions, such asReynolds number in the range of 1000e2000, and relative hu-midity up to 80%. In a similar study,Wu and Vierow [9] investigatedthe condensation of the vapor in the presence of NCG in a

les on condensation of humid air in vertical channels, Internationalci.2016.05.011

mailto:[email protected]/science/journal/12900729http://www.elsevier.com/locate/ijtshttp://dx.doi.org/10.1016/j.ijthermalsci.2016.05.011http://dx.doi.org/10.1016/j.ijthermalsci.2016.05.011http://dx.doi.org/10.1016/j.ijthermalsci.2016.05.011

I.Z. Famileh et al. / International Journal of Thermal Sciences xxx (2016) 1e142

horizontal tube and compared the condensation heat transfer co-efficient at the top and bottom of the tube. By comparing thecenterline temperature profiles and the overall heat transfer rate,the global effect of NCG on the heat transfer rate was evaluated andthe local effects of NCG on condensation process were reported.

Ambrosini et al. [10,11] attempted to compare the numericalsimulation of several CFD commercial software with the experi-mental benchmark results of the CONAN typical classical test sec-tion. The experimental correlations of Nusselt number andSherwood number for wall condensation of an external flow over avertical flat plate was proposed by them. Vyskocil et al. [12] carriedout air-steam condensation numerically and highlighted thesimulation of wall condensation ignoring the effect of volumecondensation. They compared their results with the benchmarkdata of CONAN experimental facility and predicted the condensa-tion rate for different inlet conditions. Similarly, Zschaeck et al. [13]provided a new CFDmodel of the wall condensation of vapor in thepresence of non-condensable multi components gas mixture in avertical channel and compared the numerical results with experi-mental data of CONAN experimental facility [10]. A comprehensivereview of vapor condensation in the presence of NCG was done byHuang et al. [14]. They categorized previous studies into dropwiseand filmwise condensation and focused on semi-theoretical andtheoretical models of condensation process in the presence of NCG.The effect of condensate thickness film, surface waves, interfacialshear strength and suction effects on filmwise condensation in thepresence of NCG were evaluated by them. Saraireh et al. [15] usedANSYS FLUENT commercial CFD software with the aim ofcomparing the numerical results with well-established correlationsof wall condensation parameters (condensation rate of vapor andheat flux) in the presence of air. Agrawal and Das [16] used in-housedeveloped CFD code (HDS) andmodeled unsteady form of wall filmcondensation under hydrogen distribution in an enclosure which isfilled with mixture of vapor and air for a vertical injection ofhydrogen from the bottom. They claimed that downward motion ofthe condensed film causes the concentration of hydrogen in lowerparts of the enclosure. Szijarto et al. [17] utilized RELAP5, a thermal-hydraulic system code, to trace the wall condensation and providedthe prediction of heat transfer process considering variation oftemperature, pressure and void fraction of vapor along the hori-zontal pipe. In their study, based on three different regimes ofcondensation, they defined the significant role of stratificationangle for transient condensation in a horizontal pipe. The numer-ical models of natural convection and wall condensation of humidair with time dependent wall temperature were defined by Sunet al. [18]. The thickness of the condensed filmwas discussed and itwas claimed that the thickness reflects on the flow structures. Theeffect of geometrical parameters (such as aspect ratio of cavity) onwall condensation/evaporation was also addressed.

1.2. Nanoparticles application in convection heat transfer

Modeling of the particles behavior in gaseous phase is impor-tant for several processes and there are many works in the litera-ture focused on investigation of particle deposition and suspendedparticle effects on heat transfer. Hudson [19] studied numericallythe effect of copper nanoparticles on the enhancement of laminarnatural/forced convection regime in a tube and an enclosure withdifferent aspect ratios. Different particles tracking methods forvarious enclosures, with aspect ratio between 1 and 5, wereexamined and finally it was concluded that nanoparticles has atendency to stay near the borders of an enclosure. Brereton [20]developed a Eulerian model for prediction of particle transport inan internal turbulent flow with thermophoretic term, as an eddy-viscosity-scaled multiple of the corresponding mean

Please cite this article in press as: I.Z. Famileh, et al., Effect of nanoparticJournal of Thermal Sciences (2016), http://dx.doi.org/10.1016/j.ijthermals

thermophoretic term, which is applicable for low inertia particles.Walsh et al. [21] developed an investigation of thermophoreticdeposition of aerosol particles on relatively cool cylindrical tube.Based on the solution of aerosol population, they compared parti-cles deposition in downward/upward flow through a vertical pipeand found that the free convection effects could be ignored forlower bulk Richardson number (Ri < 1). A two phase Euler-Eulermodel for prediction of conduction, convection and radiation heattransfer in dense gas-particle domains on the open-source codeOpenFOAM for high temperature solar power applications wasprovided by Marti et al. [22]. In case of a moderate rise in the walltemperature (581 K) and particle diameter of 64 mm, they high-lighted that the solid conduction accounts for about 97% of the wallto suspension heat flux. The increase of radiation heat flux portionup to 10% of the total wall to suspension heat flux is reported bythem.

In order to evaluate particles force balance, Akbar et al. [23]studied the transport of particles in a square enclosure forlaminar free convection regime using Eulerian-Lagrangian methodat ANSYS FLUENT commercial CFD software. They investigateddifferent motion mechanisms, including gravity, drag and liftforces, and thermophoresis and Brownian dispersions, for differentRayleigh numbers ranging from 100 to 800,000 and found thatmost of the particles dispersed towards thewalls, while a portion ofthe particles were collected in a quasi-steady recirculation zone.Garoosi et al. [24], used Eulerian-Lagrangian hybrid method, tomodel deposition of solid particles in natural convection regime ofan insulated square cavity with different replacement of cooler andheater elements. Tracking of 6000 discrete particles within a rangeof Rayleigh numbers (104 Ra 107) showed that thermophoresisforce could be effective at lower Rayleigh numbers. For the casewhich were studied, at lower Rayleigh numbers and non-uniformdistribution of particles; using more coolers and splitting ele-ments into smaller segments causes a significant change in depo-sition rate of particles and heat transfer rate. Afshar et al. [25]solved the Navier-Stokes and energy equations for slip flowregime in microchannel analytically and evaluated dispersion ofparticles due to the mentioned effective parameters. In their anal-ysis, it was shown that the control of entrance location of nano-particles leads to a heat transfer enhancement. Additionally, adecrease in the particle diameter causes an increase in the surfaceto volume fraction, which is affects, the heat transfer in micro-channels. In order to compare Eulerian and Lagrangian approaches,Saidi et al. [26] compared the motion of particles for the sameproblem using the two cited approaches. Their overall resultsshowed that for low particles concentration, approximately105 m2, the Eulerian approach diverges considerably and cannotbe applicable for low particles concentration unless employing along time scale. Using numerical solution of similarity trans-formations, Alam et al. [27] investigated unsteady forced convec-tion heat and mass transfer equations for thermophoreticdeposition of micro-particles driven by a rotating disk. Axial ther-mophoretic velocity, thermophoretic deposition flux and concen-tration profiles of particles were evaluated at different Schmidtnumber and it was concluded that, for larger Lewis numbers, theincreasing trend of thermophoretic velocity could be affected bythermophoretic coefficient and thermophoresis parameter.

Based on general exact solution of particle transport [28], Bertoliet al. [29] obtained several limiting solutions for heat transfer inmulti-particles systems, single particle and single phase flow. Theeffect of magneto hydrodynamic (MHD) on transportation anddeposition of micro- and nano-sized particles (particle diameter inthe range of 1 nm to 1 mm) for natural convection regime over ahorizontal and vertical plate was proposed by Guha and Samanta[30,31]. Different parameters such as: free convection, Brownian


I.Z. Famileh et al. / International Journal of Thermal Sciences xxx (2016) 1e14 3

diffusion and thermophoresis effects were included and particlesconcentration and deposition velocity of particles for differentmagnetic field parameters were reported. It was shown that themagnetic field parameter decreases the deposition velocity with anincrease in the particle diameter. The particle deposition at thebottom surface in room scale chamber with point particles injec-tion from two wall sides was numerically presented by Zhang et al.[32]. Distribution of particle-number density (count/volume) underdifferent situations was evaluated and the best agreement betweenthe modeling and the experiments was achieved for intermediateparticles size range (around 30 mm). With similar aim, Wang et al.[33] used ANSYS FLUENT commercial software and modeled par-ticles prediction in an airliner cabin for seven particle sizes (in therange of 0.1e100 mm). They tried to find the most important factorin particle deposition and provided an estimation of the position ofparticle concentrations.

