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Building and Environment 81 (2014) 340e353

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Building and Environment

journal homepage: www.elsevier .com/locate/bui ldenv

Validation of a coupled heat, vapour and liquid moisture transportmodel for porous materials implemented in CFD

M. Van Belleghem a, *, M. Steeman b, H. Janssen c, A. Janssens d, M. De Paepe a

a Ghent University, Department of Flow, Heat and Combustion Mechanics, Sint-Pietersnieuwstraat 40, B-9000 Gent, Belgiumb Ghent University, Department of Industrial Technology and Construction, Valentin Vaerwijckweg 1, B-9000 Gent, Belgiumc Building Physics Section, Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40, B-3000 Leuven, Belgiumd Ghent University, Department of Architecture and Urban Planning, Jozef Plateaustraat 22, B-9000 Gent, Belgium

a r t i c l e i n f o

Article history:Received 18 December 2013Received in revised form15 June 2014Accepted 17 June 2014Available online 10 July 2014

Keywords:Heat and moisture transferHAMCFDPorous materialDrying

* Corresponding author. Tel.: þ32 92643289; fax: þE-mail address: marnix.vanbelleghem@UGent.be (

http://dx.doi.org/10.1016/j.buildenv.2014.06.0240360-1323/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

Moisture-related damage is an important issue when looking at the performance of building envelopes.In order to accurately predict the moisture behaviour of building components, building designers canresort to Heat, Air and Moisture (HAM) models. In this paper a newly developed heat and mass transfermodel that is implemented in a 3D finite volume solver, Fluent®, is presented. This allows a simultaneousmodelling approach of both the convective conditions surrounding a porous material and the heat andmoisture transport in the porous material governed by diffusion. Unlike most HAM models that oftenconfine to constant convective transport coefficients it is now possible to better predict these convectiveboundary conditions. An important application of the model is the convective drying of porous buildingmaterials. Especially during the first drying stage, the drying rate is determined by the convectiveboundary conditions. The model was validated against a convective drying experiment from literature, inwhich a saturated ceramic brick sample is dried by flowing dry air over one side of the sample surface.Temperature and relative humidity measurements at different depths in the sample, moisture distri-bution profiles and mass loss measurements were compared with simulation results. An overall goodagreement between the coupled model and the experiments was found, however, the model predictedthe constant drying rate period better than the falling rate period. This was improved by adjusting thematerial properties. The adjustment of the material properties was supported by neutron radiographymeasurements.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

During the last decades the requirements for quality of buildingsand its envelopes have drastically increased. Where before themain function of a building was to protect people from outsideweather conditions, nowadays building users demand high-performance buildings with comfortable temperature and humid-ity levels without excessive energy use. However, damage to thebuilding envelope can reduce the building performance to a greatextent. This damage is often moisture-related and may affect theindoor comfort and indoor air quality [1,2], energy efficiency [3,4],human health and durability [5]. In order to prevent moisture-related damage, building designers need reliable predictive tools

32 92643575.M. Van Belleghem).

which can help them to design high performance buildingenvelopes.

Modelling tools describing the moisture behaviour of buildingsand its envelopes are very useful to predict and evaluate moisturerelated problems. HAM (Heat, Air and Moisture) models arefrequently being used to solve the combined transport of heat andmoisture in building components. Nowadays, a wide variety ofmodelling tools are available [6].

These HAM models can be combined with other models toimprove their performance. Examples are combined BES-HAMmodels [7,8] and CFD-HAM models [9e11]. In BES-HAM models,HAM is combined with building energy simulations to improve theprediction of building energy performance by including the hy-groscopic behaviour of building materials. In combined CFD-HAMmodels, HAM is coupled with computational fluid dynamics tobetter incorporate the coupled effect of convective transport of heatand moisture in the air and in the porous material. Steeman et al.[9] developed a coupled CFD-HAM model for the assessment of

Nomenclature

cp specific heat J/kgKC specific heat capacity J/kgKCb Stefan Boltzmann constant (5.67 � 10�8 W/m2K4)Dva diffusivity of water vapour in air m2/sE total energy Jg moisture flux kg/m2sh specific enthalpy J/kgh heat transfer coefficient (convection and radiation) W/

m2KhT convective heat transfer coefficient W/m2KhYm convective mass transfer coefficient s/mKl liquid permeability sL latent heat J/kgP pressure Papv partial vapour pressure Papc capillary pressure Paq heat flux W/m2

RH relative humidityRv specific gas constant of water vapour J/kgKT temperature Kv velocity m/sw moisture content kg/m3

Y mass fraction kg/kg

Greek symbolsd diffusion coefficient sε emissivityl heat conductivity W/mKm water vapour diffusion resistance factorr density kg/m3

j0 open porosity

Subscriptscap capillarys surfacel liquidmat materialop operatingrad radiationref referencesat saturationv vapour

AcronymsBES building energy simulationCFD computational fluid dynamicsHAM Heat, Air and Moisture

Dry

ing

rate

Time

First drying stage

Second drying stage

FRP

CRP

Fig. 1. Typical surface averaged drying rate (the dashed line indicates the drying rate incase the initial temperature is higher or lower than the wet bulb temperature), basedon [51].

M. Van Belleghem et al. / Building and Environment 81 (2014) 340e353 341

moisture-related damage in hygroscopic materials. By imple-menting a detailed HAM model into an existing CFD solver(Fluent®) he was able to model the heat and moisture transport inthe air and porousmaterial simultaneously. The coupledmodel wasvalidated using climate chamber experiments [12]. However,Steeman only modelled vapour diffusion as a transport mechanismin the porous material. With the model, it was possible to predictthe microclimate around valuable objects such as paintings. Otherattempts of combining CFD and HAM can be found in Mortensenet al. [13] and Defraeye et al. [14]. Defraeye applied an externalcoupling procedure and used a separate CFD and HAM modelwhich were then combined by transferring and setting theboundary conditions from one model to the other.

These recent attempts to combine existing HAM models withCFD showed to be promising. They allow a more detailed and ac-curate modelling of the influence of convection on the heat andmoisture transport in porous materials. However the developmentof these hygrothermal models is still on-going.

