Effects of Heat Generations on the Thermal Response of Channels Partially Filled with Non-Darcian Porous Materials

The forced convective thermal response of channels partially filled with porous materials is analytically studied. It is assumed that internal heat generations exist within both the fluid and solid phases. Effects of internal heat generations within the both phases on the thermal response of the channel resulting in the heat flux bifurcation phenomenon are discussed for the first time. No study previously analyzed the heat flux bifurcation in a non-Darcian porous medium with heat-generating porous materials. To obtain the most general thermo-hydraulic behavior, the Darcy–Brinkman equation of motion and the two-energy model (local thermal non-equilibrium) along with two practical thermal boundary conditions (models A and B) are used. Consequently, two possible thermal responses are obtained for each phase. Results show that insertion of a porous material inside a heat-convecting fluid leads to have a more uniform temperature distribution which translates to a lower thermal resistance and an enhanced heat transfer. Furthermore, it is seen that increasing the porous material thickness increases the ratio of heat transferred by the porous medium compared to that convected by the clear fluid flow. In addition, the internal heat generations drastically change the temperature distribution. Finally, it is shown that the internal heat generations can inverse the heat flux direction at the porous–fluid interface (the heat flux bifurcation phenomenon). Criteria for the heat flux bifurcation for a partially porous-filled channel are presented under the Darcy’s law of motion.