Although the effects of nanoparticles on heat transfer, especiallyconvection and radiation, were considered in recent studies, thereis no comprehensive study in the area of nanoparticles depositioneffects on phase change (condensation). In the present study, theeffect of nanoparticles on filmwise condensation of vapor in thepresence of large volume of air, as a NCG, for different inlet veloc-ities and relative humidities of vertical channel are investigated andlocal and mean values of heat and mass transfer parameters arediscussed. This investigation is divided in three different parts. Inthe first part, the effect of nanoparticles material and mass con-centration of nanoparticles are evaluated. In the second part,condensate Reynolds number, Nusselt number of the condensedfilm and Sherwood number are investigated. In the third part,based on the response of surface methodology (RSM) the objectivefunction of the investigated parameters of the present problemwere provided. Finally, using the provided correlation, the influ-ence of nanoparticles for various ranges of relative humidity andinlet velocity are investigated. Due to the small effect of nano-particles on the condensed film, the variation of condensed filmspecifications is not large. However, because of the presence ofparticles in different applications of humid air condensation, theinvestigation of these effects are significant and prediction of theexact trend of filmwise condensation in the mentioned conditionsis appreciable. Therefore, the investigation of nanoparticles effectson condensation of vapor in the presence of air is the aim of presentresearch.

2. Problem statement

Fig. 1 displays the schematic view of the CONAN typical classicaltest section (a vertical channel with the cooling system in one sideand three insulated walls). The uniform dilute gas-particle flow (amultiphase system of nanoparticles as a discrete phase and humidair) enter from the above and exit from the below side. It wasassumed that the nanoparticles were injected from an inlet surfaceuniformly and with similar hydrodynamic and thermal conditionsof the main stream. The coolant water at fixed mass flux and inlettemperature flows from below to a thin secondary channel on theother side of the cooling wall. This situation causes the condensa-tion of the vapor on the coolant wall of the main channel andbecause of the gravity force, as the only external body force, thecondensed film has a downward movement along the cooling walland the exit from below.

Asmentioned before, the aim of this paper is the investigation ofnano-particle effect on the condensation and, for this purpose; it ispreferred to select the condition with minimum convection andradiation heat flux between the main stream and the cooling wall.That is, under the considered conditions where the condensedvapor takes the form of filmwise condensation, the condensation


heat flux is greater than convection heat flux (This assumption isprepared in CONAN typical classical test section.) [34]. Therefore,there are several limitations for the inlet boundary, which causesfilmwise condensed flow. What is more, because of the low tem-perature main stream (a multiphase system of nanoparticles as adiscrete phase and humid air), the radiation heat transfer can beignored [35]. Accordingly, the effect of nanoparticles on filmwisecondensation can be investigated under thementioned geometricaland hydrodynamical specifications of the problem, which are listedin Table 1. The influence of particles deposition is much larger inturbulent flows. As such all of investigated conditions are selectedin turbulent regime.

3. Governing equations

For the mentioned process, governing equations such as: con-tinuity, momentum, energy, species transport and particles forcebalance in vertical form for steady state condition could be writtenas follows:

Continuity equation:

V$

rV! 0 (1)

Momentum equations:

V$

ruV

! vpvx

V$meffVu

(2)

V$

rvV! vp

vy V$

meffVv

rg (3)

V$

rwV

! vpvz

V$meffVw

(4)

where r and V!

are the density of humid air and the velocity vector,respectively. Additionally, u, v andw are the velocity components inx-, y- and z-directions, p is the static pressure, meff is the effectivedynamic viscosity of the mixture in every control volume, g is thegravitational acceleration.

The RNGk model is used as a turbulent model for the presentproblem. The governing equations for the turbulent kinetic energy,k, and the dissipation rate, , are as follow:

V$

rkV

! V$mtskVk Pk Gk r (5)

V$

rV! V$mt

sV

C1

kPk C2r

2

k C3Gk

k(6)

where Pk is the generation of turbulent energy due to the meanvelocity gradient and Gk is the generation of turbulent energy dueto buoyancy. The constants of turbulent model have the followingvalues: sk 1, s 1.3, C1 1.44, C2 1.92, C3 1.3 [36].

Energy equation:

V$

rCpT V

! V$leffVT V$24Xn

j1

HjMj

rjDj;mixVYj

35 (7)where Cp is the heat capacity of the humid air,leff is the effectivethermal conductivity of humid air in every control volume whichdepends on the turbulence model. Hj, Mj, rj, Dj,mix and Yj are themolar specific enthalpy, molecular weight, density, diffusivity co-efficient and mass fraction of species j, respectively.


Fig. 1. The schematic view of CONAN typical classical test section.


Transport equation for non-reaction flow:

V$

rV!Yj

V$ Jj

! Sj (8)

where Jj!

is the diffusion flux of species j and Sj is the rate of pro-duction of speciesj. For every control volume, mt, meff, leff and Deffcould be written as Eqs. (9)e(12) and detailed in Ref. [36].

mt rCmk2

(9)

meff m mt (10)

Table 1Hydrodynamical and geometrical properties of the CONAN typical classi

Thermophysical and geometrical properties

Humid air channel Length, (m)Width, (m)Side, (m)Inlet velocityInlet PressurInlet temperInlet relative

Coolant plate (interface wall) Length, (m)Width, (m)Side, (m)

Water channel (cooling side) Length, (m)Width, (m)Side, (m)Inlet mass flInlet temper


leff l Cpmtst

(11)

Deff Dj;mix mtsy

(12)

where the mentioned constants have the following values(Cm 0.09, st 1, sy 1) [36].

Particle force balance in vector form:

F!

D F!

L F!

G F!

P F!

m F!B F!

Th 0 (13)

where F!

D is the unit-mass drag force vector which is caused by therelative slip between particles and the fluid. F

!L is the shear-

induced lift force vector. F!

G; F!

P and F!

m are the buoyancy forcevector, fluid pressure gradient and shear stress force vectors,respectively. F

!B stands for the stochastic excitation due to the

Brownian motion and F!

Th represents the thermophoresis forcevector. The first term of Eq. (13) is defined as in Ref. [37]:

F!

D CDRep24z

V! Vp! (14)

where Vp!

is particles velocity vector, Rep dU Up/y is theparticle Reynolds number and CD is the drag coefficient and is givenas:

CD

8>>>>>:

24Rep

for Rep


F!

L 2Ky0:5rdij

rpddlkdkl0:25V! Vp! (18)

where K 2.594 is the constant in Saffmans lift force relation anddij is the deformation rate tensor.

In Eq. (13), the buoyancy, fluid pressure gradient and shearstress forces are defined as follows:

F!

G g!rp r

rp

(19)

F!

P 1rpVP (20)

F!

m mrpV2 V

!(21)

The last two terms represent the stochastic excitation due toBrownian motion and the thermophoretic force is defined asfollows:

F!

B Giffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi216p

ykBrd5s2Cc

TDt

s(22)

F!

Th 36m2Cs

llp Ct Kn

rprd21 3CmKn

1 2llp 2CtKn VTT (23)

where Cm 1.14, Ct 2.18 and Cs 1.17 are constants and Gi and Knare zero-mean unit variance Gussian random number and Knudsennumber, respectively.

In order to evaluate the mentioned forces and their effects oncondensation of humid air, the effect of particle size can be inves-tigated. For particles with a size of 100 nm or larger, turbulence hasa larger effect than the Brownian diffusion [39]. Therefore, theBrownian force in the particle force balance can be ignored. Itshould be mentioned that particle deposition shows a smallamount of spreading near the walls, which is due to the rather lowturbulence fluctuation velocity. Meanwhile for particles with theorder of 10 nm or smaller, both Brownian motion and thermo-phoresis are the dominant mechanisms. But variation of particlesize has a lesser effect on the cited mechanism. For particles in therange of 100 nm to 4 mm, thermophoresis could be the dominantmechanism for particle deposition and for larger particles, ther-mophoresis is negligible. Therefore, for the investigated particlesizes in the present study (d 100 nm), there is no difference indeposition rate for isothermal channel and heating/cooling chan-nel. Although the higher temperature gradient causes the greaterthermophoresis effects, for the lower temperature gradients of10 C/cm, similar to the present study, particles are still affected bythe thermophoresis mechanism [39].

In order to achieve a more efficient numerical scheme, weinvoke several physically reasonable simplifying assumptions.Based on the related literature [10,12,23,24,40e42] the followingassumptions are invoked:

Condensation could occur only at the boundaries (cooling wall)and no condensation takes place in the form of mist or fog.

Compared to the z-direction (normal direction), the velocity ofthe main flow and condensed film are much larger in the x- andy-directions.

There is no slip condition on the surfaces.


The multiphase system of nanoparticles and humid air isassumed incompressible along the channel and, during thecondensation process, the density variation is ignored. In otherwords, variation of the density is only important with respect tothe buoyancy effects. Therefore, the Boussinesq approximationis invoked. The other thermophysical properties of nano-particles and humid air are assumed constant at the averagetemperature of the process.

In the case of condensation, because of the difference betweenmolecular mass of the dry air and vapor, the buoyancy force,which is caused by mass transfer and thermal diffusion, is in adownward direction. But, based on the prior description, it is notconsiderable.

The gravitational force is the only external body force, which hasan influence on the downward motion of the condensed film.

The mixture enters uniformly at the inlet under an atmosphericpressure.

In comparison with the considered domain, the condensed filmis very thin and it could be assumed that, for each location alongthe channel, the condensed film temperature is equal to theaverage of interface surface and wall temperature.

As in several studies, because of the uniform trend of thecondensed film along the z-direction (normal direction), thefilmwise condensation simulation is considered in 2D form.

Volume fraction of nanoparticles is under 0.5% and the sus-pension is quite dilute.

The are distributed randomly at the inlet boundary. There is a local thermal equilibrium between nanoparticles andmain flow.