In this paper, a newly developed CFD-HAMmodel is described inwhich the heat and moisture transport equations for porous ma-terials are implemented into a commercial available CFD solver,Fluent®. The model includes vapour as well as liquid water trans-port. Since it is implemented into an existing CFD solver it is easierto combine it with convective transport in the air surrounding theporous material. The model is therefore specifically suited to studycases where convective boundary conditions are dominant orwhere the interaction of transport in the air and transport in theporous material is important. A few examples of such cases are theeffect of microclimates on historical artefacts [9], drying of buildingmaterials during production [15], drying of building envelopes afterrain, evaporative cooling of buildings and street canyons [16], etc.

Before this model can be applied to actual case studies, it is firstextensively validated. This paper will focus on this model valida-tion. It will highlight some important aspects when modellingcombined heat and moisture transport in porous materials, such asnumerical implementation of boundary conditions, the importanceof correct material properties and the choice of the driving

potentials to be used. In a follow-up paper a case study will beelaborated [17].

2. State of the art in convective drying modelling

In buildings, drying almost always occurs by convection. If thepartial vapour pressure of the air is lower than the vapour pressureat the surface of a porous material, moisture will be transferred tothe air and is transported away from the surface by the moving air.

Fig. 1 qualitatively depicts a typical drying rate curve of acapillary active hygroscopic material. At first, free moisture at thematerial surface evaporates from the surface and the drying rate isdetermined by the diffusion rate of water vapour into the sur-rounding air. During this constant drying rate period (CRP), mois-ture is transported from the inside of the porous material to thesurface by capillary forces. As long as this transport can sustain theevaporation rate from the surface, the drying rate will remainconstant.

M. Van Belleghem et al. / Building and Environment 81 (2014) 340e353342

If the moisture content reaches a critical level at which themoisture can no longer reach the surface at a sufficient rate, furtherdrying will cause the surface relative humidity to drop below 100%.This is the start of the second drying stage or the falling rate period(FRP). The drying rate is determined by the internal moisturediffusion transport as a result of moisture concentration gradientsin the material. As the material dries out, moisture movementdecreases further and consequently the drying rate drops. Thedrying rate continues to fall until the moisture content inside thematerial is in equilibriumwith the surrounding air. At that point thedrying rate becomes zero and drying stops.

During the CRP the temperature at the surface drops close to thewet bulb temperature. If the starting temperature in the material ishigher than the wet bulb temperature, the temperature will start todrop and accordingly the drying rate will also drop. On the otherhand, when initially the temperature is lower than the wet bulbtemperature, the material temperature starts to rise and so will thedrying rate (dashed lines in Fig. 1).

In literature, a wide range of drying models is available. Adistinction is made between analytical and numerical models. Inthe following sections, a short overview is given of the state-of-the-art modelling approaches for combined heat and mass transportduring convective drying in air.

2.1. Analytical modelling

Analytical models such as 1D models assuming constant diffu-sivity, only apply to simplified drying cases. The applied boundaryconditions are fixed temperature and humidity (Dirichlet boundaryconditions), fixed fluxes (Neumann boundary conditions) or fixedtransfer coefficients (Robin boundary conditions).

Milly [18] and more recently Abahri et al. [19] developed ananalytical solution for a coupled 1D heat and moisture transferproblem. Their models are however limited to Dirichlet and Neu-mann boundary conditions and are not sufficient when convectivedrying is studied. To model convective drying, at least a Robinboundary condition is needed. If more complex boundary condi-tions are present such as spatially are even temporally varyingboundary conditions, 1D analytical models are no longer sufficient.

Moreover, most convective drying processes cannot bemodelled using simplifications such as constant diffusivity. Formost materials and in particular building materials, the diffusivityshows a strong non-linear behaviour as function of moisture con-tent. In literature, some solutions to non-linear diffusivity can befound, e.g. Landman et al. [20] looked at the drying process of abrick.

Analytical solutions can thus only be used when simplegeometrical configurations, material properties and boundaryconditions are considered. As soon as more complex and realisticboundary conditions are to be solved, as is often the case in thebuilding context, analytical models no longer work. Buildingcomponents are generally composed of multiple layers, insertingstrong heterogeneity into the problem. At the same time theboundary conditions are not fixed in time and space, resulting intemporal and spatial distributions of temperature and moisture.Consequently, it is not feasible to solve all coupled heat and masstransport problems, especially drying problems, by simple 1Danalytical approaches.

2.2. Numerical modelling: predetermined transfer coefficients

Numerical models can be used to solve complex 2D or 3D con-figurations and to overcome some of the issues related to analyticalmodels. To incorporate the influence of airflow properties onconvective drying without modelling the convection in the air

simultaneously with the transport in the porous material, re-searchers often resort to transfer coefficients.

The simplest approach is using constant (averaged) transfercoefficients. Most HAM models use this method [7,21,22]. Bergeret al. [23] were able to study drying phenomena using a 1D finitedifference model with constant heat and mass transfer coefficientsas boundary conditions. Furthermore, their study showed that theconvective transfer coefficient determined the drying rate duringthe CRP. During the FRP the drying rate is mostly determined by theinternal transport properties and the impact of the convectivetransfer coefficients is negligible. Although these conclusions werederived with a simplified 1D model, they are generally valid.

The use of constant transfer coefficients is however only valid ifthe flow is fully developed which is often not the case even forsimple geometrical conditions. The presence of developingboundary layers or complex geometries with leading edge effects,vortex shedding, reattachment and stagnation zones may lead tolarge distributions of transfer coefficient values along the surface.Furthermore, several researchers found that the leading edge effecthas a significant impact especially during the CRP [24e26]. E.g.Masmoudi et al. [24] found that simplifying drying problems to 1Dproblems is not generally applicable because the leading edge effectwill be significant if the sample size is not clearly larger than themass or temperature boundary leading edge zones. Also Sho-kouhmand et al. [26] found that the leading edge effect was crucialin the determination of the drying time.

A more accurate and detailed study of the convective dryingprocess is possible when spatially varying transfer coefficients areused. These coefficients can be derived from analytical solutions forsimple cases or from CFD solutions whenmore complex geometriesand flow conditions are present.

The most common approach to determine the transfer co-efficients from CFD is by solving the flow with the assumption ofconstant boundary temperature and mass fraction [25,27]. Forconvective drying this approach is only strictly applicable duringthe CRP when the surface temperature is almost constant and nearto the wet bulb temperature and the surface mass fraction corre-sponds with the saturation mass fraction for that temperature.Nevertheless this approach is often used with reasonably goodresults.

