Nonlinear Heat Conductions in Rarefied Gases

Abstract

ONLINEAR problems of thermal conduction in monatomic rarefied gas confined within two concentric cylinders and spheres are studied by the four-moment method coupled with the bimodal two-stream distribution function of Beck. Finite temperature difference between the two boundary surfaces is included in the present theory. Therefore, present results are presumed to be complete solutions obtainable by the fourmoment technique with the assumed velocity distribution of the gas. Content Recently, Lees' four-moment approach1 for heat conduction problem in rarefied gases was further extended by Lou and Shih2 to investigate nonlinear problems. Instead of linearizing the problem, they employed the technique of series expansion. It was shown that the nonlinear solutions could be obtained in analytic forms. In principle, their method is suitable for any temperature difference. However, as the temperature difference is getting larger, the solutions will have to include more higherorder terms in the series; hence, they become cumbersome. In order to overcome this inconvenience, another modified fourmoment approach is proposed. Let us consider the steady heat conduction problem in a rarefied Maxwellian gas confined between two concentric cylinders, or spheres. The surface of the inner cylinder (or sphere) with radius Rf is maintained at a uniform constant temperature 7}; and the inner surface of the outer cylinder (or sphere) with radius Rn is maintained at Tu. The velocity distribution function of gas molecules f(V9 R) is assumed to be the two-steam bimodal distribution function.3 In region 1