[en] Understanding heat and mass transfers in porous materials is crucial in many areas of scientific research. Mathematical models have constantly evolved, their differences lying mainly in the choice of the driving potentials used to describe moisture flows, as well as in the complexity of characterizing the physical phenomena involved. Models developed in the field of Building Physics (HAM models) are used to describe the behavior of envelope parts and assess their impact on user comfort and energy performance. The water balance equation can be described in many ways; it is a function of the boundary conditions considered and the fact they induce high or low water content in the porous materials used.
This paper gives an overview of various formulations for this equation that are found in the Building Physics literature. It focuses first on the physically based formulation of moisture balance, drawing on the Representative Elementary Volume (REV) concept, coupled with thermodynamic flow rates description. This is then reformulated in line with various main moisture state variables offering a wide variety of expressions that are compared with available models. This approach provides access to all secondary transport coefficients associated with the process of mathematical transformation. Particular emphasis is placed on the moisture storage function choice and its impact on the final mathematical formulations. [fr] La compréhension des transferts de chaleur et de masse dans les milieux poreux est cruciale dans de nombreuses disciplines scientifiques. Les modèles mathématiques ont constamment évolués par se différencier principalement par les potentiels moteurs utilisés pour décrire les flux d'eau, ainsi que par la complexité de la description des phénomènes physiques impliqués. En Physique du Bâtiment, les modèles hygrothermiques (modèles HAM) sont importants pour décrire le comportement des parois et ainsi déterminer leur impact sur le confort intérieur autant que la performance énergétique. L'équation de bilan hydrique peut y être décrite de multiple manières et est fonction du cas étudié et le fait qu'il induise des basses ou hautes teneurs en eau dans les matériaux de construction.
Cet article propose une synthèse des différentes formes que peut prendre cette équation dans la littérature scientifique. Nous proposons de partir de l'équation de bilan hydrique physiquement basée, héritée du concept de Volume Elémentaire représentatif et de la description thermodynamique des flux. Celle-ci est ensuite reformulée en utilisant différentes variables d'état principales, offrant une grande variété d'expressions finales qui sont comparées aux modèles disponibles. La démarche offre l'accès à l'ensemble des coefficients de transport secondaires liés au processus de transformation mathématique. Un accent particulier est également porté sur le choix de la fonction de stockage d'humidité et sur son impact sur les formulations finales obtenues.
Disciplines :
Materials science & engineering
Author, co-author :
Dubois, Samuel ; Université de Liège - ULiège > Sciences et technologie de l'environnement > Agriculture de précision
Lebeau, Frédéric ; Université de Liège - ULiège > Sciences et technologie de l'environnement > Agriculture de précision
Evrard, Arnaud ; Université de Liège - ULiège > Sciences et technologie de l'environnement > Agriculture de précision
Language :
English
Title :
Non-isothermal moisture balance equation in porous media: a review of mathematical formulations in Building Physics
Alternative titles :
[fr] Equation d'équilibre d'humidité dans les matériaux poreux en conditions non-isothermiques: une synthèse des formulations mathématiques en Physique du Bâtiment
Publication date :
September 2014
Journal title :
Biotechnologie, Agronomie, Société et Environnement
ISSN :
1370-6233
eISSN :
1780-4507
Publisher :
Presses Agronomiques de Gembloux, Gembloux, Belgium
Volume :
18
Issue :
3
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
FRIA - Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture
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