ST3 Surface Transfer Coefficients

8/12/2019 ST3 Surface Transfer Coefficients

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2. SURFACE TRANSFER COEFFICIENTS

2.1 INTRODUCTION

In building simulation, transport phenomena, as air flow, heat transfer or mass transfer,

are modelled inside buildings, between bodies (walls) and air, at the outside of buildings, Boundary conditions are represented by defining a transfer of a thermodynamicproperty (flux) between these walls and the internal or external air flow, or by defining afixed state at the wall. In order to model the interaction between the wall (state) and thefluid (state) a transfer coefficient is often used, known as friction coefficient, heat transfercoefficient or mass transfer coefficient.Different authors have examined the sensitivity of thermal predictions from energysimulation programs to the modelling of internal convection (e.g. Spitler et al. (1991),Clarke (1991), Fisher and Pederson (1997)). Their work has demonstrated thatpredictions of energy demand and consumption can be strongly influenced by the choiceof (made by program developer or user) heat transfer calculation method. Differences of20-40% in energy predictions were noted by some of these authors.More importantly, the predicted benefits from design measures were, in some cases,found to be sensitive to the approach used to model internal surface convection. As aresult, the choice of heat transfer calculation method could affect the design decisionsdrawn from a simulation-based analysis. (Beausoleil-Morrison (1999)).

The transfer coefficient is in fact a modelling assumption in itself. The concept of transfercoefficients is developed in the boundary layer theory, first derived by Ludwig Prandtl in1904. Prandtl discovered that for most applications the influence of viscosity is confinedto an extremely thin region very close to the body and that the remainder of the flowcould, to a good approximation, be treated as inviscid. The pressure in the boundarylayer and in the main flow is assumed to be the same.This clearly shows that transfer coefficients are by nature an, though often good,approximation. They should be used within the constraints of the approximation. Theyare only applicable for the correct boundary conditions. As simulations advance toinclude more details, the improper use of transfer coefficients often leads to non-physicalresults.In this chapter the basic concepts of boundary layer theory are introduced and the mainparameters describing friction, heat and mass transfer are addressed. For further reviewreference is made to Kays & Crawford (1993) and Welty et al (2001).

Application to buildings is discussed through papers published during ANNEX 41 andrecent publications in literature.

2.2 BOUNDARY LAYER THEORY IN A NUTSHELL

2.2.1 Convectio n - flux laws

Among the many tasks facing the engineer is the calculation of energy-transfer andmass-transfer rates at the interface between phases in a fluid system. Most often we areconcerned with transfer at a solid-fluid interface where the fluid may be visualised asmoving relative to a stationary solid surface.


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If the fluid is at rest in the entire domain, the problem becomes one of simple heatconduction where there are temperature gradients normal to the interface or simplemass diffusion where there are mass concentration gradients normal to the surface.However, if there is fluid motion, energy and mass are transported both by potentialgradients (as in simple conduction) and by movement of the fluid itself. This complextransport process is usually referred to as convection .

Figure 1 : Heat and mass transfer from a surface in contact with a fluid

In simple convective heat transfer along a wall it is often convenient to define aconvection heat-transfer conductance or heat transfer coefficient as (Figure 1):

( )= t t hq ws&

The driving force for heat transfer ( q&) is the temperature difference between the wallsurface ( tws ) and the free fluid stream ( t ). This equation is also known as Newtons Lawof Cooling.The conductance h is in essence a fluid mechanic property of the system and t,temperature, a thermodynamic property. There are numerous non-linear applicationswere h is itself a function of the temperature difference. It is important to note that in that

case the equation remains valid as a definition of h , although it may well reduce theusefulness of the conductance concept.

In mass transfer it is convenient to define a convective mass-transfer conductance suchthat the total mass flux at the surface ( m&)is the product of the conductance g and thedriving force, being the difference in concentration at the wall (c ws ) and in the free fluidstream (c ).

t twstws

c cws c cwscws

Flow

v

q&

m&


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( )= cchm wsm& The conductance h m is essentially a fluid mechanic property of the system, whereas theconcentration is a thermodynamic property.

This second equation has the same form as the first one resulting to the rise of the heat-

and masstransfer analogies.

