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 thermodynamic property (flux) between these walls and the internal or external air flow, or by defining a fixed state at the wall. In order to model the interaction between the wall (state) and the fluid (state) a transfer coefficient is often used, known as friction coefficient, heat transfer coefficient or mass transfer coefficient. Different authors have examined the sensitivity of thermal predictions from energy simulation programs to the modelling of internal convection (e.g. Spitler et al. (1991), Clarke (1991), Fisher and Pederson (1997)). Their work has demonstrated that predictions of energy demand and consumption can be strongly influenced by the choice of (made by program developer or user) heat transfer calculation method. Differences of 20-40% 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 a result, the choice of heat transfer calculation method could affect the design decisions drawn from a simulation-based analysis. (Beausoleil-Morrison (1999)). The transfer coefficient is in fact a modelling assumption in itself. The concept of transfer coefficients is developed in the boundary layer theory, first derived by Ludwig Prandtl in 1904. Prandtl discovered that for most applications the influence of viscosity is confined to an extremely thin region very close to the body and that the remainder of the flow could, to a good approximation, be treated as inviscid. The pressure in the boundary layer 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. They are only applicable for the correct boundary conditions. As simulations advance to include more details, the improper use of transfer coefficients often leads to non-physical results. In this chapter the basic concepts of boundary layer theory are introduced and the main parameters describing friction, heat and mass transfer are addressed. For further review reference is made to Kays & Crawford (1993) and Welty et al (2001). Application to buildings is discussed through papers published during ANNEX 41 and recent publications in literature.

2.2 BOUNDARY LAYER THEORY IN A NUTSHELL

2.2.1 Convection - flux laws Among the many tasks facing the engineer is the calculation of energy-transfer and mass-transfer rates at the interface between phases in a fluid system. Most often we are concerned with transfer at a solid-fluid interface where the fluid may be visualised as moving relative to a stationary solid surface.

If the fluid is at rest in the entire domain, the problem becomes one of simple heat conduction where there are temperature gradients normal to the interface or simple mass diffusion where there are mass concentration gradients normal to the surface. However, if there is fluid motion, energy and mass are transported both by potential gradients (as in simple conduction) and by movement of the fluid itself. This complex transport 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 a convection heat-transfer conductance or heat transfer coefficient as (Figure 1):

( )∞−= tthq ws& The driving force for heat transfer ( q& ) is the temperature difference between the wall surface (tws) and the free fluid stream (t∞). This equation is also known as Newton’s Law of 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 applications were 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 the usefulness of the conductance concept. In mass transfer it is convenient to define a convective mass-transfer conductance such that the total mass flux at the surface ( m& )is the product of the conductance g and the driving force, being the difference in concentration at the wall (cws) and in the free fluid stream (c∞).

ttwstws

ccwsccwscws

Flowv

q&

m&

( )∞−= cchm wsm& The conductance hm is essentially a fluid mechanic property of the system, whereas the concentration is a thermodynamic property. This second equation has the same form as the first one resulting to the rise of the heat- and mass- transfer analogies. The form of these equations is in fact a special case of the general form of a convection coefficient as given by :

ForceDrivingxTCOEFFICIENFLUX =

2.2.2 Hydraulic, thermal and concentration boundary 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 is limited to a thin layer near the boundary of the body” , hence the term THE BOUNDARY LAYER 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. This velocity can be created by a fan, wind, …. The thickness of the boundary layer (δ) is arbitrarily 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 layer increases with distance x from the leading edge. At relatively small values of x flow within the boundary layer is laminar. At larger values of x the transition region is shown where 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 the turbulent boundary layer a small laminar sublayer exists were there are steep velocity gradients.

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

ν= ∞xvRex

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

νvL

=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, as discussed in Kays WM, Crawford ME, (1993), the hydraulic boundary layer thickness as function 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 it’s 99% free stream value to zero at the body surface. This is not a precise definition of the boundary layer thickness. It only means that the boundary layer thickness is the distance from 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 (cf):

2/2∞ρτ

=v

c f

with ρ the fluid density and τ the fluid friction or shear stress. When there is heat or mass transfer between the fluid and the surface, it is also found that 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 thermal boundary layer and the concentration boundary layer, and again the relative thinness of these boundary layers permits the introduction of boundary-layer approximations similar to those introduced for momentum. Solving the Navier-Stokes equations for the energy or concentration transport equations results in a thermal boundary layer thickness and a concentration boundary layer thickness as function of the coordinate x.

In the solution of the diffential equations the Prandtl number kc pμ

=Pr appears, relating

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

expressed by the Schmidt number ABD

Scρμ

= 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 diffusion Sc

Le Pr= . As this number relates the thermal to

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

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

2f

p

ccv

hSt =ρ

=∞

This relation can be deduced out of the boundary layer equations for laminar forced flow across a solid boundary under the conditions that the Prandtl number (Pr) is equal to one 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:

2f

c

m cvh

p

=∞

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

mp

hcv

h=

ρ ∞

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

khLNu =

AB

m

DLh

Sh =

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

( )PrRe ,FNu =

( ),ScFSh Re= For natural convection the flow is driven by buoyancy as a result of density differences in the air volume. The dimensionless number characterising this flow type is the Grashof number given by

2

3

ρνρΔ

=LgGr

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

( )Pr,GrFNu = ( )ScGrFSh ,=

For the convective heat transfer coefficient a lot of data is available. For several, relative simple geometries and different flow conditions (laminar, transitional, turbulent, forced and buoyancy driven convection) an analytical solution of the Navier-Stokes equations applied to a boundary layer exists. (See eg Kays WM, Crawford ME, 1993) For more complex geometries correlations have be determined by curve fitting dimensionless numbers to large data sets. As there are many different correlations available care has to be taken in selecting the suitable correlation. For analytical derived correlations the validity of assumptions and simplifications should be checked. For experimentally derived correlations the range and accuracy of the data set should be taken into consideration. For the mass transfer coefficient boundary layer analysis leads again to analytical solutions. Due to the fact that the differential equations for heat and mass transfer resulting from boundary layer analysis are analogues, the solutions obtained for heat transfer can be transformed into mass transfer solutions, by using the correct dimensionless number cited earlier (Welty et al (2001)). Furthermore it is very difficult to determine the convective mass transfer coefficient experimentally. Therefore this analogy is applied in a lot of cases for calculating the convective mass transfer coefficient, starting from the thermal measurements that where done. Validity of the thus obtained mass transfer coefficients is by consequence even more limited and great care should again be taken in selecting the proper correlation for the studied geometry. (See eg Kays WM, Crawford ME, 1993) For flow around buildings very little information was found about mass transfer determination, both experimentally or numerically. For flows inside buildings, most research 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 the mass transfer coefficient. Often these experiments were found to have limited validity. Secondly numerical methods, based on CFD, were used to determine mass transfer from a fluid to a porous material. Finally the heat and mass transfer analogy was looked into.

