Forced convection in a self-heating porous channel local thermal non-equilibrium model

Abstract

Laminar forced convection flow through a parallel plates channel completely filled with a saturated porous medium where occurs a uniform heat generation per unit volume with volumetric heat generation is investigated numerically. The Darcy-Brinkman model is used to describe the fluid flow. The energy transport mathematical model is based on the two equations model which assumes that there is no local thermal non-equilibrium between the fluid and the solid phases. The dimensionless governing equations with the appropriate boundary conditions are solved by direct numerical simulation. The effect of the controlling parameters, Biot number, thermal conductivities ratio, heat generation rate, and the Reynolds number on the local thermal equilibrium needed and sufficient condition is analyzed. The results reveal essentially that the local thermal equilibrium condition is unfavorably affected by the increase in the heat generation rate, the thermal conductivities ratio, and the decrease in the Biot number. In addition, for a given heat generation rate, the effect of Reynolds number on the local thermal equilibrium condition is reversed depending on the conductivities ratio threshold.