The form of these equations is in fact a special case of the general form of a convectioncoefficient as given by :

Force Driving xT COEFFICIEN FLUX =

2.2.2 Hydraulic , thermal and concentration bou ndary layer

Figure 2 : Heat and mass transfer from a surface in contact with a fluid

In 1904, Ludwig Prandtl stated : At high Reynolds number the effect of fluid friction islimited to a thin layer near the boundary of the body , hence the term THE BOUNDARYLAYER came into engineering practice.

Figure 2 shows the boundary layer developing over a flat plate under forced convection,meaning there is an external velocity v which is causing the flow over the plate. Thisvelocity can be created by a fan, wind, . The thickness of the boundary layer ( ) isarbitrarily taken as the distance away from the surface where the velocity reaches 99%of the free stream velocity. Figure 2 illustrates how the thickness of the boundary layerincreases with distance x from the leading edge. At relatively small values of x flowwithin the boundary layer is laminar. At larger values of x the transition region is shownwhere fluctuations between laminar and turbulent flow occur within the boundary layer.Finally above a certain value of x the boundary layer will always be turbulent. In theturbulent boundary layer a small laminar sublayer exists were there are steep velocitygradients.


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The criterion for the type of boundary layer is the magnitude of the Reynolds number:

= xv Re x

In general is the Reynolds number is lower than a certain value, depending on thegeometry flow, is laminar. Above a second value for the Reynolds number the flow isfully turbulent. In between transitional flow occurs. In general a Reynolds number isdefined as

vL=Re

with v a characteristic velocity in the flow and L a characteristic length.

By solving the Navier-Stokes equations for a two dimensional flow for this geometry, asdiscussed in Kays WM, Crawford ME, (1993), the hydraulic boundary layer thickness asfunction of the position along the plate can be found. The hydrodynamic or momentum

boundary layer may be defined as the region in which the fluid velocity changes from its99% free stream value to zero at the body surface. This is not a precise definition of theboundary layer thickness. It only means that the boundary layer thickness is the distancefrom the wall in which most of the velocity change takes place.Out of this analysis follows the drag coefficient also known as the friction coefficient ( c f ):

2/2=

vc f

with the fluid density and the fluid friction or shear stress.

When there is heat or mass transfer between the fluid and the surface, it is also foundthat in most practical applications the major temperature and concentration changes

occur in the region very close to the surface. This gives rise to the concept of the thermalboundary layer and the concentration boundary layer , and again the relative thinness ofthese boundary layers permits the introduction of boundary-layer approximations similarto those introduced for momentum. Solving the Navier-Stokes equations for the energyor concentration transport equations results in a thermal boundary layer thickness and aconcentration boundary layer thickness as function of the coordinate x.

In the solution of the diffential equations the Prandtl numberk

c p=Pr appears, relating

the viscous boundary layer to the thermal boundary layer. For mass transfer this is

expressed by the Schmidt number AB D

Sc

= relating the viscous boundary layer to the

concentration boundary layer.If the ratio is taken of the Prandtl number to the Schmidt number the Lewis number is

found, relating mass to thermal diffusionSc

Le Pr = . As this number relates the thermal to

the mass transfer boundary layer it will determine the analogy between heat and masstransfer.


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In the 19 th century Reynolds was the first to report on the analogous behaviour of heatand momentum transfer (Welty et al. 2001). He presented results on frictional resistanceto fluid flow in conduits which made the quantitative analogy between the two transportphenomena possible. Out of these observations the Reynolds analogy was stated. TheReynolds analogy relates the heat transfer coefficient ( h) to the skin friction coefficientusing the free stream velocity and the free stream density and heat capacity (c p):

2 f

p

ccv

hSt =

=

This relation can be deduced out of the boundary layer equations for laminar forced flowacross a solid boundary under the conditions that the Prandtl number (Pr) is equal toone and no form drag is present.The Reynolds analogy can also be applied to mass transfer in case the Schmidt number(Sc) is equal to one:

2 f

c

m c

vh

p

=

In case both Pr and Sc numbers are equal to one, and hence the Lewis number (Le) isone. Comparing both equations, a relation between the mass transfer coefficient and theheat transfer coefficient is found, hence the analogy between heat and mass transferwas founded :

m p

hcv

h =

In general the convection heat transfer coefficient is made dimensionless through thedefinition of a Nusselt-number and the mass transfer convection coefficient through thedefinition of the Sherwood-number

k hL Nu =

AB

m

D Lh

Sh =

For forced convection the heat and mass transfer coefficients can be expressed as theNusselt number as function of the Reynolds and Prandtl number :