2.2.3 Overview of useful dimensionless numbers and nomenclature

Name Symbol Definition Meaning Reynolds number Re

νvL

=Re inertial forces compared to viscous forces

Grashof number Gr 2

3

ρνρΔ

=LgGr

buoyancy forces compared to viscous forces

Nusselt number Nu

khLNu =

dimensionless heat transfer coefficient

Sherwood number Sh

AB

m

DLh

Sh = dimensionless mass transfer coefficient

Prandtle number Pr

kc pμ

=Pr viscosity to thermal diffusion

Schmidt number Sc

ABDSc

ρμ

= viscosity to mass diffusion

Stanton Number St

PrReNu

cvhSt

p

=ρ

=∞

ratio of heat transferred into a fluid to the thermal capacity of fluid

Lewis number Le

ScLe Pr

= thermal diffusion to mass diffusion

Archimedes number Ar ( )2

3

μ

ρ−ρρ=

LgAr gll

the motion of fluids due to density differences

Rayleigh number Ra Ra = Gr Pr Richardson number Ri

2ReGrRi =

Measure for comparing forced convection to buoyancy driven convection (mixed convection)

Units Heat capacity cp J/kgK Diffusion coefficient DAB m²/s Gravitational constant

g 9.81 m/s²

Heat transfer convection coefficient

h W/m²K

Mass transfer convection coefficient

hm m/s

Characteristic Length L M Flow velocity v m/s Free stream velocity

∞v m/s

Boundary layer thickness

δ m

Thermal conductivity λ W/mK Dynamic viscosity μ Pa s Kinematic viscosity ν m²/s Density ρ kg/m³

Table 1 : Dimensionless numbers and nomenclature

2.3 HEAT TRANSFER

2.3.1 Flow over and around buildings (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 large extent determined by the local wind speed. Usually, empirical formulae are used to relate the reference wind speed at a meteorological station to the local wind speed near the building surface and to relate the local wind speed to surface transfer coefficients. These formulae however are based on a limited number of measurements. Practical correlations given by Jürges (1924) give a relation between free stream wind ( ∞V ) speed and the thermal convection coefficient :

smVVhsmVVh/5;6.51.7

/5;6.50.478.0 >+=

<+=

∞∞

∞∞

Charples (1984) presented the following algorithm :

1.57.1 += locVh with Vloc the local wind speed measured at 1 m distance from the surface. It is expressed as a simple function of the reference wind speed U10 :

leewardUVwindwardUV

loc

loc

;7.14.0;2.08.1

10

10

+=+=

Also ASHRAE (ASHRAE 1975) proposed practical correlations of a similar nature :

605.0886.1 locUh =

3.005.0/25.0

/225.0

10

10

1010

+=<=

>=

UUleewardsmUif

smUifUUwindward

loc

loc

These type of correlations are proven to be very sensitive to errors. First of all the definition of the free stream wind speed around a building is not clear and secondly the relation between wind speed and the actual heat transfer coefficient is not clearly stated. This is discussed in Annex paper A41-T3-B-05-5.

2.3.2 Flow over and around buildings (CFD data) Little is known about the actual value and the variability of local wind speed and surface transfer coefficients across facades of different building geometries. In Annex paper A41-T3-B-05-5 a validated Computational Fluid Dynamics (CFD) model (FLUENT) is

used to calculate the local wind speed near the exterior surface of a cubic building model as 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 very pronounced and that using the available empirical formulae can yield large errors in HAM calculations. In Annex paper A41-T3-Br-07-2 (and Emmel M, Abadie M, Mendes N (2007)) similar conclusions were drawn using in essence the same approach. Using CFD calculations with CFX, correlations for the heat transfer coefficient were determined for the BESTEST reference case Judkoff R.D., Neymark J.S. (1995). De correlations presented in the previous paragraph were compared to the CFD calculations and both over and under predictions (to about a factor 4) of these correlations were found in relation to the CFD solutions. The paper ends with a list of new correlations determined by doing several calculations with CFD on the BESTEST geometry. These are copied here. More information 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 inside buildings (experimental data) Air flows inside buildings occur due to two main reasons. Firstly there are air streams caused 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 or density fields it creates. Secondly temperature and concentration (vapour) differences inside 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 buildings Spitler et al. (1991b) designed a full-scale experimental facility, with internal dimensions of 4.57 x 2.74 x 2.74 m and a fan system delivered air to one of the two room inlets over a range of 5 to 100 air changes per hour (ACH). The walls, floor and ceiling were covered by heated panels, each with an independent electrical resistance heater.

Figure 3 Experimental facility of Spitler et al. 1991a

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

5.021 JCCh ⋅+= with

roomgVUm

Jρ

= 0& (U0 jet inlet velocity, Vroom 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) ⎟⎟⎠

⎞⎜⎜⎝

⎛ Δβ= 2

0UTLgAr

Surface Inlet h Limits Ceiling Ceiling 11.4 + 209.7 J0.5 0.001<J<0.03 Vertical walls Ceiling 4.2 + 81.3 J0.5 0.001<J<0.03 Floor Ceiling 3.5 + 46.8 J0.5 0.001<J<0.03 Ceiling Side wall 10.6 + 59.4 J0.5 0.002<J<0.011 and Ar<0.3 Vertical walls Side wall 1.6 + 92.7 J0.5 0.002<J<0.011 Floor Side wall 3.2 + 44.0 J0.5 0.002<J<0.011 and Ar<0.3 Fisher extended Spitler’s work by investigating buoyant, wall and free jets over a range of room inlet conditions using the same enclosure. The room was also isothermal in most of the experiments. However, a single wall was chilled in one group of ceiling-diffuser experiments to examine the combined influence of buoyancy and forced effects. The experiments only examined room cooling, the incoming air stream always being colder than the air within the room and the room surfaces. Correlations were developed for three classes of flows: (1) ceiling jets in isothermal rooms, (2) free horizontal jets in isothermal rooms and (3) ceiling jets in non-isothermal rooms. For the first class, Fisher (1995) found surface convection to be independent of the inlet velocity of the ceiling jet, but rather to depend upon the jet’s volumetric flow rate. He also found the buoyancy forces of the cold jet to be negligible relative to the viscous Coanda effect, adhering the jet to the ceiling and walls. The form of the correlations, expressed in dimensionless parameters, can be described as follows: (applicable 3< ACH< 100)

