Convection slip flow in a microchannel filled with homogeneous and heterogeneous porous medium*

In this paper, we have studied the rarefied gaseous flow through a micro-tube filled with homogeneous and heterogeneous porous medium. An analytical investigation is performed to model the flow and heat transfer using Brinkman momentum along with the energy equation. Velocity slip and temperature jump conditions are utilized to account for effect of the rarefied gaseous flow at the wall of the micro-tube. A uniform heat flux boundary condition is applied at the wall of the microtube. A rigorous explicit expression for velocity, temperature, and Nusselt number are obtained. Effect of porous media shape parameter and Knudsen number on velocity, temperature and Nusselt number are analysed and compared for both homogeneous and heterogeneous cases. Results show that an increase in the velocity slip coefficient leads to an increase in Nusselt number, since an increase in the slip at the wall leads to an increased velocity, which results in higher convective heat transfer. Moreover, increasing the temperature jump coefficient reduces the Nusselt number because higher slip causes a smaller temperature gradient at the wall, which reduces the heat transfer. Results also show enhanced heat transfer characteristics for heterogeneous porous medium, as compared to homogenous porous medium.