( )Pr Re , F Nu = ( ) ,Sc F Sh Re=

For natural convection the flow is driven by buoyancy as a result of density differences inthe air volume. The dimensionless number characterising this flow type is the Grashofnumber given by

2

3

= L g Gr


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For natural convection the Grashof number takes over from the Reynoldsnumber todetermine the convection coefficients :

( )Pr ,Gr F Nu = ( )ScGr F Sh ,=

For the convective heat transfer coefficient a lot of data is available. For several, relativesimple geometries and different flow conditions (laminar, transitional, turbulent, forcedand buoyancy driven convection) an analytical solution of the Navier-Stokes equationsapplied to a boundary layer exists. (See eg Kays WM, Crawford ME, 1993)For more complex geometries correlations have be determined by curve fittingdimensionless numbers to large data sets.

As there are many different correlations available care has to be taken in selecting thesuitable correlation. For analytical derived correlations the validity of assumptions andsimplifications should be checked. For experimentally derived correlations the range andaccuracy of the data set should be taken into consideration.

For the mass transfer coefficient boundary layer analysis leads again to analyticalsolutions. Due to the fact that the differential equations for heat and mass transferresulting from boundary layer analysis are analogues, the solutions obtained for heattransfer can be transformed into mass transfer solutions, by using the correctdimensionless number cited earlier (Welty et al (2001)).Furthermore it is very difficult to determine the convective mass transfer coefficientexperimentally. Therefore this analogy is applied in a lot of cases for calculating theconvective mass transfer coefficient, starting from the thermal measurements that wheredone. Validity of the thus obtained mass transfer coefficients is by consequence evenmore limited and great care should again be taken in selecting the proper correlation forthe studied geometry. (See eg Kays WM, Crawford ME, 1993)

For flow around buildings very little information was found about mass transferdetermination, both experimentally or numerically. For flows inside buildings, mostresearch is focussing on flows over building materials or porous materials. Wadso,L ,1993 gives a very broad literature review.

During the progress of the Annex 41 new experiments were proposed to determine themass transfer coefficient. Often these experiments were found to have limited validity.Secondly numerical methods, based on CFD, were used to determine mass transferfrom a fluid to a porous material. Finally the heat and mass transfer analogy was lookedinto.


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2.3 HEAT TRANSFER

2.3.1 Flow over and around bui ldings (experimental data) Air flows around buildings are mainly of a forced nature as they are caused by wind.Exterior convective heat and mass transfer coefficients at building surfaces are to a largeextent determined by the local wind speed. Usually, empirical formulae are used to relatethe reference wind speed at a meteorological station to the local wind speed near thebuilding surface and to relate the local wind speed to surface transfer coefficients. Theseformulae however are based on a limited number of measurements.

Practical correlations given by Jrges (1924) give a relation between free stream wind( V ) speed and the thermal convection coefficient :

smV V h

smV V h

/5;6.51.7

/5;6.50.478.0 >+=


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used to calculate the local wind speed near the exterior surface of a cubic building modelas a function of wind speed, wind direction and the position on the facade.It is shown that the variation of the local wind speed across the facade is verypronounced and that using the available empirical formulae can yield large errors inHAM calculations.

In Annex paper A41-T3-Br-07-2 (and Emmel M, Abadie M, Mendes N (2007)) similarconclusions were drawn using in essence the same approach. Using CFD calculationswith CFX, correlations for the heat transfer coefficient were determined for the BESTESTreference case Judkoff R.D., Neymark J.S. (1995). De correlations presented in theprevious paragraph were compared to the CFD calculations and both over and underpredictions (to about a factor 4) of these correlations were found in relation to the CFDsolutions. The paper ends with a list of new correlations determined by doing severalcalculations with CFD on the BESTEST geometry. These are copied here. Moreinformation about validity and boundary conditions can be found in the paper.

