Second Order Mixed Convective Flow in a Long Vertical Microchannel

Abstract

The present investigation is concerned with the role of secondorder slip in the mixed convection through a long heated vertical planar microchannel with asymmetric wall temperatures. The fully developed solutions of fields and the corresponding characteristics are analytically derived on the basis of secondorder Maxwell–Smoluchowski–Burnett (MSB) slip/jump boundary conditions. Results reveal that secondorder slip has an appreciable effect on the flow but a negligible effect on the heat transfer. The effect is to raise the gas motion speeds near the heated walls and to enlarge the pressure gradient required to drive the flow. It then leads to the reduction of local flow drag, except for the case where a reversed flow region exists. The secondorder effect could be magnified by increasing the mixed convection number, the ratio of the Grashof number to the Reynolds number.