3Re21CeCCNu ⋅+= where

λ=

3/1roomhV

Nu

and 3/1Reroom

diffusere V

Vμ

ρ=

& ( diffuserV& jet volumetric flow rate m³/s)

With the free horizontal jets in isothermal rooms the buoyancy forces of the cold jet also had a negligible impact on convection from the walls and floor. Therefore the same type of 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 3< ACH< 12)

e

Ce

ArCCNu

3Re21 ⋅+=

Table 4 : Convective heat transfer correlations of Fisher (1995)

Fisher and Pedersen (1997) correlated the same data as Fisher (1995) using a different functional form. The correlations are applicable for forced convection and work in similar conditions as the correlation developed by Fisher (1995). The main difference is the position of the diffuser. These correlations are applicable in rooms with ceiling diffusers where the diffuser jet is attached to the ceiling surface. As with previous correlations, supply air temperature is used as the reference temperature. The correlations are given in Table 5. Table 5 :Convective heat transfer correlations of Fisher and Pedersen (1997)

2.3.3.2 Natural convection or buoyancy driven flow inside buildings Alamdari and Hammond (1983) are one of the first to develop correlations dedicated to building applications. Correlations that cover laminar, transitional and turbulent flow regimes for the following three configurations are given: (1) vertical surfaces, (2) stably-stratified horizontal surfaces (e.g. warm air above a cool floor) and (3) buoyant flow from horizontal surfaces (e.g. cool air above a warm floor). The correlations cover the full range of temperature and dimensions that appear in buildings. But they are not

Surface type Configuration h Walls ( ) 8.0190.0199.0 ACH⋅+− Floor ( ) 8.0116.0159.0 ACH⋅+ Ceiling

Forced convection with ceiling diffuser in isothermal rooms

( ) 8.0484.0166.0 ACH⋅+− Walls ( ) 8.0132.0110.0 ACH⋅+− Floor ( ) 8.0168.0704.0 ACH⋅+ Ceiling

Forced convection with wall diffuser (free jet)

( ) 8.000444.0064.0 ACH⋅+

Surface type Configuration h Walls ( ) 8.019.0 ACH⋅ Floor ( ) 8.013.0 ACH⋅ Ceiling

Forced convection with ceiling diffuser in isothermal rooms

( ) 8.049.0 ACH⋅

applicable for cases where buoyancy is created by thermal devices (e.g. radiator baseboard heater or fan coil) and mechanically driven jets as experienced in mechanically ventilated buildings. They are only valid for purely buoyant flow, in cases where buoyancy is caused by the temperature difference between a surface and the surrounding room air (ΔT). Alamdari and Hammond (1983) did not perform new experiments, the correlations are based on collected experimental data reported in the literature. All data is derived from experiments conducted with free standing surfaces (surfaces not part of the room), which limits the applicability of the correlations. Table 6 : Alamdari and Hammond convection correlations (Beausoleil-Morrison, 2000) (H is room height en Dh the room hydraulic diameter) Surface type Ventilation regime h Wall

[ ]6/1

63/1

64/1

23.15.1⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

Δ+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ Δ⋅ T

HT

Floor (Tsurface>Tair) Ceiling (Tsurface < Tair) [ ]

6/1

63/1

64/1

63.14.1⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

Δ+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ⋅ T

DT

h

Floor (Tsurface < Tair) Ceiling (Tsurface>Tair)

Natural convection (system is off)

5/1

6.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ⋅

hDT

Khalifa and Marshall (1990) performed experiments in a room sized test cell to produce correlations specific to internal convection within buildings. Convection correlations are developed based on measurements in an experimental chamber with room sizes: 2.95 x 2.35 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 common convection regimes, the test cell’s configuration was varied. Different heating systems (e.g. radiator, in-floor heating, convective heating) were analyzed, as was the placement of 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 to calculate the convective heat transfer coefficient. But Khalifa and Marshall (1990) measured the air temperature outside the thermal boundary layer at a distance of 60 mm from the interior surface of the wall, which is used as the reference temperature.

Khalifa generated a total of 36 correlations. Data from similar correlations were combined together in order to obtain new and more general correlations which can be applied in more than one configuration (Khalifa and Marshall 1990). By combining these similar 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 h Wall In the vicinity of the terminal device

Rooms heated by radiator Radiator not located under window Only surfaces adjacent to radiator

32.098.1 TΔ⋅

Rooms heated by radiator Radiator located under window

Wall

Rooms with heated walls Not applicable for heated walls

24.03.2 TΔ⋅

Wall Rooms heated by circulating fan heater Only for surfaces opposite to fan

25.092.2 TΔ⋅

Rooms heated by circulating fan heater For surfaces not opposite to fan Rooms with heated floor

Wall

Rooms heated by radiator Radiator not located under window For surfaces not next to radiator

23.007.2 TΔ⋅

Window Rooms heated by radiator Radiator located under window

11.007.8 TΔ⋅

Window Rooms heated by radiator Radiator not located under window

06.061.7 TΔ⋅

Rooms heated by radiator Radiator located under window

Ceiling

Rooms with heated walls

17.01.3 TΔ⋅

Rooms heated by circulating fan heater Rooms with heated floors

Ceiling

Rooms heated by radiator Radiator not located under window

13.072.2 TΔ⋅

Table 8 Khalifa and Marshall (1990) convection correlations Surface type Ventilation regime h Wall

