Macroscopic cylindrical governing equations: transport process in unsaturated porous media with a line heat source

Abstract

The paper outlines a formulation of the cylindrical transport equations which describe simultaneous heat and mass transfer in unsaturated porous materials when a line heat resource is embedded in the medium. A macroscopic continuum mechanics approach is adopted to derive the coupled continuity, momentum and energy equations. Hydrodynamic law such as Darcy's law and Darcy–Buckingham theorem are utilized to simplify the continuity and momentum equations of fluid flow. Migration of liquid due to surface tension effects is modeled in the analysis. The effects of phase change on the heat transfer are also included in the energy equation. The constituent equations are expanded in the cylindrical co-ordinate system. The resulting equations reported in this paper are found to agree with equations reported in this paper are found to agree with equations obtained by other researchers who used volume-averaging techniques to study similar phenomena in unsaturated porous materials. Copyright © 1999 John Wiley & Sons, Ltd.