Thermal conduction and viscous heating in microscale Couette flows

The direct simulation Monte Carlo (DSMC) method is used to investigate heat conduction and viscous heating in microscale Couette flows. When augmented by the slip boundary conditions, the continuum equations are found to predict thermal conductance accurately even in the transition and ballistic flow regime for Couette flows. The viscous heat generation rate, in contrast, is significantly underpredicted by the slip flow theory. We propose an alternative approach based on kinetic theory and present a compact analytic expression for the viscous dissipation rate.