Nonlinear Heat Conduction in Rarefied Gases Confined between Concentric Cylinders and Spheres

Abstract

Heat conduction problems in rarefied gases confined within the solid boundaries of two concentric cylinders and spheres have been studied using the four moment method. A two-sided velocity distribution function is assumed for the gas. The two number densities and the two temperatures in the distribution are the four unknowns of the problem. Unlike previous analyses, a series expansion of these four unknowns in terms of the temperature difference is introduced to account for problems with finite temperature differences. Closed-form solutions are thus obtainable. An example of a calculation is presented for cases retaining the second-order terms in the expansion. The results show that the heat conduction ratio of Q/Qfm, where Qfm is the heat conduction rate at the free molecular limit, is a function of the temperature difference ε. Previous results of small temperature difference are recovered by taking the limit of ε→0.