2.3. Numerical modelling: coupling HAM with CFD

In the drying models discussed up till now the flow field isassumed to be steady and solved separately from the materialmodel [28]. This can be justified if the heat and mass transfers arelow and if the fluxes through the solidefluid interface do notdisturb the velocity field. The variations in air density are ignoredand air is considered incompressible. The heat and mass transfercoefficients are then determined by solving transport in the air onlyonce and assuming constant boundary conditions at the materialsurface (temperature and moisture concentration).

When the surface of a porous material starts to dry out, largetemperature and moisture distributions along the surface canoccur. Strictly speaking, the assumption of constant boundaryconditions is then no longer valid. For instance Masmoudi et al. [24]showed the effect of heterogeneities in the moisture content dis-tribution at the surface (such as dry zones) on the transfer at theinterface. The transfer coefficients clearly showed dependency onthe surface moisture distribution. Similar results were found byDefraeye et al. [14].

To implement these effects of varying transfer coefficients, it ispossible to use CFD as a tool to predict the transfer coefficients.When CFD and HAM are combined, the heat and mass transfer inthe air and the porous material can be solved simultaneously,

M. Van Belleghem et al. / Building and Environment 81 (2014) 340e353 343

without the need of estimated transfer coefficients. Such modelsare referred to in literature as conjugate models. Defraeye et al. [29]gives a good overview of recent developments in this field ofmodelling.

An early attempt to develop a coupled model was done by Amiret al. [30]. Amir et al. developed an implicit finite difference modelthat simultaneously solved the set of equations for a laminarboundary layer and a porous thick slab immersed in the boundarylayer. The laminar velocity boundary layer was considered to besteady and independent of heat andmoisture. This allowed them tosolve the velocity boundary layer separately from the heat andmoisture transport equation. The heat and moisture transportequation in the boundary layer and in the porous material werethen solved simultaneously and coupled.

Zeghmati et al. [31] continued the work of Amir et al. byextending the model to include transient laminar natural convec-tion. The Boussinesq approximationwas assumed for the boundarylayer momentum equation. Dolinskiy et al. [32] employed a similarmodel to simulate the drying of a thick slab for the initial period ofdrying (moisture content exceeded the maximum sorption mois-ture content). The authors found that the analogy between heatand mass transfer, often employed to predict transfer coefficients,was not applicable. This was due to the fact that, for maintainingthe analogy, not only the differential equations describing the heatand mass transfer have to be analogous, but also the boundaryconditions. They found that these boundary conditions could sub-stantially differ in time and space.

Because moisture transport in the air and in the material isdescribed by different potentials, conjugate drying models oftenuse two solvers: one to solve the transport equations in the air andone to solve the transport in the porousmaterial. When two solversare used, a specific solution methodology is needed. Oliveira et al.[28] described such a solution procedure for laminar flow to studyconvective drying of a wood board and repeated the same proce-dure later to study soybean drying [33]. A finite element code wasdeveloped. In the first step the continuity and momentum equa-tions in the air were solved separately. This is allowed if the flow isassumed steady and if the impact of density on the flow isneglected. The velocity field obtained from this calculation wasassumed invariable during the rest of the simulation. Next theboundary layer was solved using boundary conditions of the firstkind (constant temperature and concentration). The results of thisnumerical analysis were used to determine the heat and moisturefluxes at the surface. These fluxes were used as boundary condi-tions of the second kind for the porous material. Transport in theporous material was then solved. The temperature and moisturedistribution in the porous material provided new boundary con-ditions for the air side for the next time step. This procedure wasrepeated until the final drying time is reached.

This explicit time marching procedure was also used by Mur-ugesan et al. [34]. They developed a 2D finite element model tostudy the drying behaviour of ceramic brick. It was stated thatbuoyancy can have a significant effect on the transport mechanismin the air andmust be taken into account by allowing changes of theflow field over time.

When explicit coupling procedures are used, two separatesolvers can be used. This brings along the advantage that twoseparately developed models can be coupled and the developer ofthe drying model should only be concerned with the imple-mentation of the coupling procedure. For example Gnoth et al.[35] developed a coupling procedure between a CFD modeldeveloped for cavities and a commercially available HAM model,Delphin® [22].

Defraeye et al. [11] coupled the commercial CFD package Fluent®

with an in house developed HAM model HAMFEM [36]. When

using an explicit coupling procedure, too large time steps will causeinstability. Time steps should be small so that heat and mass fluxesat the material boundary do not change during a time step.Defraeye improved convergence by using an adaptive time step-ping algorithm. This ensured that the optimal time step was usedduring the simulations. Nevertheless a long computational timewas still needed even for relatively simple cases.

In literature, examples can be found where an implicit couplingis used for the heat and moisture transport equations. The un-steadiness that the explicit models are facing, is overcome and asignificant reduction of computational time is noticed. De Boniset al. [37] developed a finite element model using a commercialfinite element package to study the performance of the dryingprocess of fresh-cut vegetables. Lamnatou et al. [38,39] developed afinite volume model to study the drying of apple slices.

Finally a hybrid approach is reported in literature. Saneinejadet al. [16] coupled a model for heat and mass transport with acommercial CFD model (Fluent®) and a radiation model to studythe heat and moisture transport in a street canyon. Instead ofcalculating the fluxes at the air side and passing them to the ma-terial side explicitly, the transfer coefficients were calculated first atthe air side. These transfer coefficients were then passed to thematerial side where they were implemented as an implicitboundary condition. This significantly improved convergence andsolution stability.

3. Coupled heat and moisture model including vapour andliquid water transport

3.1. Moisture transport in porous materials

Moisture in a building context can exist in three phases: vapour,liquid and solid (ice). In the present model ice and ice formation areneglected. The two remaining phases can both be stored andtransported in a porous material. The moisture content in theporous material w is the sum of the vapour content wv and theliquid content wl. The vapour content is much smaller than theliquid content and is often neglected. The moisture flux in thematerial g is the result of a vapour flux gv and liquid flux gl. This is ofcourse only an approximation since both transport mechanismscan strictly speaking not be separated. Convection of air in theporous material is neglected. The vapour diffusion flux in a porousmaterial can be described by an adjusted Fick's diffusion law.

g!v ¼ �rDva

mVY ¼ �dvVpv (1)

In this equation the total pressure is assumed constant, allowingthe use of partial vapour pressure pv instead of mass fraction Y asdriving potential. For very small pores vapour diffusion can nolonger be described by Fick's law. At these small scales collisions ofvapour molecules and pore walls become more frequent than col-lisions between molecules. The vapour transport is than referred toas Knudsen diffusion or effusion. This Knudsen diffusion is alsodriven by vapour pressure gradients. To simplify the current model,the Knudsen diffusion is not modelled separately but its effect isassumed to be incorporated in the vapour diffusion resistancefactor.