For impingement of nanoparticles with the walls, the stickycondition is considered. Because of the low concentration ofnanoparticles, this type of impingement has no considerableeffect on the results.

Applying the above-cited assumptions the governing equations,i.e., continuity, momentum, energy, transport equations and theparticle force balance can be written as:

Continuity:

V$V! 0 (24)Momentum equations:

V$

uV! 1

r

vpvx

meffr

V2u (25)

V$

vV! 1

r

vpvy

meffr

V2v g (26)

V$

wV! 1

r

vpvz

meffr

V2w (27)

Energy equation:

V$T V! leff

rCpV2T 1

rCpV$

HaMa

raDa;mixVYa

HyMy

ryDy;mixVYy

(28)

Transport equation for non-reacting flow can be written as:

V$

rYy V

! V$rDy;mix mtSctVYy

(29)

where Sct 0.7 is the turbulence Schmidt number.



The Particle force balance can now be obtained by consideringthe definition of the drag force, the buoyancy force, fluid pressuregradient and shear stress force in Eqs. (14) and (19)e(21), respec-tively, thereby yielding:

3nCDRep4d2sCc

V! Vp! rp r

rpg! 1

rpVp m

rpV2 V

! F!

th

mp 0

(30)

where mp is the mass of the particles.Using 2d wall condensation model for the condensed film, the

continuity and momentum equations could be evaluated asfollows:

Continuity:

V$V!

l 0 (31)Momentum equations:

V$

ul V!

l

1

rl

vplvx

ylV2ul (32)

V$

vl V!

l

1

rl

vplvy

ylV2vl g (33)

4. Numerical implementation

Most of the CFD reports for particle transports in single-phaseflow are done using a Eulerian-Lagrangian hybrid method. As it iselaborated below, the fluid phase is treated as a continuum phaseusing the Navier-Stokes equations, while the nanoparticles aretracked using a large number of particles through the calculatedflow field.

As mentioned before, this problem consists of a convection/condensation heat transfer in a 3d domain. Additionally, discreteparticles are injected into the main flow. A numerical method usinga CFD commercial software was adapted for our problem. For thispurpose, the species transport model in ANSYS FLUENT 15.0 wasemployed for wall condensation of vapor in the presence of NCGwith additional nano-particles. On the basis of several previousreports [12], wall condensation plays a major role and the volumecondensation is negligible. Therefore, the Eulerian wall film modelis chosen as the wall condensation model. This model is onlyapplicable for 2d thin film condensation in a 3d domain. The wallcondensation process and particles distribution are executed inANSYS FLUENT by user-defined functions (UDF). The SIMPLE algo-rithm is used for pressure-velocity coupling. The QUICK model isadapted for heat transfer and the Green-Gauss is used for diffusionterms. In order to insure that final solutions are converged, amaximum residual of 106 is adopted for all of the equations. Thedetails of this method can be found in Ref. [43]. Finally, applying aLagrangian method, the governing equation of the particle depo-sition is numerically solved.

4.1. Mesh properties and validation

The mesh structure of the test section is shown in Fig. 2. Ac-cording to this figure, a 3d structural mesh is used. The finermesh isperformed near the coolant wall, where wall condensation occurs[44]. It is more noticeable that, the velocity gradient and temper-ature gradient are more visible in this area. Various ranges of gridsizes are examined to ensure that the numerical model is inde-pendent from mesh structure at different inlet conditions. Fig. 3


presents the total condensate mass flow rate at the outlet forpure saturated humid air at Uin 2.5 m/s and Tin 80 C. It can beseen that for grid numbers larger than 106, the variation ofcondensate mass flow rate is negligible. The mentioned discrep-ancy between condensed flow rates for different grid numbers is

defined as Ec

_mfinal _mi= _mfinal

100% where _mfinal and _mi are

total condensate mass flow rate at the finest mesh and the othercoarser mesh size respectively. This error is also shown in Fig. 3 onthe y-axis on the right side. As shown in the right hand side of thisfigure, repetition of the numerical calculation with finer mesh hadno effect on the results. As such we had established the grid in-dependence for our problem. Accordingly, similar comparisonswere performed for various inlet conditions (i.e. inlet velocity,relative humidity and nanoparticles mass fraction) and the grid sizewith sufficient converged results was used. Hence, for mentionedCONAN test section, the arrangement of mesh with 106 grids isselected.

In order to validate the present numerical model, some of pre-sent results are compared with experimental data of Ambrosiniet al. [10] and numerical results of Zschaeck et al. [13] at differentinlet conditions which are listed in Table 2. Fig. 4 illustrates the localsurface heat flux of the cooling wall along the channel which isobtained for experiment P10-T30-V25 (without nano-particles).More details of the mentioned experimental results are listed inRef. [11]. It is apparent from this figure that the local surface heatflux, which is predicted by the present study, is in good agreementwith the experimental results. However a small discrepancy (i.e.,error) exists between the results. The maximum local error is lessthan 13% under the same inlet conditions. This discrepancy can bedue to the simplifying assumptions which are used for providing asimpler numerical model. Constant thermophysical properties atdifferent temperature and constant density of the humid air nearthe interface of the condensed film are important assumptionswhich affect the numerical model [12]. The accuracy of the nu-merical model at different inlet conditions (see Table 2) is evaluatedand shown in Fig. 5. The total condensate flow rate at the outlet ofthe channel, for various relative humidities of the pure humid air(without nano-particles), is calculated and compared with experi-mental data [10] and numerical results [11]. As indicated in thisfigure, the presented results of total condensate flow rate are ingood agreement with the experimental data at different inlet ve-locities and relative humidities and the maximum error betweenthe mentioned results is less than 3.8%. Therefore, Figs. 4 and 5validate the present numerical model.

4.2. Comparison of nanoparticles materials

Using nanoparticle scan effect the thermophysical characteristicof dilute gas-particle flow and this effect can result in a higherthermal conductivity which leads to a higher condensation ratio ofthe humid air. However, because of the low concentration of thenano-particles, the variation of thermophysical properties is notthe scope of the present study. The particle deposition effect oncondensation of humid air is an important problem that isconsidered in the present research. As mentioned in several worksin the literature, for small particles with diameters in the rangefrom 50 nm to 1 mm, the deposition effects of nanoparticles aremore pronounced compared with the thermophysical effects [39].Based on the particle force balance equation, see Eq. (30), for thesame particles size, the variation of particle materials could beeffective under variation of density and the other thermophysicalproperties of the nanoparticles has no effect on the condensationprocess. In order to evaluate the density of nano-particles, threedifferent nano-particles, with different densities, are examined at


Fig. 2. 2d view of mesh sample of the CONAN test section (No scale view).

Number Of Grids

Con

dens

ate

Mas

sFlo

w(g

/s)

E c(%

)

104 105 1062

2.5

3

3.5

4

4.5

5

5.5

6

0

20

40

60

80

100

120Condensate Mass FlowError, Ec

Fig. 3. Typical representation of mesh independency.

Table 2Inlet boundary condition utilized in CONAN typical classical test section.

Experiment Main test channel (humid air) Secondary channel(cooling water)

Uin (m/s) u (%) Tin (C) Tin,w (C) _min;w (kg/s)

P10-T30-V15 1.46 100 82.66 31.24 1.2171P10-T30-V20 2.02 100 80.61 31.10 1.2173P10-T30-V25 2.52 97.83 79.13 31.07 1.2168P10-T30-V30 3.01 87.35 78.73 30.91 1.2160P10-T30-V35 3.59 96.55 75.02 30.71 1.2159


different inlet velocities and relative humidities. The thermophys-ical properties of these nanoparticles (copper, silicon dioxide andsodium chloride) are listed in Table 3. To compare the physical ef-fects of these nano-particles, the local surface heat flux along thecooling wall for pure saturated humid air and the mentionednanoparticles added at Uin 2.5 m/s are presented in Fig. 6. Asillustrated in this figure, using the nanoparticles with lower densityimproves the surface heat flux by 5.5%, which leads to a greatercondensation ratio. As mentioned before, density and particlediameter are the only physical specifications of nanoparticles that


affect the force balance of the discrete phase. Therefore, additionalsilicon dioxide, sodium chloride or copper particles present thesame trend. But it seems that the lower density of silicon dioxideand sodium chloride causes a little more enhancement. Whereas,nanoparticles with higher density, such as copper, have lower effecton surface heat flux. Similar comparisons are done for other inletvelocities at different relative humidities which have a similartrend. The maximum surface heat flux was verified when usingsodium chloride for saturated humid air at Uin 3m/s. Therefore, itcould be concluded that for constant particle size, d 100 nm, thedecrease in density of nanoparticles leads to higher surface heatflux. This trend is caused by the higher turbulent deposition losses.The investigation of different nanoparticles with similar size showsthat in the highly turbulent regime, using denser nanoparticlesleads to a lower deposition performance, which is equal to a lowerimprovement in the condensation process. In the area of convec-tion heat transfer for turbulent flow a similar study was done byRomay et al. [45] presenting similar results.

