Effects of surface roughness, axial conduction, viscous dissipation, and rarefaction on heat transfer in a two–dimensional parallel plate microchannel with constant wall temperature are investigated numerically. Roughness is simulated by adding equilateral triangular obstructions with various heights on one of the plates. Air, with constant thermophysical properties, is chosen as the working fluid, and laminar, single-phase, developing flow in the slip flow regime at steady state is analyzed. Governing equations are solved by finite element method with tangential slip velocity and temperature jump boundary conditions to observe the rarefaction effect in the microchannel. Viscous dissipation effect is analyzed by changing the Brinkman number, and the axial conduction effect is analyzed by neglecting and including the corresponding term in the energy equation separately. Then, the effect of surface roughness on the Nusselt number is observed by comparing with the corresponding smooth channel results. It is found that Nusselt number decreases in the continuum case with the presence of surface roughness, while it increases with increasing roughness height in the slip flow regime, which is also more pronounced at low-rarefied flows (i.e., around Kn = 0.02). Moreover, the presence of axial conduction and viscous dissipation has increasing effects on heat transfer with increasing roughness height. Even in low velocity flows, roughness increases Nusselt number up to 33% when viscous dissipation is considered.
Thermal boundary conditions for convective heat transfer of dilute gases in slip flow regime