Large isolated vertical surface 14.003.2 TΔ⋅

Floor Large heated surface facing upward 24.027.2 TΔ⋅

Calay et al. (1998) performed an experimental study of buoyancy-driven convection in rectangular enclosures. The enclosure was one-quarter scale model of a typical room. It was based on ‘hot box’ arrangement, in which two opposing walls are heated and cooled while others are insulated and act as adiabatic walls. Four sets of experiments were performed to simulate the following convective heat-flow configurations: (1) enclosure heated from side, (2) large vertical walls as hot and cold plates, (3) small vertical walls as 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 dimensionless parameters: Nusselt, Prandtl and Grashof number. The correlations recommended by ASHREA (1985) and CIBSE (1986) and other correlations derived from tests with full size enclosures and similar configurations are used for comparing the experimental results (Table 9) Table 9 Equations employed for comparison (Calay et al. 1998) Equation Correlation, Nu Gr range Flow

condition

Configuration: stably stratified, Tw=cte

CIBSE (1986) ASHRAE (1985) Alamdari and Hammond (1983) Min et al. (1956)

0.236Gr1/4

0.218Gr1/4 0.56Gr1/5 0.065Gr0.255

108<Gr<101

0

108<Gr<101

0

108<Gr<101

0

Not specified

Laminar Laminar Laminar Not specified

Awbi and Hatton (1999) conducted experiments in two experimental chambers, with different size in order to assess scale effects (Figure 5). The first chamber had a typical room size of 2.78 x 2.78 x2.3 m. The second was considerably smaller 1 x 2.78 x 2.3 m. This chamber was kept at a low temperature, so that the wall that connected the two chambers acted as a heat sink. The main chamber was conditioned by electrically heated plates affixed to the surfaces. A single surface (wall, floor or ceiling) was heated in each experiment. All the walls were aluminium plated and long-wave radiation was taken into account.

Figure 5 Environmental chamber of Awbi and Hatton (1999)

Natural convection from heated room surfaces was characterized by a correlation of the mean 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 heat transfer coefficients on surfaces in two- and three-dimensional enclosures with primary focus on those with a direct application to heat transfer in buildings. Figures 6 to 8 give a comparison of the different correlations mentioned in Khalifa (2001).

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

2001)

Surface type Ventilation regime

Nu

Walls ( 9 x 108 < 6 x 1010) ( ) 293.0Gr289.0

Floors ( 9 x 108 < 7x 1010)

( ) 308.0Gr269.0

Ceilings ( 9 x 108 < 1 x 1011) ( ) 133.0Gr78.1

Partly heated ceilings

Buoyant with heated surface

( ) 16.0Gr517.3

Figure 7 Convective heat transfer coefficient correlations for heated plate facing upward

(heated floor/ cold ceiling) (Khalifa 2001)

Figure 8 Convective heat transfer coefficient correlations for heated plate facing

downward (heated roof/cold floor) (Khalifa 2001)

2.3.3.3 Mixed convection inside buildings Beausoleil-Morrison (2000) developed a suitable method for solving mixed flow. He created his correlations by combining the correlations for natural convection (Alamdari and Hammond 1983) and for forced convection where the air is supplied by a ceiling diffuser (Fisher 1995). In some cases the mechanical and buoyant forces will assist (act in same direction, Figure 9) while in others they will oppose (act in opposite directions) or act transversely (act in perpendicular directions). It is difficult (usually impossible) to predetermine whether a configuration will be dominated by buoyant forces or mechanical forces. Beausoleil-Morrison solves this problem by selecting and combining the appropriate correlations for forced and natural convection.

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⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−⎥⎥⎦

⎤

⎢⎢⎣

⎡

θΔθ−θ

+⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧θΔ+

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛ θΔ×

ACHH

ds

Wall

Opposing forces

[ ] ( )[ ]

[ ]

( )[ ]

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡

θΔθ−θ

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

θΔ+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ θΔ

⎜⎜⎜⎜

⎝

⎛

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−⎥⎥⎦

⎤

⎢⎢⎣

⎡

θΔθ−θ

−⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

θΔ+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ θΔ×

8.0

6/1

3/1

64/1

3

8.0

613

63/1

64/1

190.0199.0 of %80

23.15.1 of %80

190.0199.023.15.1

max

ACH

H

ACHH

ds

ds

Floor

Buoyant [ ] ( )[ ]3/1

3

8.0

613

63/1

64/1

116.0159.063.14.1⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+⎥⎥⎦

⎤

⎢⎢⎣

⎡

θΔθ−θ

+⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

θΔ+⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛ θΔ×

ACHD

ds

h

Stably stratified ( )[ ]

3/13

8.0

35/1

116.0159.06.0⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡

θΔθ−θ

+⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛ θΔACH

Dds

h

Ceiling

Buoyant [ ] ( )[ ]1

3

8.0

613

63/1

64/1

484.0166.063.14.1⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−⎥⎥⎦

⎤

⎢⎢⎣

⎡

θΔθ−θ

+⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

θΔ+⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛ θΔ×

ACHD

ds

h

The experiments of Awbi and Hatton (2000) were carried out in the same enclosure as the natural convection experiments. They only placed an air handling unit onto the ceiling of the small (cold) compartment to cool the dividing wall that separates the two compartments. The fan and heating plates were positioned on a wall, the floor and the ceiling to investigate the effect of a 3D wall jet on the surface convective heat transfer coefficient (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 for forced convection

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

Stably stratified ( )[ ]

3/13

8.0

35/1

2 484.0166.06.0⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡

θΔθ−θ

+⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛ θΔACJH

Dds

h

Surface type Ventilation regime

hcf hcf/hcn

Walls ( 9 x 108 < 6 x 1010) ( ) 873.0536.1 UW79.3 ( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡

Δ 293.0

873.0536.1

TUW3165.2

Floors ( 9 x 108 < 7x 1010) ( ) 557.0575.0 UW248.4 ( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡

Δ 308.0

557.0595.0

TUW06.2

Ceilings ( 9 x 108 < 1 x 1011)

Jet over a heated surface

( ) 772.0074.0 UW35.1 ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡

Δ 133.0

772.0074.0

TUW45.3

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

Figure 11 Experimental facility for the development of convection correlations

(Novoselac 2005)

