Gas Flow and Heat Transfer in an Enclosure Induced by a Sinusoidal Temperature

Abstract

The heat transfer and flow characteristics of rarefied gas confined within a square cavity are investigated. The cavity upper-wall is subjected to a symmetrical sinusoidal temperature with respect to its midline. Two cases are considered, one of them is that the bottom and two sidewalls are kept adiabatic, while in the other, all the enclosure walls are considered diffusely reflecting. Kinetically, the gas is simulated with the direct simulation Monte Carlo method (DSMC) in the slip and transition regimes. The DSMC results are compared with the Navier-Stokes-Fourier equation, with second order boundary conditions of velocity slip and temperature jump, (NSF) in the slip regime. Main outcomes are presented as velocity streamlines overlaid on temperature contours and macroscopic parameters plots. The Knudsen number (Kn) increase shows other vortices, beside the two classical ones that appear in the hydrodynamic and slip regime. The normal heat flux about the sinusoidally heated wall is strengthened by the flow in DSMC rather than that predicted by NSF method. Good agreement is observed between the NSF theory and DSMC method in the early slip regime, but when Kn=0.1 the NSF approach breaks down to show the secondary counter rotating eddies illustrated by the DSMC method.