Steady fully developed mixed convection flow in a vertical parallel plate microchannel with bilateral heating and filled with porous material

Abstract

This study investigated analytically the hydrodynamic and thermal behaviour of a fully developed laminar, viscous, incompressible fluid in a vertical parallel plate microchannel taking into account the velocity slip and thermal jump at the walls. The governing equations are expressed in a dimensionless form using the dimensionless quantities. The method of undetermined coefficient was employed to obtain the closed-form expression for velocity, which is used to determine the skin friction. The solution obtained is then presented graphically and the results are discussed for various dimensionless parameters entering the problem. During the course of investigation, it is found that the critical values of the mixed convection parameter Gre (which is the ratio of the Grashof number Gr to the Reynolds number Re) led to flow reversal decrease with increase in Darcy number, while it increases with increase in Knudsen number Kn. Also, the Nusselt number Nu is found to increase with increasing Darcy number.