Fully developed non-Darcian forced convection slip-flow in a micro-annulus filled with a porous medium: Analytical solution

Forced convection heat transfer in a porous annular microduct is investigated analytically for hydrodynamically and thermally fully developed flow of a dilute gas. Brinkman extended Darcy equation is used and the porous medium shape parameter, the velocity slip and the temperature jump at the walls are taken into account. Two distinct thermal boundary conditions are analyzed: constant heat flux at the outer cylinder and insulated inner cylinder and vice versa (Cases I and II). Explicit expressions for the velocity distribution, the temperature distribution and the Nusselt number have been obtained. Generally, results show that for both cases Nusselt number decreases as Knudsen number and annulus aspect ratio increase.