Analysis of non-Darcian effects on temperature differentials in porous media

Forced convection flow through a channel filled with a porous medium is investigated analytically. A non-thermal equilibrium, two-equation model is utilized to represent the fluid and solid energy transport. The Darcy–Forchheimer–Brinkman model is used to represent the fluid transport within the porous medium. Analytical solutions are obtained for both fluid and solid temperature fields incorporating the effects of various pertinent parameters such as the Biot number, the thermal conductivity ratio, the Darcy number and the inertial parameter. The present analytical solution for the two-equation model is validated against the exact solution for the one-equation model available in the literature as well as the analytical solution for the non-thermal equilibrium case based on a Darcian flow field. Error maps for the validity of one-equation model are established for various physical conditions taking into account the Darcy and inertial parameters as well as the Biot and the thermal conductivity ratio of fluid to solid phases. It is shown that the Darcy number and the inertial parameter have a lesser influence in establishing the validity of the local thermal equilibrium assumption.