Kinetic Theory Description of Conductive Heat Transfer from a Fine Wire

Abstract

The Maxwell moment method utilizing the two-sided Maxwellian distribution function is applied to the problem of conductive heat transfer between two concentric cylinders at rest. Analytical solutions are obtained for small temperature differences between the cylinders. The predicted heat transfer agrees very well with experiments performed by Bomelburg, Schäfer-Rating and Eucken. Comparison with results given by Grad's thirteen moment equations, and with those given by Fourier's "law" plus the Maxwell-Smoluchowski temperature-jump boundary condition shows that the two-sided character in the distribution function is a crucial factor in problems involving surface curvature.