Mathematical model of non-stationary heat conduction in the wall: Asymmetric problem with the boundary conditions of imperfect heat transfer

Abstract

This paper deals with the study of a non-stationary heat conduction in the solid wall. It is focused on mathematical modelling of its asymmetric heating and cooling by imperfect heat transfer to both sides of the wall. It describes method used for deriving of the long time analytical solution describing temperature distribution in the heated (cooled) wall by use Laplace transform and verification of its validity by numerical calculation with COMSOL Multiphysics software. In the tested example, the maximum difference between analytical and numerical solution was about 3.5 % considering the possible maximum and minimum temperatures in the wall under the given conditions.