Construction of a model for an enclosing structure with a heat-accumulating material with phase transition taking into account the process of solar energy accumulation

Abstract

This paper proposes a mathematical model and a procedure for calculating the thermal state of the enclosing structure of the building, which includes an energy-active panel that accumulates solar radiation due to the phase transition of the heat-accumulating material. The mathematical model is based on a two-dimensional non-stationary nonlinear equation of thermal conductivity, which describes the process of heat transfer in the bearing layer of the enclosing structure and the energy-active panel. The model also includes equations describing radiant heat transfer between opaque and translucent bodies. To correctly describe solar insolation, the ASHRAE 2009 model was used in conjunction with the daily change in the position of the Sun in the sky. To solve the system of equations that make up the mathematical model, an iterative procedure has been developed, which involves alternating solution at each time step of the two-dimensional equation of thermal conductivity and a set of algebraic equations of convective and radiant heat transfer. The study’s result established that the amount of accumulated energy in the heat-accumulating material of the phase transition during daylight hours increases significantly, from 15 to 35 %. At night, the surface temperature of the heat-accumulating element in structures using a material with a phase transition is greater than in the case of heat accumulation only in the bearing layer. As a result, it is possible to select from 70 to 120 % more accumulated heat while the presence of high-thermal partitions in a heat-accumulating material with a phase transition contributes to an increase in accumulated heat and usable heat