Table 2 : Data according to A41-T3-Br-07-2

2.3.3 Flow ins ide buildings (experimental data) Air flows inside buildings occur due to two main reasons. Firstly there are air streamscaused by ventilation systems (jets) or pressure differences between adjacent rooms(draught). These are thus of forced nature as the flow is not driven by the temperature ordensity fields it creates. Secondly temperature and concentration (vapour) differencesinside a room cause density differences and thus buoyancy.Inside buildings both forced and natural convection will occur. Sometimes they will even

operate at the same place and time. This is what is called mixed convection.

2.3.3.1 Forced convection inside buildingsSpitler et al. (1991b) designed a full-scale experimental facility, with internal dimensionsof 4.57 x 2.74 x 2.74 m and a fan system delivered air to one of the two room inlets overa range of 5 to 100 air changes per hour (ACH). The walls, floor and ceiling werecovered by heated panels, each with an independent electrical resistance heater.


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Figure 3 Experimental facility of Spitler et al. 1991a

Spitler et al. correlated the convective heat transfer coefficients to the jet momentumnumber J:

5.021 J C C h += with

room gV U m

J

= 0&

(U0 jet inlet velocity, V room room volume)

The correlations from Spitler et al. (1991b) are listed in the Table below.

Table 3.Heat transfer coefficient correlations of Spitler et al. (1991b)

=

20U TL g

Ar

Surface Inlet h LimitsCeiling Ceiling 11.4 + 209.7 J 0.5 0.001


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and 3/1Reroom

diffuser e V

V

=&

( diffuser V & jet volumetric flow rate m/s)

With the free horizontal jets in isothermal rooms the buoyancy forces of the cold jet alsohad a negligible impact on convection from the walls and floor. Therefore the same typeof equation was also used to correlate these data. Convection from the ceiling, though,was affected by buoyancy.Consequently, an alternate equation to correlate the ceiling data: (applicable for 3Tair )Ceiling (T surface T air )

Natural convection

(system is off)

5/1

6.0

h DT

Khalifa and Marshall (1990) performed experiments in a room sized test cell to producecorrelations specific to internal convection within buildings. Convection correlations aredeveloped based on measurements in an experimental chamber with room sizes: 2.95 x2.35 x 2.08 m (l x w x h). The correlations for vertical surfaces are defined for surfaces in

the vicinity of a terminal device and for other surfaces. To assess a number of commonconvection regimes, the test cells configuration was varied. Different heating systems(e.g. radiator, in-floor heating, convective heating) were analyzed, as was the placementof the heating device (e.g. underneath a window or facing a window).

Figure 4 : Experimental test room of Khalifa and Marshall (1990)

Khalifa (1989) used the average room air temperature as the reference temperature tocalculate the convective heat transfer coefficient. But Khalifa and Marshall (1990)measured the air temperature outside the thermal boundary layer at a distance of 60 mmfrom the interior surface of the wall, which is used as the reference temperature.


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Khalifa generated a total of 36 correlations. Data from similar correlations werecombined together in order to obtain new and more general correlations which can beapplied in more than one configuration (Khalifa and Marshall 1990). By combining thesesimilar results the data were collapsed into a series of 10 equations (Tables 7 and 8).

Table 7 Khalifa convection correlations (Beausoleil-Morrison 2000)Surface type Ventilation regime hWallIn the vicinity of theterminal device

Rooms heated by radiatorRadiator not located under windowOnly surfaces adjacent to radiator

32.098.1 T

Rooms heated by radiatorRadiator located under window

Wall

Rooms with heated wallsNot applicable for heated walls

24.03.2 T

Wall Rooms heated by circulating fanheaterOnly for surfaces opposite to fan

25.092.2 T

Rooms heated by circulating fanheaterFor surfaces not opposite to fanRooms with heated floor

Wall

Rooms heated by radiatorRadiator not located under windowFor surfaces not next to radiator

23.007.2 T

Window Rooms heated by radiatorRadiator located under window

11.007.8 T Window Rooms heated by radiator

Radiator not located under window06.061.7 T

Rooms heated by radiatorRadiator located under window

Ceiling

Rooms with heated walls

17.01.3 T

Rooms heated by circulating fanheaterRooms with heated floors

Ceiling

Rooms heated by radiatorRadiator not located under window

13.072.2 T

Table 8 Khalifa and Marshall (1990) convection correlationsSurface type Ventilation regime hWall

