Effect of Sudden Change of Wall Temperature in Rarefied Gas

Abstract

The response of a rarefied gas to abrupt change of temperature of bounding wall is discussed using the Bhatnager, Gross and Krook model of Boltzmann equation. The temperature change of the wall is assumed to be small and the governing equations as well as the boundary conditions are linearized. The density and temperature distributions in the gas are obtained for both short and long times. For short times the solution represents a perturbation to the linearized free molecular flow. At long times it involves essential differences from the corresponding solution based on the Navier-Stokes equation in a layer adjacent to the boundary with thickness of the order of mean free path. Numerical value of temperature jump distance is also obtained.