In these equations for diffusion the thermal diffusion or Soreteffect is neglected. It was stated in Ref. [40] and shown byWhitaker[41] and Janssen [42] that this effect is small compared to theconcentration diffusion.

The liquid flux is described by Darcy's law:

g!l ¼ �KlVpc (2)

M. Van Belleghem et al. / Building and Environment 81 (2014) 340e353344

The driving force for the liquid transport is the gradient incapillary pressure. The moisture transport equation then results in:

vwvt

¼ V$ð g!v þ g!lÞ ¼ V$

�Dva

mRvTVpv þ KlVpc

�(3)

It is now possible to transform this equation so that only twoindependent state variables remain. In this work temperature andcapillary pressure are used in analogy to the work of Grunewald[43]. The partial vapour pressure is related to the relative humidity(RH ¼ pv/pvsat) and this relative humidity is in turn related to thecapillary pressure by Kelvin's law (Eq. (4)).

pc ¼ rlRvT ln RH (4)

This results in the following equation for themoisture balance ina porous material:

vwvpc

vpcvt

¼V$ðKlVpcÞþV$Dva

mRvT

�rv

rlVpcþ

�RH

vpsatvT

�pv lnRHT

�VT�

(5)

To solve Eq. (5) threematerial properties are needed: the vapourdiffusion resistance factor m, the liquid permeability Kl and themoisture capacity vw/vpc.

0

0,005

0,01

0,015

0,02

0,025

0,03

0 10 20 30 40

Mas

s Fr

actio

n [k

g/kg

]

Temperature [°C]

3

Saturation line

2 1

Fig. 2. Psychrometric chart, saturation mass fraction indicated in blue. (For interpre-tation of the references to colour in this figure legend, the reader is referred to the webversion of this article.)

3.2. Heat transport in porous materials

Next the heat transport equations can be derived. Only transportby diffusion is assumed in the porous materials that are studiedhere. Heat is thus only transported in the porous materials due toconduction on the one hand and diffusion of moisture on the otherhand. Water vapour diffusing through the porous material trans-ports sensible as well as latent heat.

Conductive heat transport in a (porous) material can bedescribed by Fourier's law for heat conduction:

q!¼ �lmatVT (6)

The conductivity of the porous material lmat is stronglydependent on the moisture content of the material since the con-ductivity of water differs from that of the material matrix.

Water is transported through a porous material as liquid andvapour resulting in a liquid and vapour flux. Along with the liquidwater, sensible heat is transported while sensible and latent heat istransported along with the vapour diffusion.

The potential energy and kinetic energy changes in the porousmaterial can be neglected and no chemical reactions occur in thematerial. The total energy of the porous material E is thus the sumof the energy stored in the material matrix and the energy stored inthe liquid water and water vapour present in the material. Theenergy balance equation thus states that a change in stored energyis due to heat conduction and transport of latent and sensible heatalong with the moisture transport:

vEvt

¼ v

vtðrmathmat þwlhl þwvhvÞ

¼ ðrmatCmat þwlCl þwvCvÞ vTvt

þ ClTvwl

vtþ ðCvT þ LÞ vwv

vt¼ V$ðlmatVT � ClTgl � ðCvT þ LÞ g!vÞ

(7)

rmat and Cmat are the dry porous material's density and heat ca-pacity respectively. The liquid moisture content and vapour mois-ture content can be linked to the total moisture by the openporosity, taking into account that:

w ¼ wl þwv (8)

and

j0 ¼ wl

rlþwv

rv(9)

3.3. Mass fraction or capillary pressure?

When only vapour diffusion is considered, the mass fraction ofwater vapour can be used as transport potential as for exampleproposed by Steeman et al. [9]. However using mass fraction astransport potential in a porous material when liquid transport ispresent, causes some difficulties as will be discussed in thissection.

Transforming Darcy's law (Eq. (2)) for liquid transport fromcapillary pressure pc to mass fraction Y results in:

g!l ¼ �KlVpc ¼ �KlvpcvRH

vRHvY

VY � KlvpcvT

VT (10)

with

vpcvRH

¼ rlRvTRH

(11)

vpcvT

¼ rlRv ln RHþ rlRvTRH

vRHvT

(12)

It is thus mathematically possible to write Eq. (5) with massfraction and temperature as the transported variables instead ofcapillary pressure and temperature. Difficulties in solving thismodel arise however when relative humidities near to 100% areencountered. This high relative humidity is typical when liquidmoisture transport is present. Fig. 2 illustrates what happenswhen the mass fraction is near to the saturation mass fraction.This figure shows a psychometric chart with the mass fraction onthe vertical axis and the temperature on the horizontal axis. Thefigure starts from a state below the saturation line (situation ①).When the temperature is lowered, the mass fraction in the porousmaterial is constant at first. The state of the porous materialmoves along a horizontal line from situation ① to situation ②. Insituation ② the saturation mass fraction is reached. At tempera-ture T2 the air in the porous material cannot hold more watervapour than Y2. If the temperature would drop further to T3, themass fraction of water vapour in air is obliged to follow thesaturation line. This implies that at saturation the mass fraction

M. Van Belleghem et al. / Building and Environment 81 (2014) 340e353 345

becomes temperature dependent. However for a good numeri-cally solvable model, the transported variables should beindependent.

As long as the relative humidity stays well below saturation, thestate of the porousmaterial can be described by themass fraction Y.This is the casewhen only vapour transport is considered andwhentemperature changes are small. Steeman [9] confined his work tothese conditions and was thus able to use mass fraction and tem-perature as transported variables for moisture and energyrespectively.

Using mass fraction as transported variable is also allowed forisothermal liquid transport in porous materials. However, theassumption of isothermal conditions rarely holds. As an examplethe drying of a nearly saturated porous material is discussed.

