Constant Wall Temperature Nusselt and Poiseuille Numbers in Rectangular Microchannels

Slip flow convective heat transfer and friction loss characteristics are numerically evaluated for constant wall temperature rectangular microchannels. The effects of rarefaction, accommodation coefficients, aspect ratio, second-order slip boundary conditions, axial conduction, and viscous dissipation with flow work are each considered. Second-order slip boundary conditions, axial conduction, and viscous dissipation with flow work effects have not been studied previously for rectangular channel slip flows. The effects of each of these parameters on the numerically computed convective heat transfer rate and friction loss are evaluated through the Nusselt number and Poiseuille number respectively. The numerical results are obtained using a continuum-based computational fluid dynamics algorithm that includes second-order slip flow and temperature jump boundary conditions. Numerical results for the three-dimensional, fully developed Nusselt and Poiseuille numbers are presented as functions of Knudsen number, first- and second-order velocity slip and temperature jump coefficients, aspect ratio, Brinkman number, and Peclet number. Effects of rarefaction, accommodation coefficients, and aspect ratio are consistent with previously reported analytical results for rectangular channel constant wall temperature flows. The effects of second-order slip terms, axial conduction and viscous dissipation are also shown to significantly affect the Nusselt and Poiseuille numbers.