The implications of the thermal equilibrium assumption for surrounding-driven steady conduction within a saturated porous medium layer

The issue of local thermal equilibrium between a solid porous matrix and a saturating (stagnant) fluid under unidirectional steady heat diffusion is c onsidered focusing on the effect of exterior-boundary thermal conditions. W e demonstrate that in the case of exterior boundaries with uniform heat Aux , i.e., when the heat per unit of phase area flowing through each phase is equal. thermal equilibrium will ensue only when the phases have the same th ermal conductivity. When the phases are in thermal equilibrium at the exter ior boundaries, then they will be in thermal equilibrium throughout the ent ire domain independently of the properties of each phase. In this case, the ratio of the heat flowing through each phase will be uniform within the la yer and proportional to the thermal conductivity phase-ratio. With uniform heat flux at one end and thermal equilibrium at the other end of the domain , four independent criteria lead to thermal equilibrium. For a small fluid- to-solid volumetric heat transfer coefficient the medium reaches a state of maximum thermal nonequilibrium. A criterion for estimating the thermal equ ilibrium status within the layer is also derived. This criterion is importa nt for the experimental determination of the effective thermal conductivity of a saturated porous layer. (C) 1998 Elsevier Science Ltd. All rights res erved.