Fluid flow and heat transfer in two-segmented microchannels within the slip flow regime

We theoretically investigate gaseous slip flow and heat transfer in circular microchannels with two different wall materials in the lateral direction. The flow is considered as steady and fully-developed, and constant but different wall heat fluxes are assumed for the channel segments. While infinite series solutions are obtained for the velocity and temperature distributions as well as the Nusselt number, finite-element numerical simulations are also performed to confirm the validity of the analytical solutions developed. It is demonstrated that the average Nusselt number of the channel depends on several parameters comprising the Knudsen number, the Prandtl number and specific heat ratio of the gas, the momentum and thermal accommodation coefficients, and the angular span of either channel segment as well as the heat flux ratio of the two segments. It is further illustrated that the fluid velocity is strongly non-uniform in the angular direction when the channel segments have different momentum accommodation coefficients. This significantly affects the heat transfer rates, especially at high Knudsen numbers where the rarefaction effects are more significant. An inspection of the dimensionless average velocity variations shows that reducing the momentum accommodation coefficient of one channel segment while keeping that of the other one constant leads to higher average velocities, whereas the opposite is true for the influence of the thermal accommodation coefficient on the average Nusselt number. Finally, it is shown that the Nusselt number is a maximum for a symmetric wall heating.