Heat transfer through a three-layer wall considering the contribution of phase change: a novel approach to the modelling of the process

A novel analytical solution to the time-dependent heat transfer equation for a multi-layer wall considering the contribution of phase change is obtained. Based on this solution a new numerical algorithm is developed for the analysis of variations in temperature and heat flux in a three-layer wall of a building in the presence of transient ambient temperature. In this algorithm, the new analytical solution at the end of the previous time step is used as the initial condition for the following time step with adjusted values of input parameters (ambient temperature). The novel algorithm is verified based on a comparison of the predictions of COMSOL Multiphysics (version 6.1) with its predictions for the same input parameters assuming that the time dependence of the ambient temperature follows the sine law. The new code is used for the analysis of heat transfer through a three-layer building wall assuming typical continental climate conditions. The inner and outer layers were filled with polyurethane foam, while a thin middle layer, located in the centre of the wall, was filled with the phase-change material (paraffin). Using the new numerical algorithm it is demonstrated that the presence of the thin paraffin layer in the wall leads to two orders of magnitude reduction in the amplitude of temperature oscillations on the room side of the wall compared to those on its outer side. It is shown that the presence of paraffin layer in the wall leads to an increase in the phase shift between the temperature on the outer side of the wall and the heat flux on the room side from about 1 hour (homogeneous wall) to about 5.5 hours (wall with the paraffin layer).