Analytical solution of mixed electromagnetic/pressure driven gaseous flows in microchannels

The influences of wall-slip/jump conditions on the fluid flow and heat transfer for hydrodynamically and thermally fully developed electrically conducting gaseous flow subject to an electromagnetic field inside a parallel plate microchannel with constant heat flux at walls are studied under the assumptions of a low-magnetic Reynolds number. The governing equations are non-dimensionalized and then analytical solutions are derived for the friction and the heat transfer coefficients. The fluid flow and the heat transfer characteristics obtained in the analytical solutions are discussed in detail for different parameters such as the Knudsen, Hartmann, and Brinkman numbers. The velocity profiles verify that even with a constant Knudsen number, applying a stronger electromagnetic field gives rise to an increase in the slip velocity. The results also reveal that on increasing the Hartmann number, the heat transfer rate as well as the friction factor is enhanced, whereas it tends to suppress the movement of the fluid. Further, it is found that the Nusselt and the Poiseuille numbers are less sensitive to the electromagnetic field effects with increase in rarefaction.