Numerical study on horizontal convection of a rarefied gas over a non-isothermal plane wall

Abstract

A rarefied gas over an infinite plane wall with non-uniform periodic temperature distribution is considered under the effect of gravity. The Knudsen number and the Froude number are defined as the mean free path of gas molecules and the scale height at a reference state divided by the length of the period, respectively. Based on the kinetic theory of gases, the steady two-dimensional gas flow is investigated numerically for a wide range of parameters. The cases of a free molecular gas are analyzed by a deterministically accurate method, which enables the computation for large Froude numbers, i.e., vanishingly small gravity. The flow pattern is shown to be slightly effected by the Froude number when the Froude number is large, whereas the flow magnitude is proportional to the inverse of the Froude number. As a result, the flow vanishes in the limit of zero gravity. This is not a trivial consequence because the case of an infinite Froude number is different from the same setting without gravity. The cases of finite Knudsen numbers are investigated by the direct simulation Monte Carlo method for a hard sphere gas, and the flow characteristics are shown to be dominated by the presence of gravity for cases in which the Knudsen number is larger than the Froude number.