Large isolated vertical surface 14.003.2 T Floor

Large heated surface facing upward 24.027.2 T


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Calay et al. (1998) performed an experimental study of buoyancy-driven convection inrectangular enclosures. The enclosure was one-quarter scale model of a typical room. Itwas based on hot box arrangement, in which two opposing walls are heated and cooledwhile others are insulated and act as adiabatic walls. Four sets of experiments wereperformed to simulate the following convective heat-flow configurations: (1) enclosureheated from side, (2) large vertical walls as hot and cold plates, (3) small vertical wallsas hot and cold plates, (4) enclosure heated from below, (5) stably stratified convection(enclosure heated from ceiling).The convective heat transfer correlations are given in terms of dimensionlessparameters: Nusselt, Prandtl and Grashof number. The correlations recommended by

ASHREA (1985) and CIBSE (1986) and other correlations derived from tests with fullsize enclosures and similar configurations are used for comparing the experimentalresults (Table 9)

Table 9 Equations employed for comparison (Calay et al. 1998)Equation Correlation, Nu Gr range Flow

condition

Configuration: stablystratified, T w=c te CIBSE (1986)

ASHRAE (1985) Alamdari and Hammond(1983)Min et al. (1956)

0.236Gr 1/4

0.218Gr 1/4 0.56Gr 1/5 0.065Gr 0.255

10 8


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Natural convection from heated room surfaces was characterized by a correlation of themean convection heat transfer coefficient for whole wall heated surfaces.

Table 10 Awbi and Hatton (1999) natural convection correlations

Khalifa (2001) gives an extensive review of studies about natural convective heattransfer coefficients on surfaces in two- and three-dimensional enclosures with primaryfocus on those with a direct application to heat transfer in buildings. Figures 6 to 8 give acomparison of the different correlations mentioned in Khalifa (2001).

Figure 6 : Convective heat transfer coefficient correlations for vertical surfaces (Khalifa2001)

Surface type Ventilationregime

Nu

Walls( 9 x 10 8 < 6 x 10 10 ) ( )

293.0Gr 289.0

Floors( 9 x 10 8 < 7x 10 10 )

( ) 308.0Gr 269.0

Ceilings( 9 x 10 8 < 1 x 10 11 ) ( )

133.0Gr 78.1

Partly heatedceilings

Buoyant withheated surface

( ) 16.0Gr 517.3


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Figure 9 Assisting mechanical and buoyant forces

Table 11 Convective heat transfer coefficient correlations of Beausoleil-Morrison (2000)for mixed flow

Surface type h

Assisting forces

[ ] ( )[ ]1

3

8.0

613

63/1

64/1

190.0199.023.15.1

+

+

+

ACH H

d s

Wall

Opposing forces

[ ] ( )[ ]

[ ]

( )[ ]

+

+

+

+

8.0

6/1

3/1

64/1

8.0

613

63/1

64/1

190.0199.0of %80

23.15.1of %80

190.0199.023.15.1

max

ACH

H

ACH H

d s

d s

Floor

Buoyant [ ] ( )[ ]3/1

3

8.0

613

63/1

64/1

116.0159.063.14.1

+

+

+

ACH D

d s

h

Stablystratified ( )[ ]

3/13

8.0

35/1

116.0159.06.0

+

+

ACH

Dd s

h

Ceiling

Buoyant [ ] ( )[ ]1

3

8.0

613

63/1

64/1

484.0166.063.14.1

+

+

+

ACH D

d s

h


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The experiments of Awbi and Hatton (2000) were carried out in the same enclosure asthe natural convection experiments. They only placed an air handling unit onto theceiling of the small (cold) compartment to cool the dividing wall that separates the twocompartments. The fan and heating plates were positioned on a wall, the floor and theceiling to investigate the effect of a 3D wall jet on the surface convective heat transfercoefficient (Figure 10). The flow regime was a combination of natural convection,caused by the heated plates and forced convection, due to the fan.

