Unsteady Transfer of Momentum and Heat Between Concentric Cylinders

Abstract

Problems of the molecular transfer of momentum and heat in a fluid between two concentric cylinders are often encountered in the field of lubrication. It is shown herein that these problems can be solved by a generalized Fourier analysis, and that, in particular, varying boundary conditions and nonhomogeneous terms in the diffusion equation which are time-dependent can be treated by the Duhamel method from the theory of the conduction of heat in solids. Heat generated by viscous shear, as well as that externally applied, is included in the analysis.