Effect of Rarefaction, Dissipation, and Accommodation Coefficients on Heat Transfer in Microcylindrical Couette Flow

This paper examines the effects of rarefaction, dissipation, curvature, and accommodation coefficients on flow and heat transfer characteristics in rotating microdevices. The problem is modeled as a cylindrical Couette flow with a rotating shaft and stationary housing. The housing is maintained at uniform temperature while the rotating shaft is insulated. Thus, heat transfer is due to viscous dissipation only. An analytic solution is obtained for the temperature distribution in the gas filled concentric clearance between the 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 $0.001<Kn<0.1$⁠. The important effect of the momentum accommodation coefficient on velocity reversal and its impact on heat transfer is determined. The Nusselt number was found to depend on four parameters: the momentum accommodation coefficient of the stationary surface $σuo$⁠, Knudsen number Kn, ratio of housing to shaft radius $ro∕ri$⁠, and the dimensionless group $[γ∕(γ+1)](2σto−1)∕(σtoPr)$⁠. Results indicate that curvature, Knudsen number, and the accommodation coefficients have significant effects on temperature distribution, heat transfer, and Nusselt number.