Figure 10 : Different positions of the fan in case of heated ceiling

Table 12 Awbi and Hatton (2000) Convective heat transfer coefficient correlations forforced convection

Novoselac (2005) investigated the validity of the existing correlations from differentauthors for the airflow regimes in buildings. Afterwards, he developed new convectioncorrelations for surface types and airflow regimes where validation of the existingcorrelations failed by experimental measurements. The measurements were conducted

Stablystratified ( )[ ]

3/13

8.0

35/1

2 484.0166.06.0

+

+

ACJH

Dd s

h

Surface type Ventilationregime

hcf h cf /h cn

Walls( 9 x 10 8 < 6 x 10 10 ) ( )

873.0536.1 UW79.3 ( )

293.0873.0

536.1

T

UW3165.2

Floors( 9 x 10 8 < 7x 10 10 ) ( )

557.0575.0

UW248.4 ( )

308.0557.0

595.0

TU

W06.2

Ceilings( 9 x 10 8 < 1 x 10 11 )

Jet over a heatedsurface

( ) 772.0074.0 UW35.1 ( )

133.0772.0

074.0

T

UW45.3


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in an experimental chamber with typical room size (6 x 4 x 2.7 m) and typical positionsfor diffusers and radiant panels (Figure 11). Adjacent to the environmental chamber is aclimate chamber to simulate external conditions. For the correlations developed with adisplacement ventilation system, air was supplied by displacement diffusers. For theforced convection correlations with mixing ventilation systems, a high aspiration diffuser,located at the ceiling, discharge jets along the long side of the radiant panels. Thecooling panels occupied 50% of ceiling space and they were integrated into thesuspended ceiling structure.

Figure 11 Experimental facility for the development of convection correlations(Novoselac 2005)

2.3.4 Flow in side bu ildin gs (CFD data)

Awbi (1998) compared experimental results for natural CHTC of heated room surfaceswith CFD calculations. Two turbulence models were used: (1) a standard k- modelusing wall functions and (2) a low Reynolds number k- model.The logarithmic standard wall functions describe the momentum and heat transfer fromthe internal surfaces of a room. But these functions are empirically derived for forcedconvection in pipes and over flat plates. Awbi (1998) concluded that prediction of theconvective heat transfer coefficient using wall functions is extremely sensitive to thedistance of the point from the surface (y p) at which the wall function is applied. But CFDanalysis, which uses wall functions, proved to be useful in the investigation of the airflowover the heated plates and the air movement within the chamber (Awbi (1998)).Themore accurate prediction of the heat transfer from room surfaces, using a low Reynoldsnumber turbulence model, is very time consuming.

An alternative is to use an experimental determined expression for the convective heattransfer coefficient for room surfaces in a CFD code. This is what Beausoleil-Morrison(2000) and Novoselac (2005) have done with their ACA and respectively MACAalgorithms.

During the Annex 41 CFD was used to evaluate the possibilities of determining heattransfer coefficients with CFD. In [A41-T3-C-06-5 and A41-T3-C-06-6] CFD was used todetermine the heat transfer coefficient for flow between two infinite plates. A goodagreement was found in laminar flow between analytical solutions for different cases andthe CFD results if the bulk fluid temperature was used as a reference temperature (error< 10 -2 %). For turbulent forced convection a good agreement was also found and


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md h

s =

with the vapour permeability coefficient (kg/msPa)

Table 13 gives an overview.

Table 13 : vapour resistances according the Worch 2004.

2.4.3 Flow over bu ildi ng materials (numerical data)Zhang and Niu (2003) investigated for low Reynolds numbers the validity of using CFDfor determining the mass transfer coefficients. They performed experiments on a verysmall test cell (The field and laboratory emission cell (FLEC)). The authors showed thatthe numerical and experimental results correlated well for different test cases.

The study of Kaya et al (2007) deals with simultaneous heat and mass transfer duringdrying of cylindrical moist objects through an implicit finite-difference method.Instantaneous temperature and moisture distributions inside the moist material as well

as all local convective heat and mass transfer coefficients are also studied via the Fluentcomputational fluid dynamics (CFD) package. It is found that the convective heat transfercoefficients vary from 4.65 to 59.33 W/m 2K, while the convective mass transfercoefficients range between 3.59 3 10 -7 and 4.58 3 10 6 m/s, respectively. Remarkablygood agreement is obtained between the predicted results and experimental data takenfrom the literature to validate the present model.


