Rarefaction, Temperature Jump, and Viscous Dissipation Effects on Heat Transfer in Rotating Micro Devices

This paper examines the effects of rarefaction and dissipation on flow and heat transfer characteristics in rotating micro devices. The housing is assumed to be at uniform temperature while the rotating surface is insulated. Thus heat generation and transfer are due to viscous dissipation only. An analytic solution is obtained for the velocity and temperature distribution in the gas filled concentric clearance between a rotating shaft and its stationary housing. The solution is valid in the slip flow and temperature jump domain defined by the Knudsen number range of Kn < 0.1. The Nusselt number was found to depend on three parameters: the Knudsen number Kn, ratio of housing to shaft radius r_o / r_i, and Prandtl number-specific heat ratio group γ/(γ + 1) Pr. Results indicate that curvature and Knudsen number have significant effect on the Nusselt number. However, fluid temperature rise due to dissipation is negligible.