2.3.4 Flow inside buildings (CFD data) Awbi (1998) compared experimental results for natural CHTC of heated room surfaces with CFD calculations. Two turbulence models were used: (1) a standard k-� model using wall functions and (2) a low Reynolds number k-ε model. The logarithmic standard wall functions describe the momentum and heat transfer from the internal surfaces of a room. But these functions are empirically derived for forced convection in pipes and over flat plates. Awbi (1998) concluded that prediction of the convective heat transfer coefficient using wall functions is extremely sensitive to the distance of the point from the surface (yp) at which the wall function is applied. But CFD analysis, which uses wall functions, proved to be useful in the investigation of the airflow over the heated plates and the air movement within the chamber (Awbi (1998)).The more accurate prediction of the heat transfer from room surfaces, using a low Reynolds number turbulence model, is very time consuming. An alternative is to use an experimental determined expression for the convective heat transfer coefficient for room surfaces in a CFD code. This is what Beausoleil-Morrison (2000) and Novoselac (2005) have done with their ACA and respectively MACA algorithms. During the Annex 41 CFD was used to evaluate the possibilities of determining heat transfer coefficients with CFD. In [A41-T3-C-06-5 and A41-T3-C-06-6] CFD was used to determine the heat transfer coefficient for flow between two infinite plates. A good agreement was found in laminar flow between analytical solutions for different cases and the 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

different turbulence models give limited deviations in the developed zone. For a natural convection case the CFD calculations did not result in velocity profiles consistent with experimental data when using law-of-the-wall equations for forced convection. Using a Low-Re model resulted in good agreement between experiment and simulation.

2.4 MASS TRANSFER

2.4.1 Heat and mass transfer analogy As little direct experimental data is available on vapour transfer coefficients the heat and mass analogy is used to calculate the vapour transfer coefficient. This is the basis for the prEN 15061, 2004. The heat and mass transfer analogy is applicable for very specific cases. In case both Pr and Sc numbers are equal to one, and hence the Lewis number (Le) is one, the relation between the mass transfer coefficient and the heat transfer coefficient is given by :

mp

hcv

h=

ρ ∞

The Reynolds analogy is limited in its application because of the strict conditions under which it is valid. (It was deduced for laminar forced flow across a solid boundary under with no form drag.) Yet this analogy inspired researchers to seek for better analogies which are more generally applicable. Prandtl developed an analogy for heat and momentum transfer and for mass and momentum transfer considering the turbulent core and the laminar sublayer in the boundary layer equations. The effect of Pr and Sc numbers different from one is taken into account in this analogy. This led to the following equations for the heat and mass transfer coefficients:

( )1Pr512

−+=

ρ=

∞ Sc

c

p f

f

cvhSt

( )1512

−+=

∞ Scvh

Sc

cm

f

f

Von Karman extended Prandtl’s work and took the effect of the transition layer between the laminar sublayer and the turbulent core into account. This led to an extra correction term as function of respectively Pr and Sc in the two previous equations. The application of the Prandtl and Von Karman analogies is restricted to cases with negligible form drag. Both the Prandtl analogy as the Von Karman analogy reduce to the Reynolds analogy for Pr and Sc number equal to one. While Prandtl and Von Karman adapted the Reynolds analogy by considering the transfer equations in the boundary layer, Chilton and Colburn sought modifications to the Reynolds analogy using experimental data (Colburn 1933, Chilton & Colburn 1934). They suggested a simple modification for situations with Pr and Sc numbers different from unity. This was done by defining the j factor for heat transfer and the j factor for mass transfer:

2

Pr 3/2 fh

cStj ==

2Pr 3/2 fm

m

cvh

j ==∞

Colburn applied the j factor for heat transfer to a wide range of data for flow on different geometries and found it to be quite accurate for conditions where no form drag exists and for Pr between 0.5 and 50. The complete Chilton-Colburn analogy is found when equations are combined:

3/23/2Pr Schch

mp

=ρ

-

When form drag is present neither jH or jm equals cf/2, yet it has been found that equation remains valid. It is clear that the Chilton-Colburn analogy also reduces to the Reynolds analogy for Pr and Sc numbers equal to unity. Unlike the Prandtl or Von Karman analogy the relation between the heat and mass transfer coefficients is no longer function of the skin friction coefficient. The analogy between heat and momentum transfer and between mass and momentum transfer is based on the assumption that respectively the dimensionless velocity and temperature profiles and the dimensionless velocity and mass concentration profiles are similar. This is the case for forced convection flow over a solid surface without form drag. All the analogies mentioned in this paragraph, as well the theoretical deduced ones as the experimental Chilton-Colburn analogy, were developed for this case. In A41-T3-C-04-7 D. Derome presented a limited and preliminary set of experiments through which the author suggests that the analogy between heat and mass transfer gives an overprediction of the mass transfer. The author claims more research is needed into the use of the analogy. In A41-T3-B-07-4 Steeman et al. investigated the influence of conditions in which the analogy is valid and determined accuracy. CFD simulations are performed to compare simulated vapour transfer coefficients with coefficients predicted out of the heat and mass analogy. It is found that dissimilarity of the boundary conditions induces the largest differences between predicted and simulated transfer coefficients: for the average transfer coefficient the largest difference seen in the simulations is an under prediction with a factor 0.41 while for local transfer coefficients differences up to a factor 10 are found. Hence the heat and mass analogy gives a reasonable estimate of the average vapour transfer coefficient, but can lead to large errors for local coefficients.

2.4.2 Flow over and around buildings (experimental data) Little information can be found in literature about experimentally determined mass transfer coefficients for building applications. Swartz (1972) presented some experimental results for mass transfer to building surfaces under different wind speeds. Swartz reported for Vwind > 1m/s

faceleewardVh

facewindwardVh

windm

windm43.0

58.0

20

27

=

=

Worch (2004) published data for vapour transfer resistance for flows in natural en forced convection, in and around buildings. He determined vapour transfer resistances which are related to the mass transfer coefficient as :

md h

s δ=′

with δ the vapour permeability coefficient (kg/m²sPa)

Table 13 gives an overview. Table 13 : vapour resistances according the Worch 2004.

2.4.3 Flow over building materials (numerical data) Zhang and Niu (2003) investigated for low Reynolds numbers the validity of using CFD for determining the mass transfer coefficients. They performed experiments on a very small test cell (The field and laboratory emission cell (FLEC)). The authors showed that the numerical and experimental results correlated well for different test cases. The study of Kaya et al (2007) deals with simultaneous heat and mass transfer during drying 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 Fluent computational fluid dynamics (CFD) package. It is found that the convective heat transfer coefficients vary from 4.65 to 59.33 W/m2K, while the convective mass transfer coefficients range between 3.59 3 10-7 and 4.58 3 106 m/s, respectively. Remarkably good agreement is obtained between the predicted results and experimental data taken from the literature to validate the present model.

