Dilute gas flows through elliptic microchannels under H2 boundary conditions

This work presents a numerical investigation of slip flow inside microchannels characterized by an elliptic cross-section. A gaseous flow is considered, in laminar steady state condition, in hydrodynamically and thermally fully developed forced convection, accounting for the rarefaction effect. The momentum and energy equations are solved resorting to the finite element method; the numerical results are compared with analytical values available in the literature for slip flow in elliptic cross sections and in circular ducts, to validate the numerical procedure. The temperature field is determined by considering the H2 boundary condition for different combinations of heated walls among the four branches constituting the elliptic perimeter. Nusselt numbers and normalized wall temperatures in the case of two or four heated sides are presented and discussed. The influence of the cross section aspect ratio and of the rarefaction effects on the fluid behavior are investigated. The numerical results point out that the Nusselt number decreases with the Knudsen number,and increases with the aspect ratio of the elliptical channel. To evaluate the Nusselt numbers for different values of aspect ratio and Knudsen number (in all analyzed cases) a simple polynomial correlation is proposed. Finally a comparison between rectangular and elliptic microchannels has been performed, when the whole perimeter of the cross-section is heated, showing that for values of the aspect ratio greater than 0.33 the elliptic microducts are characterized by better thermal performances.