International Scientific Journal

Thermal Science - Online First

online first only

Convective and conductive thermal homogenization for nonsturated porous building materials: Application on the thermal conductivity tensor

Porous materials possess a complex structure on a microscopic scale and present strong heterogeneities, which makes their precise study extremely complex. In fact, the macroscopic behavior of these materials is strongly dependent on mechanisms that act to the scale of their components. The present work focus on the development of a macroscopic conductive; and convective fluid heat transfer model, with a heat source in the unsaturated porous materials. This model is established by periodic homogenization of energy conservation equations written on a microscopic scale in each phase (solid, liquid and gas). The resulting input parameters formulations of the sub model were explicitly identified. Numerical calculations of the homogenized thermal conductivity tensor are performed on a representative three-dimensional elementary cell of the porous medium. Finally, a sensitivity study of this tensor depending of the variation of the water content and porosity of the concerned elementary cell has been performed. This sensitivity is required to be considered in simulations to better understand the behavior of building materials and improve the prediction of energy performance.
PAPER REVISED: 2016-10-09
PAPER ACCEPTED: 2016-10-09
  1. Ferroukhi, MY., Djedjig, R., Belarbi, R., Limam, K., Abahri, K., Effect of Coupled Heat, Air and Moisture Transfers Modeling in the Wall on the Hygrothermal Behavior of Buildings, Energy Procedia, 6th International Building Physics Conference, IBPC, 78 (2015), pp. 2584-2589.
  2. Whitaker, S., Simultaneous Heat, Mass, and Momentum Transfer in Porous Media: A Theory of Drying. Advances in Heat Transfer, 13(1977), pp. 119-203.
  3. Whitaker, S., Advances in theory of fluid motion in porous media. Industrial & Engineering Chemistry, 61(1969), 12, pp. 14-28.
  4. Moyne, C., Batsale, J.C., Degiovanni, A., Approche expérimentale et théorique de la conductivité thermique des milieux poreux humides—II. Théorie, International Journal of Heat and Mass Transfer, 31(1988), 11, pp. 2319-2330.
  5. Goyeau, B., Macroscopic Conduction Models by Volume Averaging for Two-Phase Systems. In: Thermal Nanosystems and Nanomaterials, Springer Berlin Heidelberg, Berlin, Germany, 2009, pp. 95-105.
  6. Quintard, M., Whitaker, S., One- and Two-Equation Models for Transient Diffusion processes in Two-Phase Systems, Advances in Heat Transfer, 23(1993), pp. 369-464.
  7. Bourbatache, M.K., Modélisation du transfert des ions chlorures dans les matériaux cimentaires par homogénéisation périodique, Ph. D. thesis, La Rochelle University, FR, 2009.
  8. Sanchez-Palencia, E., Non-homogeneous media and vibration theory. Springer-Verlag, Berlin., New York, USA, 1980.
  9. Keller, J.B., Effective Behavior of Heterogeneous Media, in: Statistical Mechanics and Statistical Methods in Theory and Application, Springer US, Boston, MA, 1977, pp. 631-644.
  10. Auriault, J.L., Adler, P.M., Taylor dispersion in porous media: Analysis by multiple scale expansions, Advances in Water Resources, 18 (1995), 4, pp. 217-226.
  11. Bensoussan, A., Lions, J.L., Papanicolaou, G., Asymptotic analysis for periodic structures, Studies in mathematics and its applications, Elsevier North-Holland, Amsterdam ; New York : New York. 1978.
  12. Bourbatache, K., Millet, O., Aït-Mokhtar, A., Ionic transfer in charged porous media. Periodic homogenization and parametric study on 2D microstructures, International Journal of Heat and Mass Transfer, 55 (2012), 21-22, pp. 5979-5991.
  13. Auriault, J.L., Ene, H.I., Macroscopic modelling of heat transfer in composites with interfacial thermal barrier, International Journal of Heat and Mass Transfer, 37 (1994), 18, pp. 2885-2892.
  14. Auriault, J.L., Effective macroscopic description for heat conduction in periodic composites, International Journal of Heat and Mass Transfer, 26(1983), 6, pp. 861-869.
  15. Moyne, C., Amaral Souto, H.P., Multi-scale approach for conduction heat transfer: one- and two-equation models: Part 1: theory, Computational and Applied Mathematics, 33(2014), 2, pp. 257-274.
  16. Lewandowska, J., Laurent, J.P., Humidity transfer in unsaturated heterogeneous porous media by homogenization, Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy, 25(2000), 2, pp. 175-181.
  17. Mchirgui, W., Millet, O., Amiri, O., Modelling moisture transport for a predominant water vapour diffusion in a partially saturated porous media. European Journal of Environmental and Civil Engineering, 17(2013), 3, pp. 202-218.
  18. Auriault, J.L., Geindreau, C., Orgéas, L., Upscaling Forchheimer law, Transport in Porous Media 70(2007), 2, pp. 213-229.
  19. Allaire, G., Brizzi, R., Mikelić, A., Piatnitski, A., Two-scale expansion with drift approach to the Taylor dispersion for reactive transport through porous media, Chemical Engineering Science 65(2010), 7, pp. 2292-2300.
  20. Attinger, S., Dimitrova, J., Kinzelbach, W., Homogenization of the transport behavior of nonlinearly adsorbing pollutants in physically and chemically heterogeneous aquifers, Advances in Water Resources, 32(2009), 5, pp. 767-777.
  21. Bourbatache, K., Millet, O., Aït-Mokhtar, A., Amiri, O., Modeling the Chlorides Transport in Cementitious Materials By Periodic Homogenization, Transport in Porous Media 94(2012), 1, pp. 437-459.
  22. Auriault, J.L., Lewandowska, J., Diffusion non linéaire en milieux poreux, Comptes Rendus de l'Académie des Sciences, Series IIB., Mechanics-Physics-Chemistry-Astronomy, 324(1997), 5, pp. 293-298, 1997
  23. Darquennes, A., Wang, Y., Benboudjema, F., Nahas, G., Monitoring internal sulphate reactions by X-ray tomography, 15th Euroseminar on Microscopy Applied to Building Materials., Delft, the Netherlands, 2015.
  24. Duval, F., modelisation du renoyage d'un lit de particules : contribution à l'estimation des proprietes de transport macroscopiques, Ph. D. thesis, INPT Toulouse. FR, 2002,
  25. Abahri, K., Modélisation des transferts couplés de chaleur, d'air et d'humidité dans les matériaux poreux de construction, Ph. D. thesis, La Rochelle University, FR, 2012.
  26. COMSOL, COMSOL Multiphysics User's Guide, Version 4.3, 2012.
  27. Zhang, W., Min, H., Gu, X., Xi, Y., Xing, Y., Mesoscale model for thermal conductivity of concrete, Construction and Building Materials, 98(2015), 15, pp. 8-16.
  28. Trabelsi, A., Etudes numérique et expérimentale des transferts hygrothermiques dans les matériaux poreux de construction, Ph. D. thesis, La Rochelle University, FR, 2010.
  29. Issaadi, N., Effets de la variabilité des propriétés de matériaux cimentaires sur les transferts hygrothermiques : développement d'une approche probabiliste, Ph. D. thesis, La Rochelle University, FR, 2015.