Forced convection in porous microchannels with viscous dissipation in local thermal non-equilibrium conditions

• Forced convection in flat-plate microchannels filled with porous media is studied.
• Viscous dissipation, first-order velocity slip and temperature jump are considered.
• An analytical solution for Darcy–Brinkman flow model and LTNE condition is derived.
• Closed-form expressions for the viscous dissipation and Nusselt number are shown.
• A complete parametric study is conducted for air-saturated porous media.

Fully developed, steady-state forced convection, in parallel-plate microchannels, filled with a porous medium saturated with rarefied gases at high temperatures, in local thermal non-equilibrium (LTNE) condition, is investigated for the first-order slip-flow regime (0 ≤ Kn ≤ 0.1). Both velocity and temperature jumps at the walls are accounted for. An analytic solution is proposed for the Darcy–extended Brinkman flow model with assigned uniform heat flux at the microchannel walls and viscous heat dissipation in the fluid phase. The solution for NTLE includes the shear work done by the slipping effects. A closed-form expression of the Nusselt number is derived. A validation analysis with respect to the case of channels filled with saturated porous medium is accomplished. The results show that the internal dissipation increases as the velocity slip increases. In addition, the heat dissipation strongly affects the fluid temperature profiles. The increases in velocity slip and temperature jump lead to decreases of temperature gradients in the fluid and solid along the sections. The heat transfer at channel walls is enhanced due to an increase in the bulk heat transfer.