Analysis of flow and heat transfer at the interface region of a porous medium

Abstract

Fluid flow and heat transfer at the interface region are analyzed in depth for three general and fundamental classes of problems in porous media. These are the interface region between two different porous media, the interface region between a fluid region and a porous medium, and the interface region between an impermeable medium and a porous medium. These three types of interface zones constitute a complete investigation of the interface interactions in a saturated porous medium. Detailed analytical solutions, for both the velocity and temperature distributions are derived for all of these interface conditions. The analytical temperature distributions are found in terms of confluent hypergeometric functions for two different regimes, which are found to cover almost the entire range of real fluids. The numerical and analytical results are found to be in excellent agreement. The numerical and analytical results are also checked against an empirically based hypothesis for one of the interface conditions, namely the interface between a fluid region and a porous medium, and are found to be in excellent agreement with that experimental hypothesis.