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2.4.4 Flow over building materials (experimental data)

Tremblay et al (2000) measured heat and mass transfer coefficients over a flat piece ofwood inserted in a duct. They showed that the measured data correlated well with theanalytical solution for a turbulent duct flow

8.03.0

Re023.0 ScSh = During the Annex 41 several papers were presented in which experiments werepresented to determine the mass transfer coefficient.

Hedegaard et al (A41-T3-Dk-05-4) proposed a modified cup method to derive a masstransfer resistance Z (msPa/kg). To perform the cup method measurements speciallydeveloped equipment has been used. The cup test facility consists of a closedventilation system where both temperature and RH can be controlled. A diagram of theequipment can be seen in Figure 12 (1).

Figure 12: Test setup of Hedegaard et al (A41-T3-Dk-05-4)

During the test the temperature, RH, airflow velocity and pressure is recordedautomatically and the weight of the cups is entered at each weighing. It is possible to

test 12 ordinary cups and 12 inverted cups at the same time. In Figure 12 (2) a picture ofthe test chamber is shown. In the picture two holes can be seen in the front plate and byuse of these the samples are weighed on the balance seen in the bottom. A moredetailed description of the used equipment is given by Hansen (1989). The air iscirculated by a fan in a squared duct, which is stretched out to a flat 60 cm wide duct of 5cm height in the lower part of the system. In this flat part of the duct the cup samples arein contact with the chamber air. The circulation ensures that the airflow velocity on theexterior side of the cups can be controlled. Different airflow rates can be set.Different materials were tested under different conditions as shown in table 2


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Table 14 : Samples tested by Hedegaard et al (A41-T3-Dk-05-4)

The results of the tests A1-A5 do not clearly indicate how the air flow influences the totalresistance of the material sample. It was impossible to conclude anything about theinfluence of the airflow velocities influence on the surface resistances.The results of the tests B1-B4 with the glass fibre membranes were somewhat ruinedbecause the salt solution in the wet cup crept up at the sides of the cups and onto thematerial samples. In the cases with most salt on the samples the material resistance washighly reduced. Therefore, the tests of the surface resistances with wet cups wereabandoned.The results shown for the tests C1-C4 consists of a number of measurements withdifferent airflow velocities based on the measuring results from each cup. An example ofthe weight uptake results for the tests with paper are given in Figure 13 for the dry cupsin test C1. In the figure the numbers in the legend refer to the airflow velocity above theboundary layer of the material surface of the given cup. The slopes of the lines incombination with the exposed surface area and the vapor water pressure difference overthe samples are used to calculate the total resistance of the samples. The slopes of thelines in Figure 13 are for 2-layers of paper. The calculated total resistances in this case

are between 8.96107 and 1.2310

8 Pa m

2 s/ kg. The lowest surface resistance is for the

case with a velocity of 0.34 m/s and the highest value corresponds to an airflow velocityof 0.06 m/s. These airflow velocities also have the steepest and the flattest slopesrespectively in Figure 13. The measured weight uptake rates have been post processedand the corresponding surface coefficients have been found. The corresponding surfaceresistances as a function of the airflow velocity above the boundary layer of the four testsC1-C4 are shown in Figure 14. The results shown in the figure are based on at least 5weightings where the weight change rate is constant within 5% of the mean value,which is required by the EN ISO 12572:2001 standard. However, in most cases theweight change rate was constant within 2% of the mean value. In the figure a trendlinecalculated by the least squares fit for all measured test results by use of a power functionare added.

The measured results in Figure 14 show that there is a tendency of higher surfaceresistances for lower airflow velocities. This was expected. However, if the surfaceresistances from the measurements are compared with the estimated surfaceresistances, it is found that the measured values are higher than predicted. This couldbe a sign of that the equations slightly underestimate the surface resistances. Forcomparison the results of Bednar & Dreyer (2003) showed that the moisture transfercoefficient for drying is around 1810 -05 kg/(h m 2 Pa) for a room with .still. air. Thisnumber can be converted to a surface resistance value of 2.010 7 Pa m 2 s/ kg . Thisnumber seems quite small compared to measurement results where both the estimated


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and the measured surface resistances for velocities less than 0.2 m/s are higher.However, it was a drying experiment where the sample was wet and since the liquidmass transfer within the sample is faster than evaporation this can explain the lowervalue. In the present study the difference between the estimated values by use of Lewisrelation and the measured values decreases as the airflow velocity is increased.However, the normal airflow velocities in dwellings near construction surfaces are oftenquite small so there the underestimated values could be a problem.

