On Thermal Contact of Two Axially Symmetric Elastic Solids

A contact problem of two elastic convex and axially symmetric solids heated (or cooled) to temperatures of different values is considered. Pertinent formulae have been derived for relations between the contact pressure, geometrical characteristics of the solids and distributions of heat flux over the contacting region. We have analysed: 1. The problem of the loss of the contact between two solids pressed together with active heat fluxes. We discuss the cases for which the contact of the axially symmetric solids can take the form of a circle, or an annulus. 2. The problem of a paradox when the mathematically well posed contact problem of thermoelasticity leads to a physically unacceptable solution with a region of overlapping materials. Here we discuss a generalization of the cooled sphere paradox. The heat flux functions are continuously differentiable, of constant sign. The conditions have been derived for the cases when the paradox can be avoided.