A wet material that is nearly saturated will have a mass fractionof water vapour close to saturation and the relative humidity in thematerial will be almost 100%. During a convective drying process,water evaporates from the surface into the air flowing over theporous material. The amount of energy needed for this phasechange (from liquid to vapour state) is the latent heat of evapora-tion. This energy is taken from the surrounding air and the porousmaterial, thus resulting in a temperature drop of the material.When no other heat sources are present, the temperature of theporous material surface can drop to the wet bulb temperature. Thistemperature drop can be significant (e.g. air at 30 �C and 40% RHhas a wet bulb temperature of ±20 �C). Since the mass fraction wasalready near saturation, a sudden drop in the temperature wouldmean that the mass fraction would also have to decrease. In otherwords the mass fraction becomes temperature dependent. Themass fraction modelling approach proposed by Steeman [9] is thusno longer applicable for liquid transport phenomena such asconvective drying.

From this discussion it is clear that the mass fraction cannot beused as the transported variable if liquid transport is included.Therefore the capillary pressure is proposed as the transportedvariable. The capillary pressure is not restricted by saturationconditions and is a better way to describe the state of a wet (nearlysaturated) porous material.

3.4. Numerical implementation of the boundary conditions

As boundary conditions at the porous surfaces facing the air,heat andmass fluxed are imposed. These fluxes are calculated usingEqs. (13) and (14):

q ¼ hT�Tref � Ts

�(13)

g ¼ hYm�Yref � Ys

�(14)

Tref and Yref are reference values for temperature and massfraction taken outside the boundary layer and Ts and Ys are thetemperature and mass fraction at the surface of the porousmaterial.

The differential equations describing heat and moisture trans-port in the porous material are solved numerically together withthe boundary conditions using a finite volume solver. Therefore theproblem is discretized in time and space. To obtain a convergedsolution several iterations are needed within each time step. Whenthe current iteration is indicated with superscript m and the nextiteration is indicated with superscript mþ1, the flux boundaryconditions can be written as:

qmþ1 ¼ hT�Tref � Tmþ1

s

�(15)

gmþ1 ¼ hYm�Yref � Ymþ1

s

�(16)

This is the so-called implicit formulation. For the heat transportequation temperature is the transported variable which allows thedirect implementation of Eq. (15). However the mass transportequations use capillary pressure as transported variable, thus Eq.(16) has to be reformulated to capillary pressure. The mass fractionat the boundary Ys is a non-linear function of the capillary pressure.However Eq. (16) can be linearized around Ym

s .

gmþ1 ¼ hYm�Yref � Ymþ1

s

�¼ hYmYref � hYmY

mþ1s

¼ hYmYref � hYm

"psatrRvT

exp

pmþ1c

rlRvT

!#

zhYmYref � hYmpsatrRvT

�1

r lRvTexp

�pmc

rlRvT

�pmþ1c

þ exp�

pmcrlRvT

�� 1rlRvT

exp�

pmcrlRvT

�pmc

�(17)

4. Experimental validation

The coupled heat and moisture model is validated bymeans of aconvective drying experiment from literature [11]. In what follows,it will be shown that heat and mass transport cannot be solvedseparately when studying convective drying. At the same timedrying rates are strongly determined by convective transport in theair.

In the first section, the experimental setup will be shortlydescribed. Next, the simulation results of the coupled model arecompared with the experimental data. Finally, neutron radiographymeasurements showing the moisture distribution in the bricksample were compared with the results of the coupled model.

4.1. Experimental setup

Defraeye [11] constructed a small wind tunnel from transparentpolymethyl methacrylate (PMMA) to perform convective dryingexperiments on building materials such as ceramic brick. A sche-matic representation of the wind tunnel with the test section isfound in Fig. 3a. Air is drawn in by a fan, passes over a flowstraightener (honeycomb) and flows through a convergent sectionbefore entering the test section. A detail of the test section is foundin Fig. 3b.

The sample of ceramic brick measuring 10 mm by 30 mm by90 mm, was placed in a container of plexiglass (PMMA). Theplexiglass had a thickness of 4mm. The sample of ceramic brickwaswetted and placed in the wind tunnel in such a way that the topsurface of the sample faces the air flowing through the tunnel. Thesample was wetted to a moisture content of 126 kg/m3 whichcorresponds approximately to the capillary moisture content(130 kg/m3). At the bottom of the container a layer of 20 mm XPSinsulation was installed. The front and back side of the containerwere covered with 15 mm of XPS insulation, the side walls of thebrick sample were insulated with 30 mm of XPS. The sides of thesample were made impermeable for moisture. The open circuitwind tunnel was placed in a climate chamber where the meantemperature was set to 23.8 �C (with a standard deviation of 0.2 �C)and the mean relative humidity was set to 44% (with a standarddeviation of 0.8%).

In the experiments, dry air flows over the top surface of thebrick and the brick is dried out from one side, while the other sides

Fig. 3. Schematic representation of wind tunnel and test section used to perform drying experiments. Based on [11].

M. Van Belleghem et al. / Building and Environment 81 (2014) 340e353346

M. Van Belleghem et al. / Building and Environment 81 (2014) 340e353 347

are impermeable for moisture. During the drying experimenttemperatures at the side of the ceramic brick were measured withthermocouples. Fig. 3a shows the location of these thermocouples.In total 6 thermocouples were installed at a side wall. The tem-perature was measured at a depth of 10 mm, 20 mm and 30 mmfrom the materialeair interface and 10 mm in the lower insulation(at 40 mm from the interface). To measure the inflow effect andthe effect of a developing moisture and temperature boundarylayer, a thermocouple was installed upstream and downstream ofthe centre thermocouples, both at a depth of 10 mm. The accuracyof the thermocouples, as reported by Defraeye [11] was 0.1 �C. Theweight change of the test sample was continuously monitored by abalance. The balance was calibrated to an accuracy of 0.01 g but inpractice this accuracy was found to be 0.1 g due to the impact ofairflow on the balance. The velocity at the inlet of the test sectionand the turbulence intensity were measured with a PIV (particleimage velocimetry) system. Defraeye [11] performed an extensivestudy on the accuracy of these PIV measurements. He concludedthat a quantitative estimate of the uncertainty of the PIV mea-surements is difficult because of the presence of different sourcesof error in these measurement. Therefore best practice guidelineswere followed. To obtain a reliable time-averaged mean air ve-locity, sufficient statistically independent double PIV images haveto be taken. In his study 120 images at 2 Hz were found to besufficient. This led to an uncertainty of about 2% on the mean airvelocity.

The test section can be assumed symmetric along the x-axissince the flow in the channel was found to be two-dimensional dueto the high width to height ratio [44].

