Forced convection gaseous slip flow in a porous circular microtube: An exact solution

• An exact solution for gaseous slip flow in a porous circular microtube is proposed.
• Local thermal non-equilibrium condition considers the temperature difference between the fluid and solid phases.
• Effects of rarefaction and various thermophysical parameters on the heat transfer are investigated.
• Our analytical results can be extended to handle more complicated microchannels with multiply connected cross sections.

Rarefied phenomena can occur when a gas flows through a microchannel. However, most available convective solutions were obtained under the local thermal equilibrium condition. In this study, gaseous slip flow in a circular microtube filled with a porous medium is analytically investigated under the local thermal non-equilibrium condition. The first-order velocity slip and temperature jump conditions at the tube wall are invoked in order to account for the rarefaction effects. Rigorous analytical solutions are obtained for the velocity and temperature distributions as well as the average Nusselt number. Theoretical predictions are then compared to those of existing limiting cases in the literature. Results indicate that the degree of rarefaction, represented by the Knudsen number ranging from 10−3 to 10−1, has a significant effect on the velocity, temperature, pressure drop and heat transport within the microtube for various combinations of pertinent parameters such as the porosity, effective thermal conductivity ratio, Biot number and porous media shape factor.