HEAT CONDUCTION IN A RAREFIED GAS BETWEEN CONCENTRIC CYLINDERS.
CALIFORNIA UNIV BERKELEY DIV OF AERONAUTICAL SCIENCES
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Heat conduction through a rarefied gas contained between concentric cylinders is studied analytically. Emphasis is placed on the connection with the experimental determination of thermal accommodation coefficients by the low-pressure method. The linearized BGKW-model equation is used, and the linearization procedure based on small relative temperature difference is justified. Two coupled linear integral equations of the perturbed temperature and density are then formulated. A variational principle for the heat flux is found for arbitrary Knudsen number. An asymptotic analysis is carried out for the case of mean free path much greater than the inner but of the same order as the outer cylinder radius, which corresponds to typical operating conditions of the experiment mentioned above. The lowest order deviation of the heat flux from its free-molecular value is of OlnKnKn and is the same as that obtained by the Knudsen iteration method. Numerical calculations are performed to find the next order correction term. It is found that for mean free path 20 or more times the inner cylinder radius the relative error introduced by using the free-molecular value for the heat flux is less than 5, provided that the ratio of the mean free path over the outer cylinder radius is at least 0.2. Author
- Fluid Mechanics