Viscous Dissipative Forced Convection in a Channel Partially Filled with Porous Medium

Partial filling of a porous medium in a channel of a certain configuration attracts attention, as it tends to enhance convective heat transfer while reducing pressure drop remarkably, as compared to a fully filled porous channel. In this study, forced convection heat transfer in a channel partially filled with a porous medium adjoining the wall is investigated analytically, where viscous dissipation is accounted for under local thermal nonequilibrium (LTNE) conditions. Because of viscous dissipation, the newly derived exact temperature profile reveals a magnified temperature difference between the fluid and solid phases and a more intense heat-flux bifurcation in cases where the heat transfer in the porous medium is dominated by solid conduction. The Nusselt-number depiction as a function of Darcy number at a fixed porous medium thickness reveals the existence of a Darcy number that maximizes the Nusselt number and highlights the competition between the convection heat transfer and heat source in the form of viscous dissipation, as Darcy number increases. The strong dependency of the Nusselt number on Brinkman number, in cases where the thermal resistance to fluid conduction is dominant, demonstrates the importance of incorporating viscous dissipation effects to the temperature field under LTNE condition.