On the effects of internal heat sources upon forced convection in porous channels with asymmetric thick walls

Thermal behaviour of a porous channel with thick, solid walls featuring uneven wall thicknesses and asymmetric external thermal boundary conditions is analysed theoretically. The system is under forced convection and the fluid and solid phases in this configuration include internal heat sources with varying strengths. Two types of asymmetric boundary conditions are considered. These include constant but different prescribed temperatures on the upper and lower solid walls and a combination of constant heat flux and convective boundary conditions on the two sides of the channel. The Darcy–Brinkman model of momentum transport and the two-equation energy model are utilised to develop analytical solutions for the temperature fields and Nusselt number. A comprehensive parametric study is, subsequently, conducted. The results clearly show the pronounced effect of the internal heat sources upon the Nusselt number and temperature fields of the system. In particular, the existence of these source terms intensifies the occurrence of a bifurcation phenomenon in the temperature fields. In keeping with the recent literature, it is demonstrated that the inclusion of internal heat sources leads to deviations from the local thermal equilibrium. Nonetheless, the results imply that the extent of these deviations depends on the thermal boundary conditions and also the specific phase in which heat is generated or consumed.