4.3. Comparison of nanoparticles mass concentration

In order to evaluate the nanoparticles mass concentration, theReynolds number of the condensed film at the outlet of the channelis reported for various values of relative humidity of humid air(4 100 nanoparticles mass flow rate/humid air mass flowrate 0), and, humid air with suspended nano-particles, (4 0.5%and 1%). The present comparison verified that the variation ofnanoparticles mass concentration has a direct effect on thecondensation of the humid air and this trend is analogous to theone verified at the investigated inlet velocities for a wide range ofrelative humilities, u 50e100%. These results should be inter-preted with caution because, as mentioned before, there are otherparameters, which were assumed constant or have been ignored inthe present problem. However, additional nanoparticles leads to agreater pressure drop and this effect is not very encouraging forconvection heat transfer enhancement but it is significant at least inthe phase change process. Accordingly, it could be concluded thatcondensation of the humid air in the presence of nanoparticleswould be improved; nevertheless, the effect of mass concentrationof nanoparticles is more considerable at higher relative humidities.At a constant inlet velocity (Uin 2.5 m/s), for lower relative hu-midity (u 50%), additional 0.5% of nano-particle mass concen-tration leads to a 10.1% increase in the condensate Reynoldsnumber. Alternatively, it can be stated that a 1% of nano-particlemass concentration causes 16.6% increase in the condensate Rey-nolds number. This improvement is more prominent for saturatedhumid air, where using nanoparticles increases the condensateReynolds number between 21.8% and 43.6%. Comparison ofcondensate Reynolds number shows that, at higher relative hu-midities, using nanoparticles is more noticeable (see Fig. 7).


Y (m)

Surf

ace

Hea

tFlu

x(k

W/m

2 )

0 0.5 1 1.5 20

2

4

6

8

10

12

14

16

18

20Ambrosini et al. (Experimental)Present studyZschaeck et al. (Numerical)

Fig. 4. Comparison of local surface heat flux between present results, experimentalresults by Ambrosini et al. [9] and numerical results by Zschaeck et al. [12] forexperiment P10-T30-V25.

Con

dens

ate

Mas

sFlo

w(g

/s)

0

0.5

1

1.5

2

2.5

3

3.5

4Ambrosini et al. [10] (Experimental)Present studyAmbrosini et al. [11] (Numerical)

P10-T30-V15 P10-T30-V20 P10-T30-V25 P10-T30-V30 P10-T30-V35

Fig. 5. Comparison of condensed mass flow at the outlet between the present results,experimental results [10] and numerical results [11] for different experiments.

Table 3Thermophysical properties of nano-particles.

Nano-particles Diameter (nm) Density (kg/m3) Specific heat capacity (J/kg K) Thermal conductivity (W/m K)

Copper 100 8300 420 401.0Silicon dioxide 100 2220 745 1.38Sodium chloride 100 2165 853 6.50

Y/L

Surf

ace

Hea

tFlu

x(k

W/m

2 )

0 0.2 0.4 0.6 0.8 110

20

30

40

50

Humid airHumid air with copperHumid air with silicon dioxideHumid air with sodium chloride

Uin=2.5 m/s

Fig. 6. Comparison of local surface heat flux for different nano-particles.


4.4. Evaluation of heat and mass transfer parameters

The influence of nanoparticles on condensation of humid airdepends on inlet conditions, such as inlet velocity and relativehumidity. To distinguish between these two parameters, the local


surface heat flux along the channel for various inlet velocities(Uin 1.5, 2, 2.5 and 3 m/s) and relative humidity (u 50, 75 and100%) are compared in Fig. 8. As seen in this figure, the effect ofnanoparticles on surface heat flux is more substantial at higherinlet velocities. Further, this improvement is more intense forsaturated humid air and in the sameway, the local surface heat fluxincreases with the rise of relative humidity in the presence of nano-particles. Particularly, using nanoparticles can be neglected whenthe relative humidity is less than 50% (no noticeable increase insurface heat flux was detected). In order to assess this trend, itcould be expressed that, both interaction of particle inertia andinhomogeneity of the turbulence in the channel, especially near themass transfer interface, causes particle deposition from the moreturbulent region to less turbulent regions-this is called turbopho-resis [20]. Turbophoresis is due to gradient of velocities that shouldbe considered at high Reynolds number of themain flowand has anoperative effect on nanoparticle deposition. Hence, based on thismechanism, for higher inlet velocities, which translates to higherReynolds numbers for the main flow, the stronger deposition ofnanoparticles would occur that leads to an increase in masstransfer. Accordingly, for lower inlet velocities, the fluctuation ofstreamline is lower, so that the effect of turbophoresis woulddisappear. In terms of the particle force balance, these trends couldbe interpreted by deposition efficiency measurement which isstudied by Romay et al. [45] for convection heat transfer in cooling

tube. As they observed, the deposition efficiency of NaCl particles isalmost 1% for smallest particles (100 nm) and 3% for largest parti-cles (700 nm) at Re 5517. Meanwhile, corresponding depositionefficiency are 5% and 43% for smallest and largest particles atRe 9656, respectively. Therefore, higher Reynolds number of the



inlet flow leads to an increase in turbulence levels, which is leadingto an increase in deposition efficiency. This behavior improves bothconvection and condensation processes.

Using the nanoparticles influences heat and mass transfer. Assuch the Reynolds number for condensed film at the outlet of thechannel is reported for different inlet velocities and relative hu-midities and compared with pure humid air for each condition (seeFig. 9). Comparison of the condensate Reynolds number for purehumid air and humid air with suspended nanoparticles (4 0.5%),reveals that using nanoparticles improves the mass transfer coef-ficient which accelerates the condensation rate. Similar to localsurface heat flux, this trend is not uniform and strongly depends onthe inlet velocity. For example, compared to the pure humid aircase, the increase in the condensate Reynolds number is between9.5% and 11.4% when the relative humidity increases from 50% to100% at Uin 3 m/s and this variation is between 2.1% and 4.8% atUin 1.5 m/s. As mentioned before, the absorption of nanoparticlesin the condensed film is ignored. This assumption is due to ignoringthe inertial impact. In other words, the strong forward movementin the turbulent regime reduces the collision of nanoparticles withthewalls and the surface of the condensed film. Also, because of thelow mass concentration of nanoparticles, 4 0.5%, the absorptionof nanoparticles by the condensed film is insignificant in case of acollision. Therefore, possible absorbed particles have no consider-able effect on the condensed film.

Using the same conditions employed in Figs. 9 and 10 providesthe results obtained for mean Nusselt number of the condensedfilm. The effects of nanoparticles on the mean Nusselt number,Nuf 1=L

RNuf ydy, for different relative humidities and inlet

velocities are shown in this figure. We can deduce that usingnanoparticles increases the mean Nusselt number, but the Nusseltnumber enhancement is not constant and depends on the inletvelocity. The maximum improvement in the Nusselt numbers is2.6% for inlet velocity of Uin 1.5 m/s and 4.7% for Uin 3 m/s.There are several explanations for these results. According to thedefinition of the condensed Nusselt number, Nuf y hf yy=lf ,using nanoparticles causes more condensed flow which leads to ahigher condensate Reynolds number, a shown in Fig. 9, and a higher

(%)

Re f,

out

50 60 70 80 90 10020

30

40

50

60

70

80

= 1% = 0.5% = 0%

Fig. 7. The effect of mass fraction of nanoparticles on the condensed film Reynoldsnumber at the outlet for different relative humidities at fixed inlet velocity(Uin 2.5 m/s).


convection heat transfer coefficient in the condensed film. There-fore, a similar trend of the condensate Reynolds number could beobserved for the mean Nusselt number of the condensed film.

The effects of nanoparticles on mass transfer, can be categorizedthrough an evaluation of the Sherwood number. For humid air as amixture of vapor and NCG, the Sherwood number represents theratio of vapor mass transfer to the rate of diffusion and can bedefined as follows [10,34]:

Shy yrD

_m00I

log

Yn;bulkYn;wall

! (34)

where _m00I is condensation mass flux at the interface, and Yn is

mass fraction of the air.The local Sherwood numbers along the channel for different

relative humidities at a fixed inlet velocity, Uin 3 m/s, arecompared in Fig. 11. It can be observed from this figure that thenanoparticles augments the mass flux, and this trend increasesalong the channel. According to prior results, the effect of nano-particles is more significant for higher relative humidities. An in-crease of the turbophoresis effect along the channel results in anincrease in the influence of nanoparticles. Analogous comparisonswere done for various ranges of the inlet velocities in the turbulentregime and the same trends of the mentioned effects wereobserved. As such, using the nanoparticles could be important for alonger heat exchanger. In the other words, because of the increaseof the nanoparticles fluctuation along the channel and an increasein the turbophoresis force, the mass flux of the condensate andconsequently the local Sherwood number will increase.

In order to assess the influence of nanoparticles on the totalmass transfer, themean Sherwood number, Sh 1=LR Shydy, asa function of the relative humidity for different inlet velocities ispresented in Fig. 12. The results presented in this figure display theinfluence of the nanoparticles on the total mass flux of vapor fromthe main flow to the condensed film. It can be seen that whennanoparticles are added to the main flow, there is no significantdifference on the mean Sherwood number for lower inlet velocitiesand a clear benefit of the nanoparticles on the mass flux of thecondensation could not be identified in the presented figure. Forhigher inlet velocities, nanoparticles enhance the mean Sherwoodnumber between 6 and 12.3%. Based on the last two figures, it canbe concluded that, for higher Reynolds number of the main flow,there is substantial evidence of improvement in the local and meanSherwood numbers when nanoparticles were added to the mainflow. As mentioned before, the mass concentration of nanoparticleswas assumed constant, 4 0.5%. It is recommended that aninvestigation of different nanoparticle mass concentrations andtheir effect on heat and mass transfer parameters to be performedin the future.

