Analytical and Numerical Study on Thermally Developing Forced Convective Flow in a Channel Filled with a Highly Porous Medium Under Local Thermal Non-Equilibrium

Abstract

An analytical and numerical study was made on thermally developing forced convective flow in a channel filled with a fluid-saturated porous medium, subject to constant heat flux, under local thermal non-equilibrium. The Brinkman-extended Darcy model was employed to investigate the combined effects of the Darcy number, Biot number, effective thermal conductivity ratio and Graetz number on the longitudinal thermal development in a channel filled with a highly porous medium. 3D convective regime maps were constructed for wide ranges of the parameters, using a 3D coordinate system based on the Biot, Darcy and Graetz number coordinates. The 3D convective regime maps proposed in this study enable one to identify the three distinctive thermal regions possible along the longitudinal coordinate in a channel, namely the entrance developing region, transition region and fully developed region, depending on the relative thicknesses of the fluid and solid thermal boundary layers. It has been found that the Darcy number strongly influences the heat transfer rate in the developing region, yielding a higher Nusselt number for a lower Darcy number, whereas both Biot number and the effective thermal conductivity ratio markedly influence the level of the fully developed Nusselt number. The heat transfer performance evaluation carried out under equal pumping power for the aluminum foam embedded channel saturated with air reveals that a substantial heat transfer argumentation is possible by filling the channel with an aluminum foam.