Pressure-Driven Gas Flows in Long Rectangular Microchannels With Uniform Heat Flux Boundary Conditions

This paper focuses on the numerical simulation of pressure-driven gas flow in long microchannels, with uniform heat flux wall boundary conditions. The flow is assumed to be two-dimensional and the momentum and energy equations are solved, considering variable properties, rarefaction effects, including velocity slip, thermal creep and temperature jump, compressibility effects and viscous dissipation. A combined serial-parallel algorithm is employed to simulate the flow in long microchannels. The numerical solution is found to be much more involved than that for the isothermal boundary conditions and the convergence of the scheme to be much slower, as expected. The numerical results are also quite different and, in some cases, quite unexpected. The thermal and hydraulic characteristics are carefully examined and analyzed. It is found that a nonlinear temperature profile arises along the microchannel due to the combined effects of pressure work and viscous dissipation. Similarly, compressibility effects lead to a nonlinear centerline pressure profile. The ratio of pressure work to viscous dissipation is investigated as a function of the Knudsen number and is found to increase with the Knudsen number. The rarefaction effects are found to increase the Nusselt number near the outlet and to decrease it near the inlet. An increase in the inlet/outlet pressure ratio is seen to significantly enhance microchannel cooling.