Using nanoparticles, as an enhancement method for enhancingthe convective heat transfer, has been investigated in severalpublications in the literature especially for natural convection inclosed circuit [24]. The evaluation of particle deposition effect onboth convection and condensation heat transfer is themost strikingresult to emerge from the data. Although, the presence of nano-particles could improve both of the mentioned heat transfermechanisms, the assessment of these two mechanisms and findingthe most effective heat transfer method, could be significant. Theeffect of nanoparticles on convection/condensation portions of to-tal heat transfer, which are absorbed by the cooling wall, is shownon Fig. 13. The convection and condensation heat transfer as twomain mechanisms of heat transfer of the mentioned problem aremeasured for different inlet velocities and relative humidities for


(a) (b)

(c) (d)

Y/L

Surf

ace

Hea

tFlu

x(k

W/m

2 )

0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60 Uin=1.5 m/sHumid airHumid air with particles

Y/L

Surf

ace

Hea

tFlu

x(k

W/m

2 )

0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60 Uin=2 m/sHumid airHumid air with particles

Y/L

Surf

ace

Hea

tFlu

x(k

W/m

2 )

0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60 Uin=2.5 m/sHumid airHumid air with particles

Y/L

Surf

ace

Hea

tFlu

x(k

W/m

2 )

0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60 Uin=3 m/sHumid airHumid air with particles

=50, 75 and 100% =50, 75 and 100%

=50, 75 and 100% =50, 75 and 100%

Fig. 8. Comparison of the local surface heat flux at the cooling wall between humid air and humid air with nanoparticles for different relative humidities and inlet velocities.

(%)

Re f,

out

50 60 70 80 90 10020

30

40

50

60

70

80

90 Humid airHumid air with particles, =0.5%

Uin=1.5, 2, 2.5 and 3 m/s

Fig. 9. Comparison of the condensed film Reynolds number at the outlet between purehumid air humid air with nanoparticles for different relative humidities and inletvelocities.

(%)

Nu f

50 60 70 80 90 100500

600

700

800

900

1000 Humid airHumid air with particles, =0.5%

Uin=1.5, 2, 2.5 and 3 m/s

Fig. 10. The comparison of mean Nusselt number of the condensed film between purehumid air and humid air with nanoparticles for different relative humidities and inletvelocities.


Please cite this article in press as: I.Z. Famileh, et al., Effect of nanoparticles on condensation of humid air in vertical channels, InternationalJournal of Thermal Sciences (2016), http://dx.doi.org/10.1016/j.ijthermalsci.2016.05.011

Fig. 12. Variation of the mean Sherwood number for different relative humidities andinlet velocities.


both pure humid air (Fig. 13(a)) and humid air with suspendednanoparticles (4 0.5%, Fig. 13(b)). The comparison of these twofigures shows that using nanoparticles generally increases the totalheat flux. But, the improvement in the convection portion is moresignificant than the condensation portion. A comparison of thementioned portions at a fixed relative humidity reveals that thisimprovement can possibly be more considerable for higher inletvelocities. Similarly, for a fixed inlet velocity, nanoparticles aremore effective on convection portion for higher relative humidities,so that, the average improvement of the convection portion is 16.7%when nanoparticles are added to the saturated humid air, while thisimprovement is 10.1% for the condensation portion. Hence, nano-particle effects on the condensation process are more limited ascompared to the convection enhancement. It should be mentionedthat this comparison was done for the CONAN test experiment.

The Sherwood number of the mentioned process can becompared with the Sherwood number over a flat plate where it isdefined as follows [11]:

Shy 0:0296Re0:8y Sc0:33 (35)

where Shy, Rey rUiny/m and Sc m/rD are the local Sherwoodnumber, the local Reynolds number and the Schmidt number,respectively. The local Sherwood number can be expressed as fol-lows [10]:

Shy m

00I

MvcDy ln

Xn;bulk

Xn;interface

! (36)

where y is the distance from the inlet, m00I is the condensation

rate at interface, c is molar concentration, Mv is molecular weight ofvapor, Xn,bulk and Xn,interface are the molar fractions of air in the bulkand at the interface, respectively. Fig.14 compares themass transferover a vertical flat plate as a function of local Reynolds number andthe calculated local Sherwood number for saturated humid air andsaturated humid air with suspended nanoparticles, u 100% and4 0.5% at constant inlet velocity, Uin 3m/s. The improvement inthe local Sherwood number due to additional nanoparticles is

Y / L

Loca

lShe

rwoo

dN

umbe

r,Sh

y

0 0.2 0.4 0.6 0.8 1

400

800

1200

1600

2000

2400 Uin=3m/sHumid airHumid air with particles, =0.5%

=50, 75 and 100%

Fig. 11. The effect of nanoparticles on the local Sherwood number for different relativehumidities at given inlet velocity (Uin 3 m/s).


sensible along the channel. There is little discrepancy between thepresented results and the mentioned correlation which is due toassumptions described earlier in this paper.

5. Response surface methodology

As mentioned before, the impact of the nanoparticles effects onheat and mass transfer enhancement is the main directive of thepresent study. Therefore, calculation of the perfect size of thedesign parameters (Uin, u, 4), using a multi-objective function,could be an effective solution. A general multi-objective functioncan be presented as:

Fx f1x; f2x; f3x; :::; fnx;n 2 (37)where x [x1,x2,x3,,xN] are the N design parameters and fi are

the nth objective functions. The basis of statistical methods is onallocating the single function with the special weight for each one,which is formed as follows:

Fx minXni0

fifix (38)

where fi is the estimated weight of the single objective func-tion. Selection and modification of the single objectives weight isthe first step in finding the general effects of the nanoparticles in awide range of the cited parameters. Also, this method is applicablein the optimization process [46]. This study uses the responsesurface methodology (RSM) to carry out the multi-objective func-tion of the main process. Generally, this function is unknown andRSM can propose the suitable approximation of the multi-objectivefunction. RSM is a group of mathematical and statistical techniquesfor empirical model building for design of experiments [47]. In fact,RSM estimated a response function (output variable) based on anumber of simple numerical or experimental observations on anindependent variable (input variable). In this method, the responsefunction usually is formed in low-order polynomial (second order).Proposing the simple response surface, based on fewer simulationor experiments, is one of the benefits of this method [46]. It shouldbe mentioned that RSM is one of the available statistical methodsand generally, it is the best methodology. In designing an


(a) Pure humid air. (b) Humid air with nano-particles, =0.5%.

(%)

Hea

t(kW

)

50 75 1002

4

6

8

10

12

14

16 Uin = 3 m/sUin = 1.5 m/sUin = 3 m/sUin = 1.5 m/s

Convection portion

Condensation portion

(%)

Hea

t(kW

)

50 75 1002

4

6

8

10

12

14

16 Uin = 3 m/sUin = 1.5 m/sUin = 3 m/sUin = 1.5 m/s

Convection portion

Condensation portion

Fig. 13. Condensation/convection portion of total heat transfer for: (a) humid air and (b) humid air with nanoparticles at different relative humidities and inlet velocities.


experiment, many techniques are available and each of thesetechniques could be utilized for a specific problem. As such in thepresent condensation process, RSM is chosen. Details of the ad-vantages of RSM can be found in Ref. [48]. Originally, RSM wasdeveloped by Box and Draper [49]. In this method several regres-sion techniques are used to compute the weight coefficients.Choosing the regression technique and the method of data pro-cessing, are not the aim of this study and the detailed informationabout regression method selection and design of the numericalsimulations can be found in Ref. [50].

The objective function created by RSM is formulated as:

Fx f0 Xni1

fixi Xni1

Xnj1

fijxixj (39)

The objective functions of condensed Reynolds number at theoutlet and the mean Sherwood number of the process are

Rey

Shy/Sc0.33

103 104 105101

102

103

0.0296Rey0.8

Humid airHumid air with particles

Fig. 14. Mean Sherwood number.


calculated for the range of inlet velocities from 1.5 to 3 m/s. Figs. 15and 16 show the contour plot of the condensed Reynolds number(at the outlet) and the mean Sherwood number based on thevariation of relative humidity and mass concentration of nano-particles for Uin 2.5 m/s. From Fig. 15, it is apparent that thenanoparticles have a uniform trend for low relative humidities aswell as higher values. For the lower relative humidity, variation ofcondensed Reynolds number is smoother, while for higher relativehumidities, this behavior is more pronounced and variation ofconcentration of nanoparticles has a direct effect on the enhance-ment of the condensation process. Consequently, the mass transferhas the same effect with respect to the variation of nanoparticlesconcentration, where for lower relative humidities, additionalnanoparticles have a lower impact on the mean Sherwood number.However, an increase in the relative humidity, results in a morenoticeable variation of the mean Sherwood number. It should benoted that even though nanoparticles improve heat and masstransfer processes; the influence of nanoparticles concentration isnot substantial at lower humidities, especially when mass con-centration of the nanoparticles is between 0 and 0.72%.

