Analytical considerations of slip flow and heat transfer through microfoams in mini/microchannels with asymmetric wall heat fluxes

Forced convection in a mini/microchannel filled with microfoam is analytically studied in the condition of uniform but asymmetrical heat fluxes. Velocity slip, thermal slip, local thermal non-equilibrium (LTNE) effect, and asymmetric heat fluxes imposed on the two parallel-plates sandwiching the microfoams are especially considered. For two walls with different heat fluxes, solid and fluid temperatures at the boundary are equal to each other based on self-coupling conditions. Explicit expressions for velocity and temperatures of solid and fluid are derived and the analytical solution agrees well with existing references. This solution can predict velocity, temperatures, friction loss and thermal performance of porous microchannel for wide ranges of Knudsen number and HF ratio. With the increased Knudsen number, the friction factor gradually decreases and the decreasing amplitude in slip flow region is very large. With the increased shape factor, the dimensionless pressure drop sharply decreases for small shape factor, while its value gradually approaches 1 for large shape factor. A maximum Nusselt number exists with the increase in Knudsen number. Heat transfer can be enhanced by increasing effective Biot number or decreasing thermal conductivity ratio. The analytical solution is symmetrical on the axis ξ = 1 in the region 0 < ξ < + ∞.