The Effect of Creep Flow on Two-Dimensional Isoflux Microchannels

Micro channel convective heat transfer and friction loss characteristics are numerically evaluated for gaseous, two-dimensional, steady state, laminar, constant wall heat flux flows. The effects of Knudsen number, accommodation coefficients, second order slip boundary conditions, creep flow, and thermal/hydrodynamic developing flow are considered. These effects are compared through the Poisuelle number and Nusselt number. Numerical values for the Poisuelle and Nusselt numbers are obtained using a continuum based three-dimensional, unsteady, compressible computational fluid dynamics algorithm that has been modified with slip boundary conditions. To verify the numerical results, analytic solutions for the hydrodynamically and thermally fully developed Poisuelle and Nusselt numbers have been derived. The fully developed analytic Poisuelle and Nusselt numbers are given as a function of Knudsen number, the first and second order velocity slip and temperature jump coefficients, the Brinkman number, and the ratio of the thermal creep velocity to the mean velocity. Excellent agreement between the numerical and analytical data is demonstrated. Second order slip terms and creep velocity are shown to have significant effects on the Poisuelle and Nusselt numbers.