6. Conclusions

The objective of the present study was the systematically assessand analyze the effect of using nanoparticles on the filmwisecondensation enhancement. For this purpose, the governingequations for turbulent flow and mass diffusion were modelednumerically and the condensation of humid air at different relativehumidities and inlet velocities was simulated. The hydrodynamical,thermal and diffusion processes for filmwise condensation wereinvestigated and ultimately, the following results were concluded:

Using denser nanoparticles leads to a lower deposition effi-ciency and a lower turbulence level for particles, which resultsin an enhancement of the heat and mass transfer process.

For all of the investigated conditions, using nanoparticles im-proves the condensation rate. However, the enhancement trendis not uniform for the cited conditions. The maximum observedmass transfer improvement is 12.3%.

For low relative humidities, using nanoparticles has a lowereffect on the condensation process. While, for saturated humidair, nanoparticles has a pronounced effect on the cited process.


Fig. 15. Contour plot of Reynolds number of condensed film at the outlet (Uin 2.5 m/s).

Fig. 16. Contour plot of Mean Sherwood number (Uin 2.5 m/s).


Concentration of nanoparticles has a significant effect on theReynolds number of the condensed film and on the Sherwoodnumber, where this effects is more impressive for higher relativehumidities. It should be mentioned that for saturated humid air,using higher concentration of nanoparticles is more significant.

Since the application of humid air condensation is one of themost important processes for the HVAC equipments, the evaluationof the condensation process is important. Obviously, using nano-particles enhances the heat and mass transfer processes The aboveresults could be useful for finding the optimum conditions for usingnanoparticles to enhance the heat and mass transfer processes.

List of symbols

c molar concentration, (mol/m3)Cc Stokes-Cunninghum slip correctionCD drag coefficientCp heat capacity at constant pressure, (J/kg K)d diameter of particles, (m)dij deformation rate tensor


D diffusivity coefficient, (m2/s)Ec error, Ec

_mfinal _mi= _mfinal

100%FB!

Brownian force

FD!

drag force per unit particle mass

FG!

Buoyancy force

FL!

shear-induced lift force

FP!

fluid pressure gradient force

FTh!

thermophoretic force

Fm!

shear stress forceg gravitational acceleration, (m/s2)Gi zero-mean unit variance Gussian random numberGk generation of turbulent energy due to buoyancyh convection heat transfer coefficient, (W/m2 K)H molar specific enthalpy, (J/kmol)

J!

vapor mass flux, (kg/m2 s)k turbulent kinetic energy, (m2/s2)Kn Knudsen numberL length, (m)_mi total condensate mass flow rate at the primary mesh size,

(kg/s)_mfinal total condensate mass flow rate at the finest mesh size,

(kg/s)_m00I condensation mass flux, (kg/m

2 s)mp mass of particles, (kg)M molecular weight, (kg/kmol)Nu Nusselt numberNu mean Nusselt numberp pressure, (Pa)Pk generation of turbulent energy due to shearq00 local surface heat flux, (W/m2)Rep particle Reynolds number, Rep dU Up/ys ratio of particle density to fluid densityS rate of production, (kg/m3 s)Sc Schmidt numberSh Sherwood number

Sh mean Sherwood numbert time, (s)T temperature, (K)u velocity components in x-directions, (m/s)U mean velocity, (m/s)v velocity components in y-directions, (m/s)

V!

velocity vectorw velocity components in z-directions, (m/s)x Cartesian coordinate normal to cooling wall, (m)X molar fractiony Cartesian coordinate along the channel, (m)Y mass fractionz Cartesian coordinate along the width of channel, (m)

Greek symbols turbulent energy dissipation, (m2/s3)z particle relaxation time, (s)g molecular mean free path, (m)l thermal conductivity, (W/m K)m Dynamic viscosity, (kg/ms)r density, (kg/m3)sk turbulent Prandtl numbers for ks turbulent Prandtl numbers for

t stressed tensor, t m

VV! VV!T 23VV

!I

y kinetic viscosity, (kg/m s)



4 mass concentration of nanoparticles4 100*(nanoparticles mass flow rate/total mass flowrate), (%)

f estimated weight of the single objective functionu relative humidity, (%)

Subscriptsa airave averageD drageff effectiveexp experimentalf filmi initialin inletI interfacej Species jl liquidmix mixturen noncondensable (air)Ns Number of parametersp particlest turbulenceTh thermophoreticv vaporw water

References

[1] Ali A, Vafai K, Khaled AR. Comparative study between parallel and counterflow configurations between air and falling film desiccant in the presence ofnanoparticle suspensions. Int J Energy Res 2003;27:725e45.

[2] Verma SK, Tiwari AK. Progress of nanofluid application in solar collectors: areview. Energy Convers Manag 2015;100:324e46.

[3] Webb RL, Kim N-H. Principl of enhanced heat transfer. New York, NY, USA:Taylor Francis; 1994.

[4] Amiri A, Vafai K. Analysis of dispersion effects and non-thermal equilibrium,non-Darcian, variable porosity incompressible flow through porous media. IntJ Heat Mass Transf 1994;37:939e54.

[5] Caruso G, Di Maio DV. Heat and mass transfer analogy applied to condensationin the presence of noncondensable gases inside inclined tubes. Int J Heat MassTransf 2014;68:401e14.

[6] Vafai K, Sozen M. An investigation of a latent heat storage porous bed andcondensing flow through it. J Heat Transf 1990;112:1014e22.

[7] Desrayaud G, Lauriat G. Heat and mass transfer analogy for condensation ofhumid air in a vertical channel. Heat Mass Transf 2001;37:67e76.

[8] Rao VD, Krishna VM, Sharma K, Rao PM. Convective condensation of vapor inthe presence of a non-condensable gas of high concentration in laminar flowin a vertical pipe. Int J Heat Mass Transf 2008;51:6090e101.

[9] Wu T, Vierow K. Local heat transfer measurements of steam/air mixtures inhorizontal condenser tubes. Int J Heat Mass Transf 2006;49:2491e501.

[10] Ambrosini W, Bucci M, Forgione N, Oriolo F, Paci S, Magnaud J, et al. Com-parison and analysis of the condensation benchmark results. In: The 3rd Eu-ropean review meeting on severe accident research (ERMSAR-2008).Nesseber, Vigo Hotel, Bulgaria: Citeseer; 2008. p. 23e5.

[11] Ambrosini W, Forgione N, Merli F, Oriolo F, Paci S, Kljenak I, et al. Lessonlearned from the SARNET wall condensation benchmarks. Ann Nucl energy2014;74:153e64.

[12] Vyskocil L, Schmid J, Macek J. CFD simulation of airesteam flow withcondensation. Nucl Eng Des 2014;279:147e57.

[13] Zschaeck G, Frank T, Burns A. CFD modelling and validation of wall conden-sation in the presence of non-condensable gases. Nucl Eng Des 2014;279:137e46.

[14] Huang J, Zhang J, Wang L. Review of vapor condensation heat and masstransfer in the presence of non-condensable gas. Appl Therm Eng 2015;89:469e84.

[15] Saraireh M, Thorpe G. Simulation of heat and mass transfer involving vaporcondensation in the presence of non-condensable gases in plane channels. In:ASME/JSME 2011 8th thermal engineering joint conference. American Societyof Mechanical Engineers; 2011. p. T10026-T-10.

[16] Agrawal N, Das SK. Numerical studies on hydrogen distribution in enclosuresin the presence of condensing steam. J Heat Transf 2015;137:121008.

[17] Szijarto R, Freixa J, Prasser H-M. Simulation of condensation in a closed,slightly inclined horizontal pipe with a modified RELAP5 code. Nucl Eng Des2014;273:288e97.


[18] Sun H, Lauriat G, Nicolas X. Natural convection and wall condensation orevaporation in humid air-filled cavities subjected to wall temperature varia-tions. Int J Therm Sci 2011;50:663e79.

[19] Hudson A. Computational analysis to enhance laminar flow convective heattransfer rate in an enclosure using aerosol nanofluids [Electronic Theses &Dissertations]. Georgia Southern University; 2013.

[20] Brereton G. Eulerian model for prediction of particle transport and depositionin turbulent duct flows with thermophoresis. Aerosol Sci Technol 2015;49:802e15.

[21] Walsh JK, Weimer A, Hrenya C. Thermophoretic deposition of aerosol particlesin laminar tube flow with mixed convection. J Aerosol Sci 2006;37:715e34.

[22] Marti J, Haselbacher A, Steinfeld A. A numerical investigation of gas-particlesuspensions as heat transfer media for high-temperature concentrated solarpower. Int J Heat Mass Transf 2015;90:1056e70.

[23] Akbar M, Rahman M, Ghiaasiaan S. Particle transport in a small squareenclosure in laminar natural convection. J Aerosol Sci 2009;40:747e61.

[24] Garoosi F, Shakibaeinia A, Bagheri G. EulerianeLagrangian modeling of solidparticle behavior in a square cavity with several pairs of heaters and coolersinside. Powder Technol 2015;280:239e55.