4.2. Simulation model and settings

The experiments of Defraeye were used as a validation study forthe newly developed coupled heat and moisture model. Pre-liminary simulations showed that 1D and 2D simulations were notsufficient to capture the heat and mass transport in the setupaccurately and to incorporate phenomena such as the leading edgeeffect [10]. Therefore, a complex 3D simulation model of the brickwas developed including the insulation and plexiglass out of whichthe sample container is built up.

Fig. 4. Schematic representation in 3D of the test sample.

Fig. 4 shows a 3D view of the test sample of ceramic brickembedded in the insulation and the plexiglass. The sample ofceramic brick measured 10 mm thick by 30 mm deep by 90 mmlong. Only half of the setup has been modelled due to symmetry,which considerably reduced the computational effort.

The inlet conditions of the air were measured by Defraeye [11]:the air inlet temperature was 23.8 �C (with a standard deviation of0.2 �C) and the air inlet relative humidity was 44% (with a standarddeviation of 0.8%). The temperature of the surroundings was con-stant and corresponded to the temperature of the climatic chamber(23.8 �C).

The side faces facing the climate chamber (bottom, front, backand left face) of the setupwere assumed impermeable formoisture.Moisture exchange is only possible at the top face. Heat can flowthrough all faces. At the side walls the heat flux is determined byEq. (13), with Ts the temperature at the outer surface of the plex-iglass and Tref the temperature of the surroundings (i.e. 23.8 �C).The heat transfer coefficient h is estimated at 8 W/m2K and in-corporates both the effect of convection and radiation.

Due to the 2D airflow in the wind tunnel, the heat and masstransfer at the top face of the brick was assumed two-dimensionaland varied along the length of the duct. The corresponding heatand mass transfer coefficients used for the simulations weredetermined by means of CFD simulations of the wind tunnelassuming a constant temperature at the bottom. Defraeyemeasured the velocity profile and turbulent intensity at the inlet ofthe test setup [11]. Fig. 5 shows these measured values for velocityand turbulent intensity. These measurements were used as inputfor the CFD simulation, together with the measured temperatureand humidity.

The computational domain for the CFD simulation of the air flowwas taken similar to that used by Defraeye [11] for his simulations.A 2D channel was simulated, corresponding to flow between twoparallel plates. The channel had a height of 10 mm as depicted inFig. 3a. An inflow section of 15 mm was taken and an outflowsection of 30 mm. These sections were adiabatic and impermeablefor moisture. An appropriate grid was built consisting out of 4x103

quadrilateral control volumes. The grid was dense near the surfacesof the parallel plates and coarser to the centre. Steady Reynolds-averaged NaviereStokes (RANS) was used in combination with aturbulence model. Here the realizable k-ε model was used withLRNM to take care of the viscosity affected region. Second orderdiscretisation schemes were used. The SIMPLE algorithm was usedfor pressureevelocity coupling. Pressure interpolation was secondorder.

The mass transfer coefficient was determined through the heatand mass analogy. This analogy was shown to be valid by Defraeye

Fig. 5. Velocity profile (m/s) and turbulence intensity (e) as measured by Defraeye[11].

Table 2Parameters in Eq. (22) [45].

i 1 2 3

ai 1.35e�5 4e�6 5e�7ni 6 2 0.7mi 0.8333 2 0.4wi 0.36 0.25 0.39wi adjusted 0.5 0.25 0.25Ks 1.15e�9t 4.003

M. Van Belleghem et al. / Building and Environment 81 (2014) 340e353348

[11] and by preliminary studies [10]. Especially during the constantdrying rate period, when the temperature and moisture massfraction at the surface are almost constant, this analogy applies. Apower-law approximation of these coefficients as a function of theposition in the duct is given by Eq. (18) a and b.

hT ðxÞ ¼ 7:7577x�0:2958 (18a)

hYmðxÞ ¼ rRvT5:514$10�8x�0:2958 (18b)

Radiation at the brickeair interface was taken into account in asimplified way by assuming that the brick top surface only sees theupper wall of the wind tunnel, which results in a view factor of 1.The temperature of the top wall of the wind tunnel was measured.An average value of 23.3 �C was found.

The radiant heat flux at the brickeair interface can be calculatedas:

qrad ¼ Cb1ε1þ 1

ε2� 1

�T4roof � T4s

�(19)

with qrad (W/m2) the radiant heat flux between the roof of thewindtunnel and the brick surface, Troof the temperature at the top wall ofthe wind tunnel, Ts the surface temperature of the brick and ε1 andε2 the emissivity of the roof and the brick surface, which areassumed to be 0.97 and 0.93 respectively.

For these simulations a grid sizing 114 � 93 � 35 was used(371,070 cells). The grid was denser near the top. A grid indepen-dency test was carried out by performing a simulation with adenser grid. This simulation showed no significant difference withthe original grid. Therefore, the original grid of 114 � 93 � 35 wasretained for the current simulations. For these transient simula-tions a time step of 60 s was taken. In total a drying period of 12 hwas simulated, resulting in a total of 720 time steps.

The material properties of ceramic brick that have been used inthe simulations are shown in Table 1. They have been determinedexperimentally by Ref. [45]. The vapour diffusion coefficient dv wasapproximated by Eq. (20) and the moisture retention curve w(pc)was formulated by Eq. (21) [45]:

dv ¼ 2:61� 10�5

mdryRvT

1��

wwcap

�

0:503�1�

�w

wcap

��2

þ 0:497

(20)

wðpcÞ ¼ wcap

"0:846

�1þ

�1:394� 10�5pc

�4��0:75

þ 0:154�1þ

�0:9011� 10�5pc

�1:69��0:408#

(21)

The liquid permeability Kl is given by Eq. (22) [45]. The corre-sponding coefficients are listed in Table 2.

Table 1Material properties of ceramic brick [45].

Property Value

Density r [kg/m3] 2087Thermal conductivity l [W/mK] 1 þ 0.0047 wSpecific heat cp [J/kgK] 840Water vapour resistance diffusion factor mdry [e] 24.79Capillary moisture content wcap [kg/m3] 130Open porosity j0 [e] 0.13

Kl ¼ KsX3

wi

�1þ ð�aipeÞ�ni

��mi

t

"i¼1

#

�

0BBBB@P3

i¼1aiwi

1�

"ð�aipcÞni

1þð�aipcÞni

#!mi

P3i¼1aiwi

1CCCCA (22)

4.3. Comparison between simulations and experiments

4.3.1. Temperature change and scaled mass lossTemperatures measured at depths of 10 mm, 20 mm, 30 mm (at

the interface brick/insulation) and 40mm (10mm in the insulation)are compared with the simulations. Fig. 6 compares the measuredtemperatures with the simulations. The dashed line shows thesimulation outcome using the original material properties as re-ported in Table 1 and Eqs. (20)e(22). The red and green lines inFig. 6 are explained in Section 4.4. A measurement uncertainty of0.1 �C was reported [11] and is indicated in Fig. 6.

