A boundary layer analysis for entrance region heat transfer in vertical microchannels within the slip flow regime

A boundary layer integral analysis has been executed to investigate the heat transfer characteristics of natural convection gas flows in symmetrically heated vertical microchannels, under the conditions of large channel aspect ratios, in the slip flow regime. It has been revealed that for low values of Rayleigh number, the entrance region length is only a small fraction of the total channel extent. For higher values of Rayleigh number, however, effects of the developing region are non-trivial, and two counteracting heat transfer mechanisms need to be aptly taken into consideration for interpreting the Nusselt number values. In the present study, the proportionate enhancement in the average Nusselt number with wall-slip effects has been observed to become more prominent for higher values of Knudsen number. However, the relative augmentation in the rate of heat transfer tends to get somewhat arrested for higher values of Rayleigh number, as attributable to the counteracting influences of augmented rates of advective transport and reduced wall-adjacent temperature gradients. For all cases, the boundary layer theory based predictions have been found to agree excellently with the corresponding results obtained from full-scale numerical predictions.