[25] Afshar H, Shams M, Nainian S, Ahmadi G. Microchannel heat transfer anddispersion of nanoparticles in slip flow regime with constant heat flux. IntCommun Heat Mass Transf 2009;36:1060e6.

[26] Saidi M, Rismanian M, Monjezi M, Zendehbad M, Fatehiboroujeni S. Com-parison between Lagrangian and Eulerian approaches in predicting motion ofmicron-sized particles in laminar flows. Atmos Environ 2014;89:199e206.

[27] Alam M, Hossain SC, Rahman M. Transient thermophoretic particle depositionon forced convective heat and mass transfer flow due to a rotating disk. AinShams Eng J 2015;7:441e52.

[28] Bertoli SL. Radiant and convective heat transfer on pneumatic transport ofparticles: an analytical study. Int J Heat Mass Transf 2000;43:2345e63.

[29] Bertoli SL, Valle JAB, Gerent AG, de Almeida J. Heat transfer at pneumaticparticle transportdlimit solutions. Powder Technol 2012;232:64e77.

[30] Guha A, Samanta S. Effect of thermophoresis on the motion of aerosol parti-cles in natural convective flow on horizontal plates. Int J Heat Mass Transf2014;68:42e50.

[31] Guha A, Samanta S. Effect of thermophoresis and its mathematical models onthe transport and deposition of aerosol particles in natural convective flow onvertical and horizontal plates. J Aerosol Sci 2014;77:85e101.

[32] Zhang N, Zheng ZC, Glasgow L, Braley B. Simulation of particle deposition atthe bottom surface in a room-scale chamber with particle injection. AdvPowder Technol 2010;21:256e67.

[33] Wang M, Lin C-H, Chen Q. Determination of particle deposition in enclosedspaces by Detached Eddy Simulation with the Lagrangian method. AtmosEnviron 2011;45:5376e84.

[34] Ambrosini W, Forgione N, Manfredini A, Oriolo F. On various forms of the heatand mass transfer analogy: discussion and application to condensation ex-periments. Nucl Eng Des 2006;236:1013e27.

[35] Jena SK, Mahapatra SK. Numerical modeling of interaction between surfaceradiation and natural convection of atmospheric aerosol in presence oftransverse magnetic field. Appl Math Model 2013;37:527e39.

[36] Fluent A. 12.0 theory guide. Ansys Inc.; 2009. p. 5.[37] Bagheri G, Salmanzadeh M, Golkarfard V, Ahmadi G. Simulation of solid

particles behavior in a heated cavity at high Rayleigh numbers. Aerosol SciTechnol 2012;46:1382e91.

[38] Saffman P. The lift on a small sphere in a slow shear flow. J Fluid Mech1965;22:385e400.

[39] He C, Ahmadi G. Particle deposition with thermophoresis in laminar andturbulent duct flows. Aerosol Sci Technol 1998;29:525e46.

[40] Akbar M, Ghiaasiaan S. Radiation heat transfer and soot thermophoresis inlaminar tube flow. Numer Heat Transf Part A Appl 2005;47:653e70.

[41] Faghri A, Zhang Y, Howell JR. Advanced heat and mass transfer. Global DigitalPress; 2010.

[42] Laaroussi N, Lauriat G. Conjugate thermosolutal convection and condensationof humid air in cavities. Int J Therm Sci 2008;47:1571e86.

[43] Lahooti M. Navier stokes solution based on finite volume method: SIMPLEalgorithm. Isfahan University of Technology; 2011.

[44] Ambrosini W, Bucci M, Forgione N, Manfredini A, Oriolo F. Experiments andmodelling techniques for heat and mass transfer in light water reactors. Sci-ence and Technology of Nuclear Installations; 2009. p. 2009.

[45] Romay FJ, Takagaki SS, Pui DY, Liu BY. Thermophoretic deposition of aerosolparticles in turbulent pipe flow. J Aerosol Sci 1998;29:943e59.

[46] Khuri AI, Mukhopadhyay S. Response surface methodology. Wiley InterdiscipRev Comput Stat 2010;2:128e49.

[47] Alvarez L. Design optimization based on genetic programming. UK: Depart-ment of Civil and Environmental Engineering, University of Bradford; 2000.

[48] Venter G, Haftka RT, Starnes Jr JH. Construction of response surfaces for designoptimization applications. In: Proc 6-th AIAA/NASA/ISSMO symp on multi-disciplinary and structural optimization; 1996. p. 548e64.

[49] Box GE, Draper NR. Empirical model-building and response surfaces. JohnWiley & Sons; 1987.

[50] Myers RH, Montgomery DC, Anderson-Cook CM. Response surface method-ology: process and product optimization using designed experiments. JohnWiley & Sons; 2009.


