A modified temperature-jump method for the transition and low-pressure regime

For modeling the gas heat conduction at arbitrary Knudsen numbers and for a broad range of geometries, we propose a modified temperature-jump method. Within the modified approach, we make a distinction between an inner convex surface and an outer concave surface enclosing the inner surface. For prob lems, where only a single geometric length is involved, i.e., for large par allel plates, long concentric cylinders and concentric spheres, the new met hod coincides at any Knudsen number with the interpolation formula accordin g to Sherman, and therefore also with the known solutions of the Boltzmann equation obtained by the four momenta method. For the general case, where m ore than one geometric length is involved, the modified temperature method is trivially correct in the limit of high pressure and identical with Knuds en's formula in the limit of low pressure. For intermediate pressure, where there is a lack of known solutions of the Boltzmann equation for general g eometries, we present experimental data for the special two-dimensional pla te-in-tube configuration and compare it with results of the modified temper ature-jump method stating good agreement. The results match slightly better compared to the standard temperature method and significantly better compa red to the interpolation formula according to Sherman. For arbitrary geomet ries and Knudsen numbers, the modified temperature method shows no principa l restrictions and may be a simple approximative alternative to the solutio n of the Boltzmann equation which is rather cumbersome.