2.4.4 Flow over building materials (experimental data) Tremblay et al (2000) measured heat and mass transfer coefficients over a flat piece of wood inserted in a duct. They showed that the measured data correlated well with the analytical solution for a turbulent duct flow

8.03.0 Re023.0 ScSh = During the Annex 41 several papers were presented in which experiments were presented to determine the mass transfer coefficient. Hedegaard et al (A41-T3-Dk-05-4) proposed a modified ‘cup method’ to derive a mass transfer resistance Z (m²sPa/kg). To perform the cup method measurements specially developed equipment has been used. The cup test facility consists of a closed ventilation system where both temperature and RH can be controlled. A diagram of the equipment 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 recorded automatically 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 of the test chamber is shown. In the picture two holes can be seen in the front plate and by use of these the samples are weighed on the balance seen in the bottom. A more detailed description of the used equipment is given by Hansen (1989). The air is circulated by a fan in a squared duct, which is stretched out to a flat 60 cm wide duct of 5 cm height in the lower part of the system. In this flat part of the duct the cup samples are in contact with the chamber air. The circulation ensures that the airflow velocity on the exterior 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

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 total resistance of the material sample. It was impossible to conclude anything about the influence of the airflow velocities influence on the surface resistances. The results of the tests B1-B4 with the glass fibre membranes were somewhat ruined because the salt solution in the wet cup crept up at the sides of the cups and onto the material samples. In the cases with most salt on the samples the material resistance was highly reduced. Therefore, the tests of the surface resistances with wet cups were abandoned. The results shown for the tests C1-C4 consists of a number of measurements with different airflow velocities based on the measuring results from each cup. An example of the weight uptake results for the tests with paper are given in Figure 13 for the dry cups in test C1. In the figure the numbers in the legend refer to the airflow velocity above the boundary layer of the material surface of the given cup. The slopes of the lines in combination with the exposed surface area and the vapor water pressure difference over the samples are used to calculate the total resistance of the samples. The slopes of the lines in Figure 13 are for 2-layers of paper. The calculated total resistances in this case are between 8.96·107 and 1.23·108 Pa m2 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 velocity of 0.06 m/s. These airflow velocities also have the steepest and the flattest slopes respectively in Figure 13. The measured weight uptake rates have been post processed and the corresponding surface coefficients have been found. The corresponding surface resistances as a function of the airflow velocity above the boundary layer of the four tests C1-C4 are shown in Figure 14. The results shown in the figure are based on at least 5 weightings 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 the weight change rate was constant within ± 2% of the mean value. In the figure a trendline calculated by the least squares fit for all measured test results by use of a power function are added. The measured results in Figure 14 show that there is a tendency of higher surface resistances for lower airflow velocities. This was expected. However, if the surface resistances from the measurements are compared with the estimated surface resistances, it is found that the measured values are higher than predicted. This could be a sign of that the equations slightly underestimate the surface resistances. For comparison the results of Bednar & Dreyer (2003) showed that the moisture transfer coefficient for drying is around 18·10-05 kg/(h m2 Pa) for a room with .still. air. This number can be converted to a surface resistance value of 2.0·107 Pa m2 s/ kg . This number seems quite small compared to measurement results where both the estimated

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 liquid mass transfer within the sample is faster than evaporation this can explain the lower value. In the present study the difference between the estimated values by use of Lewis relation and the measured values decreases as the airflow velocity is increased. However, the normal airflow velocities in dwellings near construction surfaces are often quite small so there the underestimated values could be a problem.

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

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 as the air velocity on the convective surface mass transfer coefficients at different axial positions in a rectangular cross-section wind tunnel. Experimental work has been performed 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 samples holders had a square shape with length and width equal to 60 mm and was mounted in line with the bottom surface of the wind tunnel, so that the air stream passed over the water surface (Figure 15).

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 moisture transport 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 experiments were carried out for a moist air temperature of 20 °C. Some results are shown in Figure 16. Each figure shows the surface mass transfer coefficient on the vertical axis in units kg/ (Pa·s ·m2). The horizontal axis shows the airflow velocity at the tunnel entrance. Further, each diagram includes results from 5 measurements, noted Measurement 1 to 5, and the average of these measurements (noted “Average Measurement”). In addition the figures include results from correlations found in literature which are noted “Theory 1 Laminar”, “Theory 1 Turbulent”, and “Theory 2”, respectively. Notice that “Theory 2” is intended 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 flat water surface. The measurements showed that a convex surface had a higher mass transfer coefficient than a flat surface. A concave water surface has a lower mass transfer coefficient than a flat water surface (this can not be expressed by the correlations presented in this paper). The water supply system was also quite difficult to control. Still, the measured results show the same trend. Questions could also be raised about whether the measured results represent an ideal external flow or not. For a position of 37 cm (for cup 1) and 61 cm (for cup3) from the tunnel entrance the velocity boundary layer thickness will be about 4 cm and 5 cm (calculated with an equation from White, 1999), respectively, at a velocity of 0,1 m/s. At a free stream velocity of 1 m/s the boundary 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 for low 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 for external flow, for all velocities. The figures show that the surface mass transfer coefficient was a function of the airflow velocity ,local position and the relative humidity All figures show that the surface moisture transfer coefficient increases with the air velocity. This is because an increased

velocity reduced the boundary layer thickness. The measurements show that an increase in the RH resulted in a decrease in the surface mass transfer coefficients. An increased distance from the tunnel entrance resulted in a reduction of the surface moisture transfer coefficient.

