Simulation of transient heat transfer in multilayer walls with photovoltaic cell and air by using efficient numerical methods

Abstract

This paper focuses on simulating nonlinear transient heat transfer in multilayer walls under varying heat loads, using efficient numerical algorithms. The algorithms employed are completely explicit and unconditionally stable for the linear conduction-convection case. The study investigates heat transfer through building walls, considering different wall geometries and heat load scenarios, encompassing both cooling and heating. Our primary objective is to analyse how heat transfer depends on the wall materials and evaluate algorithm performance in cases involving heat transfer between solid surfaces and fluid (convection) on the outdoor surface, particularly across an air gap between insulation and Photovoltaic Cells (PVC). The results reveal that insulation prevents heat from entering the building, maintaining a comfortable indoor environment. Forced convection significantly enhances heat dissipation, especially during cooling operations to protect PVC with limited working temperature. Furthermore, the simulations highlight the air gap's efficiency in cooling PVC and reducing maximum temperatures on the insulation's outer surface, especially under forced convection conditions. The test results show that the leapfrog hopscotch algorithm offers the best solution for this highly stiff system, followed by the asymmetric and shifted hopscotch algorithms. This study offers insights into optimizing heat transfer within multilayer walls, with implications for building energy efficiency and thermal comfort.

Keywords

• Transient heat transfer
• Non-linear heat transfer
• Thermal insulation
• Photovoltaic cell
• Explicit stable numerical methods