http://refhub.elsevier.com/S1290-0729(16)30195-8/sref1http://refhub.elsevier.com/S1290-0729(16)30195-8/sref1http://refhub.elsevier.com/S1290-0729(16)30195-8/sref1http://refhub.elsevier.com/S1290-0729(16)30195-8/sref1http://refhub.elsevier.com/S1290-0729(16)30195-8/sref2http://refhub.elsevier.com/S1290-0729(16)30195-8/sref2http://refhub.elsevier.com/S1290-0729(16)30195-8/sref2http://refhub.elsevier.com/S1290-0729(16)30195-8/sref3http://refhub.elsevier.com/S1290-0729(16)30195-8/sref3http://refhub.elsevier.com/S1290-0729(16)30195-8/sref4http://refhub.elsevier.com/S1290-0729(16)30195-8/sref4http://refhub.elsevier.com/S1290-0729(16)30195-8/sref4http://refhub.elsevier.com/S1290-0729(16)30195-8/sref4http://refhub.elsevier.com/S1290-0729(16)30195-8/sref5http://refhub.elsevier.com/S1290-0729(16)30195-8/sref5http://refhub.elsevier.com/S1290-0729(16)30195-8/sref5http://refhub.elsevier.com/S1290-0729(16)30195-8/sref5http://refhub.elsevier.com/S1290-0729(16)30195-8/sref6http://refhub.elsevier.com/S1290-0729(16)30195-8/sref6http://refhub.elsevier.com/S1290-0729(16)30195-8/sref6http://refhub.elsevier.com/S1290-0729(16)30195-8/sref7http://refhub.elsevier.com/S1290-0729(16)30195-8/sref7http://refhub.elsevier.com/S1290-0729(16)30195-8/sref7http://refhub.elsevier.com/S1290-0729(16)30195-8/sref8http://refhub.elsevier.com/S1290-0729(16)30195-8/sref8http://refhub.elsevier.com/S1290-0729(16)30195-8/sref8http://refhub.elsevier.com/S1290-0729(16)30195-8/sref8http://refhub.elsevier.com/S1290-0729(16)30195-8/sref9http://refhub.elsevier.com/S1290-0729(16)30195-8/sref9http://refhub.elsevier.com/S1290-0729(16)30195-8/sref9http://refhub.elsevier.com/S1290-0729(16)30195-8/sref10http://refhub.elsevier.com/S1290-0729(16)30195-8/sref10http://refhub.elsevier.com/S1290-0729(16)30195-8/sref10http://refhub.elsevier.com/S1290-0729(16)30195-8/sref10http://refhub.elsevier.com/S1290-0729(16)30195-8/sref10http://refhub.elsevier.com/S1290-0729(16)30195-8/sref11http://refhub.elsevier.com/S1290-0729(16)30195-8/sref11http://refhub.elsevier.com/S1290-0729(16)30195-8/sref11http://refhub.elsevier.com/S1290-0729(16)30195-8/sref11http://refhub.elsevier.com/S1290-0729(16)30195-8/sref12http://refhub.elsevier.com/S1290-0729(16)30195-8/sref12http://refhub.elsevier.com/S1290-0729(16)30195-8/sref12http://refhub.elsevier.com/S1290-0729(16)30195-8/sref12http://refhub.elsevier.com/S1290-0729(16)30195-8/sref13http://refhub.elsevier.com/S1290-0729(16)30195-8/sref13http://refhub.elsevier.com/S1290-0729(16)30195-8/sref13http://refhub.elsevier.com/S1290-0729(16)30195-8/sref13http://refhub.elsevier.com/S1290-0729(16)30195-8/sref14http://refhub.elsevier.com/S1290-0729(16)30195-8/sref14http://refhub.elsevier.com/S1290-0729(16)30195-8/sref14http://refhub.elsevier.com/S1290-0729(16)30195-8/sref14http://refhub.elsevier.com/S1290-0729(16)30195-8/sref15http://refhub.elsevier.com/S1290-0729(16)30195-8/sref15http://refhub.elsevier.com/S1290-0729(16)30195-8/sref15http://refhub.elsevier.com/S1290-0729(16)30195-8/sref15http://refhub.elsevier.com/S1290-0729(16)30195-8/sref16http://refhub.elsevier.com/S1290-0729(16)30195-8/sref16http://refhub.elsevier.com/S1290-0729(16)30195-8/sref17http://refhub.elsevier.com/S1290-0729(16)30195-8/sref17http://refhub.elsevier.com/S1290-0729(16)30195-8/sref17http://refhub.elsevier.com/S1290-0729(16)30195-8/sref17http://refhub.elsevier.com/S1290-0729(16)30195-8/sref17http://refhub.elsevier.com/S1290-0729(16)30195-8/sref17http://refhub.elsevier.com/S1290-0729(16)30195-8/sref18http://refhub.elsevier.com/S1290-0729(16)30195-8/sref18http://refhub.elsevier.com/S1290-0729(16)30195-8/sref18http://refhub.elsevier.com/S1290-0729(16)30195-8/sref18http://refhub.elsevier.com/S1290-0729(16)30195-8/sref19http://refhub.elsevier.com/S1290-0729(16)30195-8/sref19http://refhub.elsevier.com/S1290-0729(16)30195-8/sref19http://refhub.elsevier.com/S1290-0729(16)30195-8/sref20http://refhub.elsevier.com/S1290-0729(16)30195-8/sref20http://refhub.elsevier.com/S1290-0729(16)30195-8/sref20http://refhub.elsevier.com/S1290-0729(16)30195-8/sref20http://refhub.elsevier.com/S1290-0729(16)30195-8/sref21http://refhub.elsevier.com/S1290-0729(16)30195-8/sref21http://refhub.elsevier.com/S1290-0729(16)30195-8/sref21http://refhub.elsevier.com/S1290-0729(16)30195-8/sref22http://refhub.elsevier.com/S1290-0729(16)30195-8/sref22http://refhub.elsevier.com/S1290-0729(16)30195-8/sref22http://refhub.elsevier.com/S1290-0729(16)30195-8/sref22http://refhub.elsevier.com/S1290-0729(16)30195-8/sref23http://refhub.elsevier.com/S1290-0729(16)30195-8/sref23http://refhub.elsevier.com/S1290-0729(16)30195-8/sref23http://refhub.elsevier.com/S1290-0729(16)30195-8/sref24http://refhub.elsevier.com/S1290-0729(16)30195-8/sref24http://refhub.elsevier.com/S1290-0729(16)30195-8/sref24http://refhub.elsevier.com/S1290-0729(16)30195-8/sref24http://refhub.elsevier.com/S1290-0729(16)30195-8/sref24http://refhub.elsevier.com/S1290-0729(16)30195-8/sref25http://refhub.elsevier.com/S1290-0729(16)30195-8/sref25http://refhub.elsevier.com/S1290-0729(16)30195-8/sref25http://refhub.elsevier.com/S1290-0729(16)30195-8/sref25http://refhub.elsevier.com/S1290-0729(16)30195-8/sref26http://refhub.elsevier.com/S1290-0729(16)30195-8/sref26http://refhub.elsevier.com/S1290-0729(16)30195-8/sref26http://refhub.elsevier.com/S1290-0729(16)30195-8/sref26http://refhub.elsevier.com/S1290-0729(16)30195-8/sref27http://refhub.elsevier.com/S1290-0729(16)30195-8/sref27http://refhub.elsevier.com/S1290-0729(16)30195-8/sref27http://refhub.elsevier.com/S1290-0729(16)30195-8/sref27http://refhub.elsevier.com/S1290-0729(16)30195-8/sref28http://refhub.elsevier.com/S1290-0729(16)30195-8/sref28http://refhub.elsevier.com/S1290-0729(16)30195-8/sref28http://refhub.elsevier.com/S1290-0729(16)30195-8/sref29http://refhub.elsevier.com/S1290-0729(16)30195-8/sref29http://refhub.elsevier.com/S1290-0729(16)30195-8/sref29http://refhub.elsevier.com/S1290-0729(16)30195-8/sref29http://refhub.elsevier.com/S1290-0729(16)30195-8/sref30http://refhub.elsevier.com/S1290-0729(16)30195-8/sref30http://refhub.elsevier.com/S1290-0729(16)30195-8/sref30http://refhub.elsevier.com/S1290-0729(16)30195-8/sref30http://refhub.elsevier.com/S1290-0729(16)30195-8/sref31http://refhub.elsevier.com/S1290-0729(16)30195-8/sref31http://refhub.elsevier.com/S1290-0729(16)30195-8/sref31http://refhub.elsevier.com/S1290-0729(16)30195-8/sref31http://refhub.elsevier.com/S1290-0729(16)30195-8/sref32http://refhub.elsevier.com/S1290-0729(16)30195-8/sref32http://refhub.elsevier.com/S1290-0729(16)30195-8/sref32http://refhub.elsevier.com/S1290-0729(16)30195-8/sref32http://refhub.elsevier.com/S1290-0729(16)30195-8/sref33http://refhub.elsevier.com/S1290-0729(16)30195-8/sref33http://refhub.elsevier.com/S1290-0729(16)30195-8/sref33http://refhub.elsevier.com/S1290-0729(16)30195-8/sref33http://refhub.elsevier.com/S1290-0729(16)30195-8/sref34http://refhub.elsevier.com/S1290-0729(16)30195-8/sref34http://refhub.elsevier.com/S1290-0729(16)30195-8/sref34http://refhub.elsevier.com/S1290-0729(16)30195-8/sref34http://refhub.elsevier.com/S1290-0729(16)30195-8/sref35http://refhub.elsevier.com/S1290-0729(16)30195-8/sref35http://refhub.elsevier.com/S1290-0729(16)30195-8/sref35http://refhub.elsevier.com/S1290-0729(16)30195-8/sref35http://refhub.elsevier.com/S1290-0729(16)30195-8/sref36http://refhub.elsevier.com/S1290-0729(16)30195-8/sref37http://refhub.elsevier.com/S1290-0729(16)30195-8/sref37http://refhub.elsevier.com/S1290-0729(16)30195-8/sref37http://refhub.elsevier.com/S1290-0729(16)30195-8/sref37http://refhub.elsevier.com/S1290-0729(16)30195-8/sref38http://refhub.elsevier.com/S1290-0729(16)30195-8/sref38http://refhub.elsevier.com/S1290-0729(16)30195-8/sref38http://refhub.elsevier.com/S1290-0729(16)30195-8/sref39http://refhub.elsevier.com/S1290-0729(16)30195-8/sref39http://refhub.elsevier.com/S1290-0729(16)30195-8/sref39http://refhub.elsevier.com/S1290-0729(16)30195-8/sref40http://refhub.elsevier.com/S1290-0729(16)30195-8/sref40http://refhub.elsevier.com/S1290-0729(16)30195-8/sref40http://refhub.elsevier.com/S1290-0729(16)30195-8/sref41http://refhub.elsevier.com/S1290-0729(16)30195-8/sref41http://refhub.elsevier.com/S1290-0729(16)30195-8/sref42http://refhub.elsevier.com/S1290-0729(16)30195-8/sref42http://refhub.elsevier.com/S1290-0729(16)30195-8/sref42http://refhub.elsevier.com/S1290-0729(16)30195-8/sref43http://refhub.elsevier.com/S1290-0729(16)30195-8/sref43http://refhub.elsevier.com/S1290-0729(16)30195-8/sref44http://refhub.elsevier.com/S1290-0729(16)30195-8/sref44http://refhub.elsevier.com/S1290-0729(16)30195-8/sref44http://refhub.elsevier.com/S1290-0729(16)30195-8/sref45http://refhub.elsevier.com/S1290-0729(16)30195-8/sref45http://refhub.elsevier.com/S1290-0729(16)30195-8/sref45http://refhub.elsevier.com/S1290-0729(16)30195-8/sref46http://refhub.elsevier.com/S1290-0729(16)30195-8/sref46http://refhub.elsevier.com/S1290-0729(16)30195-8/sref46http://refhub.elsevier.com/S1290-0729(16)30195-8/sref47http://refhub.elsevier.com/S1290-0729(16)30195-8/sref47http://refhub.elsevier.com/S1290-0729(16)30195-8/sref48http://refhub.elsevier.com/S1290-0729(16)30195-8/sref48http://refhub.elsevier.com/S1290-0729(16)30195-8/sref48http://refhub.elsevier.com/S1290-0729(16)30195-8/sref48http://refhub.elsevier.com/S1290-0729(16)30195-8/sref49http://refhub.elsevier.com/S1290-0729(16)30195-8/sref49http://refhub.elsevier.com/S1290-0729(16)30195-8/sref49http://refhub.elsevier.com/S1290-0729(16)30195-8/sref50http://refhub.elsevier.com/S1290-0729(16)30195-8/sref50http://refhub.elsevier.com/S1290-0729(16)30195-8/sref50http://refhub.elsevier.com/S1290-0729(16)30195-8/sref50

Effect of nanoparticles on condensation of humid air in vertical channels1. Introduction1.1. Condensation of humid air1.2. Nanoparticles application in convection heat transfer

2. Problem statement3. Governing equations4. Numerical implementation4.1. Mesh properties and validation4.2. Comparison of nanoparticles materials4.3. Comparison of nanoparticles mass concentration4.4. Evaluation of heat and mass transfer parameters5. Response surface methodology

6. ConclusionsList of symbolsReferences

Documents

International Journal of Thermal Sciencesvafai.engr.ucr.edu/Publications/2016a/Iman Zeynali Famileh.pdf · Effect of nanoparticles on condensation of humid air in vertical channels