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 theoretical results. Lack of resemblance between the measured data and theoretical equations may be because the theoretical equations do not take into account all the processes taking place (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 coefficient between a forced convection airflow and a free water surface using the transient moisture transfer (TMT) facility at the University of Saskatchewan. A pan of water is

situated in the test section and forms the lower panel of the rectangular duct, where a hydrodynamically fully developed laminar or turbulent airflow is passed over the surface of the water. As the air passes through the test section, it loses heat and gains moisture to/from the water. As a result, the thermal and concentrations boundary layers are developing through the short test section. The experimental data shows that the convective mass transfer coefficient is a function of the Reynolds number (570 < Re < 8,100 investigated) and the relative humidity of the air stream (15% to 80% RH investigated). The air humidity can change the mass transfer coefficient by as much as 35%. For example with Re = 1500, the measured Sherwood number is 5.1 and 6.9 (hm = 0.0031 and 0.0042 m/s) when the air humidity is 80% RH and 18% RH respectively. The transient moisture transport (TMT) facility is an experimental apparatus that determines the transient heat and moisture transport properties of porous materials. The test section within the TMT is a horizontal rectangular duct, where heat and mass transfer occurs at the bottom wall surface. The facility passes air at varying velocities, temperatures and relative humidity’s above the surface of materials and measures the change in mass, relative humidity, and temperature in the material as a function of time. To fully document experimental results for the TMT, the convective mass transfer coefficient of this facility is required Mass transfer coefficients are usually determined from experiments based on the adiabatic evaporation of a liquid and this method is applied in this paper. Since water vapor transfer is the only form of mass transfer in the TMT facility when experimenting on porous materials, distilled water is used as the evaporating liquid to ensure that the same Schmidt number (Sc) is present in both experiments. The convective mass transfer coefficient is determined for the horizontal rectangular duct by measuring the evaporation rate from a rectangular tray of water that is located in the lower panel of the duct. The vapor density difference between the bulk air stream and the surface of the water is also measured in order to determine the concentration difference at the surface of the duct. A side-view and an expanded top-view schematic of the ducting upstream and downstream of the rectangular test section are shown in Fig. 17(a and b). All of the rectangular ducting shown have a width (W) of 298 mm. A variable speed vacuum pump supplies a hydrodynamically developed airflow at the entrance of the test section by means of a developing section upstream of the test section (Fig. 17(a)). First, the air flows through a 1100 mm long duct that has a constant cross sectional area, which has several screens installed inside of it to aid in the straightening of the airflow. The air then passes through a 995 mm long converging section that has a convergence angle of 5° to minimize the dynamic losses in the duct and aid in the development of the flow. Following the converging section, the air enters a 500 mm long straight duct that delivers the air to the test section. The air then passes through the 765 mm test section (close-up view shown in Fig. 17(c)) and then through a 890 mm downstream section. The ducts immediately upstream and downstream of the test section have the same hydraulic diameter as the test section when the evaporation pan is full of water (i.e., h = 0 in Fig. 17(d)). The side and top views of the test section within the TMT facility are also shown in Fig. 1. A tray with a water surface width (w) of 280 mm and a length (L) of 600 mm forms the lower panel of the duct (height (H) = 20.5 mm) in the test section. The air is delivered to the test section from an environmental chamber that controls the temperature and relative humidity of the air upstream of the test section within ± 0.1°C and ± 2% RH respectively. The temperature and relative humidity of the air is measured upstream and downstream of the test section with humidity/temperature transmitters.

Figure 17 : TMT test setup of Iskra and Simonson (A41-T3-C-06-3)

Laminar flow Figure 18 presents the convective mass transfer coefficients, hm (m/s) for a range of Re and air relative humidity. The convective mass transfer coefficients decrease when the relative humidity of the air entering the test section is increased. The convective mass transfer coefficients can change as much as 35% when the air relative humidity varies from 18 to 80% RH. To fully capture the effects of the relative humidity on the convective mass transfer coefficient, the Rayleigh number (Ra=Re Pr) is used, which takes into account the temperature and relative humidity of the air at the surface of the water and

in the bulk airflow. The convective mass transfer coefficient (hm) is non-dimensionalized with the use of Sh and this data is presented in Fig. 19. The Sh is determined for laminar flow between a Re of 570 and 2,100, which corresponds to a X* between 0.011 and 0.037, and a Ra of 6,300 and 83,000. A general trend of increasing Sh as Re increases (X* decreases),is found which is expected since the length of the test section is not long enough for the temperature and concentration boundary layers to become fully developed. As Re increases, the thermal and concentration boundary layers become thinner and less developed over the surface of the water. A thinner boundary layer results in a larger concentration gradient at the surface of the water, which contributes to an increase in forced convection mass transfer at the surface of the water.

with

Figure 18 : Mass transfer coefficient as function of Re en relative humidity Iskra and

Simonson (A41-T3-C-06-3)

( Figure 19 : Sh as function of Re en relative humidity Iskra and Simonson (A41-T3-C-06-

3) Turbulent flow Turbulent flow experiments are performed in order to develop a relationship for Sh that includes both developing flow (X*) and buoyancy forces (Ra), and also to further verify the experiments by comparing to an experiment in the literature which is for turbulent flow. The turbulent flow data of the present work covers a range of Re between 3,100 and 8,100, and Ra between 20,900 and 46,000. The various Ra are created by the air relative humidity between 15% RH and 60% RH at a constant air temperature of 23°C. The results that as Ra increases, Sh increases. The contribution of natural convection compared to that of forced convection is measured by Ri=Gr/Re². It is found that this ratio is approximately 20 times less than that for the laminar flow experiments, which suggests that the contribution of natural convection evaporation is smaller in the presence of forced convection turbulent flow than in laminar flow. Nevertheless, the effects of Ra exists and the experimental data in the turbulent region are correlated with X* and Ra, which results in

2.5 CONCLUSION Transfer coefficients for heat and mass transfer between air flows and building surfaces are the result of modelling assumptions under the boundary layer theory. For heat transfer coefficients a lot of experimental data is available to determine the convection transfer coefficient, both for natural and forced convection. Care must be taken when selecting the appropriate geometry and flow regime. Recently CFD simulations are also used for determining the heat transfer coefficient. The first results show that the accuracy is good. Further validation is needed.

Mass transfer coefficients are not readily determined experimentally. Little information can be found in literature. Mostly the heat transfer coefficient is determined and mass transfer is calculated with the heat and mass transfer analogy. Again, and even more, care must be taken when selecting the appropriate geometry and flow regime. New experimental methods were proposed during the annex but still a lot of development has to be done.