Figure 13 : Test results of Hedegaard et al (A41-T3-Dk-05-4)


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Fi

Figure 14 : Test results of Hedegaard et al (A41-T3-Dk-05-4)

Talev et al (A41-T3-N-06-2) explore the role of transport properties of moist air as well asthe air velocity on the convective surface mass transfer coefficients at different axialpositions in a rectangular cross-section wind tunnel. Experimental work has beenperformed to determine the local mass transfer coefficients using three equal, horizontal

water cups, placed inline after one another in the tunnel. Each of the three samplesholders had a square shape with length and width equal to 60 mm and was mounted inline with the bottom surface of the wind tunnel, so that the air stream passed over thewater surface (Figure 15).


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Figure 15 : Test setup of Talev et al (A41-T3-N-06-2)

A series of experiments was performed to determine the resistance of the moisturetransport between the free water surface and moist air as a function of air velocity,distance from the tunnel opening and the relative humidity (RH). All the experimentswere carried out for a moist air temperature of 20 C. Some results are shown in Figure16. Each figure shows the surface mass transfer coefficient on the vertical axis in unitskg/ (Pas m 2). The horizontal axis shows the airflow velocity at the tunnel entrance.Further, each diagram includes results from 5 measurements, noted Measurement 1 to5, and the average of these measurements (noted Average Measurement). In additionthe figures include results from correlations found in literature which are noted Theory 1Laminar, Theory 1 Turbulent, and Theory 2, respectively. Notice that Theory 2 isintended for airflow velocity lower than 5 m/s.First the results in the figures show that there is some spread in the experimental data.This is mainly attributed by the fact that there was very difficult to maintain a perfectly flatwater surface. The measurements showed that a convex surface had a higher masstransfer coefficient than a flat surface. A concave water surface has a lower masstransfer coefficient than a flat water surface (this can not be expressed by thecorrelations presented in this paper). The water supply system was also quite difficult tocontrol. Still, the measured results show the same trend. Questions could also be raisedabout whether the measured results represent an ideal external flow or not. For aposition of 37 cm (for cup 1) and 61 cm (for cup3) from the tunnel entrance the velocityboundary layer thickness will be about 4 cm and 5 cm (calculated with an equation fromWhite, 1999), respectively, at a velocity of 0,1 m/s. At a free stream velocity of 1 m/s theboundary layer thickness will be about 1, 2 cm for cup 1 and 1,5 cm for cup 3. Generally,a large Reynolds number represents a thinner boundary layer (at a fixed position, x),while a small Reynolds number represents in a thicker boundary layer. Thus, data forlow velocities may therefore not be representative for a real external flow. (Later,experiments will be carried out in a modified wind tunnel to ensure the results are forexternal flow, for all velocities.The figures show that the surface mass transfer coefficient was a function of the airflowvelocity ,local position and the relative humidity All figures show that the surfacemoisture transfer coefficient increases with the air velocity. This is because an increased


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Figure 16 : Test results of Talev et al (A41-T3-N-06-2)

In general, there is quite poor agreement between the measured and the theoreticalresults. Lack of resemblance between the measured data and theoretical equations maybe because the theoretical equations do not take into account all the processes takingplace (e.g. thermal radiation, blowing effects (non-zero transverse velocity at interface),etc.). Further analysis is required in order to explain the observed discrepancies.

C Iskra and CJ. Simonson (A41-T3-C-06-3) (See also Iskra and Simonson CJ (2007)and ANNEX 41 Subtask 2; 3.3) measured the convective mass transfer coefficientbetween a forced convection airflow and a free water surface using the transientmoisture transfer (TMT) facility at the University of Saskatchewan. A pan of water is


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situated in the test section and forms the lower panel of the rectangular duct, where ahydrodynamically fully developed laminar or turbulent airflow is passed over the surfaceof the water. As the air passes through the test section, it loses heat and gains moistureto/from the water. As a result, the thermal and concentrations boundary layers aredeveloping through the short test section. The experimental data shows that theconvective mass transfer coefficient is a function of the Reynolds number (570 < Re

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ST3 Surface Transfer Coefficients