Overall a good agreement between the model and the experi-ments is found. The largest deviations are found near the surface.The temperature at a depth of 10 mm is slightly underestimated bythe model (0.3e0.4 �C). Also the onset of the FRP (when the tem-perature starts to rise again) is delayed in the simulations (seeFig. 6(a)e(c)). This leads to a temperature mismatch of up to 1 �Cbetween measured and predicted temperatures. Nevertheless, theequilibrium temperature (the lowest temperatures in Fig. 6) isclosely approximated by the model (within the error bars). Deeperin the material, the approximation becomes even better. At a depthof 40 mm (10 mm in the insulation), the agreement is almostperfect (within the error bars). This indicates that the appliedboundary conditions closely approach reality.

Fig. 7 compares the measurements and simulation results of thetemperatures along the length of the sample at a depth of 10 mm inthe sample. Although there is no perfect match between simula-tions and experiments the trends are well predicted: the upstreamtemperature reaches the same equilibrium temperature as thecentre temperature both in the simulations and the measurements.However dry-out occurs sooner upstream which results in a fasteroccurring temperature rise upstream. Downstream the tempera-ture is higher both in themeasurements and in the simulations. Theonset of dry-out happens later here and this delays the temperaturerise.

During the experiments, the weight change of the sample wasalso monitored (Fig. 8). The mass loss was scaled using the initialmoisture content of the brick sample: i.e. 3.4 g. Due to this smallinitial moisture content and relative high weight of the sample andtest section itself (i.e. ±827 g), the weight change was difficult tomeasure. An uncertainty of 0.1 g on the weight measurement wasreported [11], the uncertainty on theweight changewas 0.14 g. Thisresulted in an uncertainty of 4% on the scaled mass loss.

Fig. 6. Comparison between heat and moisture transport model with original material data ( ), model with adjusted retention curve ( ) and model with adjusted liquidpermeability ( ). Temperature measurement indicated by (▪).

17

18

19

20

21

22

23

24

0 2 4 6 8 10 12Time [hours]

Tem

pera

ture

[°C

]

Fig. 7. Simulated temperature in the ceramic brick, upstream of the centre (blue), inthe centre (black) and downstream (red). Comparison with measurements upstream(B), centre (,) and downstream (:). (For interpretation of the references to colour inthis figure legend, the reader is referred to the web version of this article.)

Fig. 8. Scaled mass loss. Comparison of experiment (-), CFD-HAM simulation withoriginal material properties ( ), with adjusted retention curve ( ) and adjustedliquid permeability ( ).

M. Van Belleghem et al. / Building and Environment 81 (2014) 340e353 349

Fig. 9. Comparison of the measured ( ) and simulated ( ) moisture content dis-tribution in the ceramic brick sample over time. Timedifference between two lines is 1 h.

M. Van Belleghem et al. / Building and Environment 81 (2014) 340e353350

The experiments clearly show a constant slope in the mass losscurve for the first 3 h (Fig. 8). During this initial drying rate period(CRP) the moisture content in the brick decreases linearly. A similarduration was found in the simulations. Next, the FRP starts: this isshown by a decreasing slope of the mass loss curve in Fig. 8.Comparison of the measurements and the simulations shows thatthe mass loss during the CRP is well-predicted but that there is anoverestimation of the mass loss during the FRP.

4.3.2. Moisture distribution profilesIt is clear from the previous analysis that the model is able to

predict the correct trends but that there is still a significant devi-ation between the measured and predicted mass loss. To explainthe cause for this deviation, measurement data are needed of themoisture distribution inside the brick. Data provided by the SwissFederal Laboratories for Materials Science and Technology (EMPA)was therefore used to further study the moisture transport in theceramic brick. With neutron radiography this research group wasable tomeasure themoisture content evolution in the ceramic brickover the depth of the sample. More details on the used measure-ment setup can be found in Refs. [46e48].

Fig. 9a shows the comparison of the moisture content distri-bution in the ceramic brick over time for the simulation and themeasurements. This comparison shows that during the first hoursthe agreement is fairly good, but at later times (after 3 h) thesimulation shows a faster decrease of the moisture contentcompared to themeasurements. This is in agreement with themassmeasurements and simulation shown in Fig. 8, which showed agood agreement during the CRP (first 3 h) and afterwards anoverestimation of the simulated mass loss.

It should be noted that for a correct comparison between themeasured and the modelled moisture content only the central re-gion in the brick, between 0.5 cm and 2.5 cm, should be compared.This is due to some scattering that was present in the neutronradiography measurements. This resulted in a falsely decreasingmoisture content at the bottom of the sample and a too fastdecreasing moisture content at the top.

4.4. Influence of material properties

Material properties have a large impact on these simulations.Correct material properties play a major role in the validationprocess, since uncertainty on material properties can be large andthe consequences correspondingly. Previous studies have alreadyshown that the hygric material properties, namely retentioncurve, permeability and water vapour resistance diffusion factorare the most important [11,49,50]. Fig. 8 shows a systematicoverestimation of the mass loss in the brick, which raises thesuspicion that the deviation is caused by uncertainties in thematerial properties. Defraeye did not list uncertainties on themeasured material properties that he provided in his study [11],but he performed a similar study [50] on ceramic brick. In thispaper standard deviations on the measured material propertieswere listed. Table 3 lists these standard deviations as reported byDefraeye [50]

The comparison of measurements and simulations in Figs. 6 and8 showed that the first drying period is well captured. This suggeststhat the permeability and the retention curve at high moisturecontents agree well with reality. The large deviations occur duringthe second drying rate period.

To investigate the effect of the material properties on themodelling outcome, the main parameters (permeability, retentioncurve and water vapour resistance diffusion factor) were examinedcloser. First of all it was found that increasing the water vapourresistance diffusion factor from 24.79 to 32 had no significant

Table 3Standard deviations of material properties as listed by Ref. [50].