REFERENCES ASHRAE (1975) Task Group, Procedure for determining heating and cooling loads for computerising energy calculations, in: Algorithms for Building Heat Transfer Subroutines, ASHRAE Publications, New York. Alamdari F. and Hammond G.P. (1983). Improved data correlations for buoyancy-driven convection in rooms. Building Services Engineering Research and Technology 4 (3): 106-112. Awbi H.B. and Hatton A. (1999). Natural convection from heated room surfaces. Energy and Buildings 30(3): 233-244. Awbi H.B. and Hatton A. (2000). Mixed convection from heated room surfaces. Energy and Buildings 32(2): 153-166. Beausoleil-Morrison I. (1999). Modelling mixed convection heat transfer at internal building surfaces. Proc. International Building Performance Simulation Association. Kyoto, Japan. Beausoleil-Morrison I. (2000). The adaptive coupling of heat and air flow modelling within dynamic whole-building simulation. Ph.D. thesis, University of Strathclyde, Glasgow, UK. Bednar, T. & Dreyer, J. (2003). Determination of moisture surface transfer coefficients under transient conditions. Proceedings of the 2nd International Conference on Building Physics, Leuven, Belgium, p.233-236. ISBN 90 5809 565 7. Chilton, T.H. and Colburn. A.P., (1934), Mass Transfer (Absorption) Coefficients Prediction from Data on Heat Transfer and Fluid Friction. Industrial and Engineering Chemistry,. 26: 1183-1187. CIBSE (1986). CIBSE Guide, Vols. A, B and C, CIBSE, London. Clarke J.A. (2001) Energy simulation in building design. 2nd Edition. Oxford, Butterworth-Heinemann. Colburn, A.P., (1933), A method of correlating forced convection heat transfer data and a comparison with fluid friction. Transactions of the American Institute of Chemical Engineers,. 29: 174-210.

Fisher D.E. (1995). An experimental investigation of mixed convection heat transfer in a rectangular enclosure. Ph.D. thesis, University of Illinois, Urbana, USA. Fisher D.E. and Pedersen C.O. (1997). Convective heat transfer in building energy and thermal load calculations. ASHRAE Transactions 103 (2): 137-148. Hansen, K.(1989). Equipment for and results of water vapour transmission tests using cup methods. Proceedings from the ICHMT Symposium .Heat and Mass Transfer in Building Materials and Structures.. Dubrovnik, Yugoslavia.

Iskra CR, Simonson CJ (2007) Convective mass transfer coefficient for a hydrodynamically developed airflow in a short rectangular duct. International Journal of Heat and Mass Transfer 50: 2376-2393 Judkoff R.D., Neymark J.S. (1995), Building Energy Simulation Test (BESTEST) and Diagnostic Method, NREL/TP-472-6231, Golden, Colorado National Renewable Energy Laboratory. Kaya A, Aydin O, Dincer I (2007) Numerical modeling of heat and mass transfer during forced convection drying of rectangular moist objects. International Journal of Heat and Mass Transfer 49: 3094-3103 Khalifa A.J.N. (1989). Heat transfer processes in buildings. Ph.D. Thesis, University of Wales College of Cardiff, Cardiff, UK. Khalifa A.J.N. (2001). Natural convective heat transfer coefficient – a review: I. Isolated vertical and horizontal surfaces. Energy Conversion and Management 42(4): 491-504. Khalifa A.J.N. (2001). Natural convective heat transfer coefficient – a review: II. Surfaces in two- and three-dimensional enclosures. Energy Conversion and Management 42(4): 505-517. Khalifa A.J.N. and M. R.H. (1990). Validation of heat transfer coefficients on interior building surfaces using a real-sized indoor test cell. International Journal of Heat and Mass Transfer 33(10): 2219-2236. Kays WM, Crawford ME (1993), Convective Heat and Mass Transfer, McGraw-Hill. Emmel M, Abadie M, Mendes N (2007) New external convective heat transfer coefficient correlations for isolated low-rise buildings Energy and Buildings 39 335–342 Min T., Schutrum L., et al. (1956). Natural convection and radiation in a panel heated room. ASHRAE Transactions 62: 337-358. Novoselac A. (2005). Combined airflow and energy simulation program for building mechanical system design. Ph.D. thesis, Pennsylvania State University, Pennsylvania, USA. prEN 15026, 2004, Hygrothermal performance of building components and building elements – Assessment of moisture transfer by numerical simulation.

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Spitler J.D., Pedersen C.O., et al. (1991a). An experimental facility for investigation of interior convective heat transfer. ASHRAE Transactions 97(1): 497-504. Spitler J.D., Pedersen C.O., et al. (1991b). Interior convective heat transfer in buildings with large ventilative flow rates. ASHRAE Transactions 97(1): 505-515. Swartz B. (1972) Die Wärme- und Stoffübertragung an Ausswandoberflächen Dissertation des Verfassers an der Universität Stuttgart, Institut für Bauphysic Fraunhofer-Geselschaft Aussenstelle Holzkirchen. Tremblay C, Cloutier A, Fortin Y (2000) Experimental determination of the convective heat and mass transfer coefficients for wood drying. Wood Science and Technology 34: 253-276 Wadso L (1993) Surface Mass-Transfer Coefficients for Wood. Drying Technology 11: 1227-1249 Welty JR, Wicks CE, Wilson RE, Rorrer G (2001), Fundamentals of Momentum, Heat and Mass Transfer, John Wiley & Sons. Worch A (2004) The Behaviour of Vapour Transfer on Building Material Surfaces: The Vapour Transfer Resistance. Journal of Thermal Envelope and Building Science 28: 187-200 DOI 10.1177/1097196304044398 Zhang LZ, Niu JL (2003) Laminar fluid flow and mass transfer in a standard field and laboratory emission cell. International Journal of Heat and Mass Transfer 46: 91-100 Papers presented during ANNEX 41

A41-T3-C-04-7 D. Derome, Experimental determination of the convective mass transfer coefficient A41-T3-Dk-05-4 L Hedegaard Mortensen, C. Rode, R Peuhkuri Effect of airflow velocity on moisture exchange at surfaces A41-T3-N-06-2 G Talev, A Gustavsen and E Næss The influence of air velocity and transport properties on the surface mass transfer coefficient in a rectangular tunnel – theory and experiments A41-T3-C-06-3 C Iskra, CJ. Simonson Effect of air humidity on the convective mass transfer coefficient in a rectangular duct A41-T3-Br-07-2 Marcelo G. Emmel, Marc O. Abadie, Nathan Mendes New external convective heat transfer coefficient correlations for isolated low-rise buildings A41-T3-B-07-4 H.-J. Steeman, A. Janssens, M. De Paepe About the use of the heat and mass analogy in building simulation