Asymmetrical heating in rarefied flows through circular microchannels

This work is aimed at contributing to the thermal analysis of slip flow through circular microducts, providing an analytical solution to the energy conservation equation for partially heated walls. A uniform wall heat flux (H2 boundary conditions) is considered on the heated perimeter of the cross section while the remaining arc length is assumed to be adiabatic. The gaseous flow is considered laminar, fully developed, in steady state condition, and forced convection. The temperature profile, wall temperature distribution, and Nusselt number are presented as functions of both the heated perimeter of the cross section and the Knudsen number, resorting to simple converging series of trigonometric functions. The proposed solution can be useful for the design of the microfluidic devices such as micro heat sinks and micro heat exchangers.