Prediction of temperature distribution and Nusselt number in rectangular microchannels at wall slip condition for all versions of constant heat flux

Abstract

Slip-flow in rectangular microchannels heated at constant and uniform heat flux (H2 boundary condition) is studied. The study is extended to the eight possible thermal versions that are formed of different combinations of heated and adiabatic walls. The paper aims to show the effect of different thermal versions on heat transfer in microchannel. The velocity distribution that is required in determining of temperature distribution is obtained from the literature. Mathematical similarity between the heat conduction and convection problems is used to determine the temperature distribution in the microchannel. The solution of a heat conduction problem, available in the literature, is adapted to the heat convection problem in the microchannel. The velocity and temperature distributions thus found are used to determine the average Nusselt number for all the eight thermal versions. For the case studied, it is found that rarefaction has a decreasing effect on heat transfer in the microchannels exposed to any of the eight thermal versions. The results of the paper for the special case of no-slip-flow agree exactly with the results found for macrochannels in the literature.