Heat Transfer through a Vertical Partition Separating a Porous Layer and a Fluid Space

Abstract

A simple one-dimensional theory about the heat transfer through a conductive partition separating porous medium and Newtonian fluid reservoirs at different temperatures has been developed. In the present study we assume that the porous reservoir has a higher themperature than that of fluid reservoir. According to the theory a unique nondimensional parameter σ is identified as a single parameter to govern the convection-conduction conjugate problem. The parameter is defined by σ=(1.323B)^<2/3>, where B is the Bejan number defined by B=(k_pRa^<1/2>_H)/(kRa^<1/4>_C), where k_p, k, Ra^<1/2>_H and Ra^<1/4>_C are the porous medium thermal conductivity, reservoir fluid thermal conductivity, Darcy-modified Rayleigh number based on the partition height, and the fluid reservoir Rayleigh number based on the partition height respectively. The present one-dimensional theory is well compared with Bejan's results for average partition temperature and the overall Nusselt number.