Analytical solution for heat transfer in temperature gradient calendering

An analytical solution is derived for the temperature field of the paper during the temperature gradient calendering process. The solution takes into account the change in volume of the paper being calendered. The previous solutions presented in literature are based on the assumption of incompressible semi-infinite conduction. The validity of the present solution is verified by comparison with a numerical solution of the problem. It is shown that the simple result given in the literature underestimates the temperature penetration depth by as much as 30%.