Heat Transfer in Solids. Dual Phase Lag, Thermal Stationary Waves and the Development of Thermal Strings Model: Masonry Wall Case Study

Abstract

The purpose of this study is the development of an analytical solution based computational tool for heat transfer in solids. The proposed method extends the Dual Phase Lag theory by the introduction of the solid body that is considered as a pulsating thermal string whose oscillations correspond to temperature fluctuations. These oscillations give stationary thermal waves in every axis. The combination of the three dimensional 3D Thermal Strings provided the ability to describe the temperature changes of solid bodies, the calculation of the relaxation time required towards equilibrium, and the thermal load required to keep a non-equilibrium state.  The model is based on the analytical solution of the heat transfer equation in three dimensions, so it can deal for the whole solid body e.g. a wall element. It is proved that these oscillations are critical dumped ones and the model uses mathematical formulations to calculate the time required for an area to reach a “target temperature” which describes the final temperature. The solution depends on the initial and boundary conditions of the solid. The validation and reliability of the Thermal Strings model were obtained by comparing the results of the proposed model against the classic heat transfer which found to be identical.