When can we avoid paradoxes in the contact problems of two thermoelastic cylinders

We discuss the problem of a contact of two parallel elastic cylinders heated to different temperatures. The purpose of our investigation is to derive the conditions which have to be satisfied so that the solution to the thermoelastic problem is physically meaningfull (i.e. the paradox of ''the cooled cylinder'' can be avoided). 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. The paper has been illustrated by an example and diagrams.