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

The paper outlines a formulation of the cylindrical transport equations whi ch describe simultaneous heat and mass transfer in unsaturated porous mater ials when a line heat resource is embedded in the medium. A macroscopic con tinuum mechanics approach is adopted to derive the coupled continuity, mome ntum and energy equations. Hydrodynamic law such as Darcy's law and Darcy-B uckingham theorem are utilized to simplify the continuity and momentum equa tions 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 a re also included in the energy equation. The constituent equations are expa nded in the cylindrical co-ordinate system. The resulting equations reporte d in this paper are found to agree with equations reported in this paper ar e found to agree with equations obtained by other researchers who used volu me-averaging techniques to study similar phenomena in unsaturated porous ma terials. Copyright (C) 1999 John Wiley & Sons, Ltd.