Property Standard deviation

r 1%cp 5%l 5%mdry 18%Wcap 5%Kl 1% on Kl, and 1% on pc on logelog scale

M. Van Belleghem et al. / Building and Environment 81 (2014) 340e353 351

impact on the mass loss in the brick and on the moisturedistribution.

Next the vapour retention curvewas adjusted in such away thatthe curve only changed at high capillary pressures, so it would notaffect the drying behaviour during the first drying period. Fig. 10shows the original retention curve as found by Ref. [45] and theadjusted curve. The adjusted moisture retention curve can beformulated by Eq. (23).

wðpcÞ ¼ wcap

"0:5�1þ

�1:394� 10�5pc

�4��0:75

þ 0:5�1þ

�0:9011� 10�5pc

�1:69��0:408#

(23)

Fig. 9b shows the simulation results of the moisture distributionfor the adjusted moisture retention curve. When comparing Fig. 9bwith Fig. 9a, a better agreement is shownwhen the retention curveis adjusted. However, the agreement only improves for the overallmoisture content in the brick. The distribution of the moisturecontent deviates from the one measured by neutron radiography.For the altered retention curve the drying front moves too fast intothe brick compared to the measurements.

Adjusting the retention curve thus improves the overall mois-ture content prediction, as also shown in Fig. 8, but does notimprove the moisture content distribution. This suggests that de-viations between measurements and simulations with the originalmaterial data cannot solely be caused by uncertainties in the esti-mated retention curve.

To further study this, the liquid permeability was also altered.The original retention curve [45] and the adjusted curve are shownin Fig. 11. The adjusted liquid permeability can be approximatedwith Eq. (22) and by using “wi adjusted” instead of “wi” as listed inTable 2.

Fig. 10. Retention curve of brick: original curve [45] ( ) and adjusted curve ( ).

By lowering the permeability, a better agreement can be foundbetween measurements and simulations as shown in Fig. 9c. Theagreement is also better for the overall moisture content (Fig. 8).Although uncertainty exists on all material parameters, in this caseit is most likely that the largest deviations are caused by the un-certainty on the liquid permeability.

Of course some deviations between the measurements and thesimulations can still be observed after the material properties areadjusted. This can be mainly attributed to uncertainties in theimplemented boundary and initial conditions.

During the simulations, the heat transfer coefficient at the sidewalls was estimated and the inlet temperature was assumed to beconstant, though in reality the temperature varied slightly. Also anuncertainty of 2% on the inlet velocity profile that was measuredusing PIV, was found [11].

Finally it can be stated that some of the deviations are caused byuncertainty in the numerical modelling, but this is rather difficult toquantify. Only an improvement of the modelling techniques canovercome or reduce this uncertainty. Possible uncertainties arisingfrom the numerical model are:

-Errors caused by discretisation-Errors caused by simplifications in the model (simplified radi-ation modelling, assuming perfect straight and aligned surfaces,assuming constant transfer coefficients at some surfaces …)

Of course, a model is always a simplification of reality. The art ofmodelling is to apply the correct choices for simplifications so thatthe simulation result is acceptably close to reality.

4.5. Discussion

Fig. 8 compares the mass loss computed with the original ma-terial data and the mass loss computed with the adjusted retentioncurve and liquid permeability. Both changes agree well with themass loss measurements. But, as shown in Fig. 9, a good predictionof the mass loss does not imply a good prediction of the moisturecontent distribution. It can thus be stated that both mass loss andmoisture distribution predictions should be validated before aconclusion can be drawn on the correctness of the model and theused material properties.

Nevertheless, a good agreement for moisture does not guar-antee a good agreement for temperature as is seen in Fig. 6. Sinceheat and moisture transport in porous materials are stronglycoupled, changes in retention curve or liquid permeability haveconsequences for both temperature and moisture distribution.

Fig. 11. Liquid permeability of ceramic brick: original curve [45] ( ) and adjustedcurve ( ).

M. Van Belleghem et al. / Building and Environment 81 (2014) 340e353352

Where before the model underestimated the temperature, themodel now seems to overestimate the temperature both for theadjusted retention curve and the adjusted liquid permeability.Since the model with the adjusted retention curve and the modelwith the adjusted permeability result in similar mass loss curves(Fig. 8), the drying rates for both cases will be similar. And since thetemperature in the brick is to a great extent determined by thedrying rate due to the latent heat loss, the predicted temperaturecurves are similar for both cases.

The original model thus underpredicts the temperaturewhereasthe adjusted models overpredict the temperature. However, themagnitude of difference between measurements and simulationsfor the original case and the altered cases is similar. Themodel withan adjusted retention curve and the model with an adjustedpermeability do not result in a worse agreement of temperature,but at the same time there is also no improvement. It is thusdifficult to make a sound conclusion on the impact that the ad-justments have on the temperature course in the material.

5. Conclusion

In this paper a newly developed coupled heat and moisturemodel including vapour and liquid moisture transport was pre-sented. The model enables to describe the coupled heat and masstransfer in porous building materials. Contrary to some heat andmoisture models that only include vapour transport, the newlydeveloped model has a broader application range, as it can be usedto study vapour diffusion through porous materials and capillarymoisture transport. The model lends itself to study the dryingphenomena of porous materials.

In this paper the new model was described and validatedagainst a drying experiment from literature, in which ceramic brickis used as a porous material. The validation study showed that theexperimental results agreed well with the simulations results of a3D model. Nevertheless, some deviations could be noted whichwere attributed to uncertainty of the material properties, especiallyof the liquid permeability and retention curve. By altering the liquidpermeability or retention curve, the agreement between simula-tions and measurements improved.

Comparison with neutron radiography measurements revealedthat a good agreement of the overall moisture content does notguarantee a good agreement of the moisture distribution in theporous material. The moisture distribution measurements showedthat the best agreement was found for an adjusted liquid perme-ability. Adjusting the sorption isotherm resulted in a drying frontmoving too fast into the porous material.

Acknowledgements

The results presented in this paper were obtained within theframe the research project IWT-SB/81322/Van Belleghem fundedby the Flemish Institute for the Promotion and Innovation by Sci-ence and Technology in Flanders and IWT SBO-050451 projectHeat, Air andMoisture Performance Engineering: AWhole BuildingApproach. Their financial support is gratefully acknowledged.

Special thanks go to Prof. Dominique Derome and Dr. PeterMoonen from EMPA Zurich and to Dr. Thijs Defraeye formKULeuven for their willingness to provide some of the necessarymeasurement data.

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