Analytical modelling using Green’s functions of heat transfer in a flat solar air collector

Abstract

We have developed a purely analytical model to simulate the thermal behaviour of a flat solar air collector operating in forced convection.The mathematical model developed is based on a direct solution using Green’s functions of the linear equation for heat propagation in the air flowing through the rectangular flow path, interacting with the solid walls of the solar collector. Given the speed of the air flow and the mean solar heat flux, this approach can be used analytically to determine the two-dimensional temperature profile throughout the fluid.This analytical model is confirmed experimentally, and can determine the local and mean temperature field in the fluid and, in particular, the surface convective heat flow. It is also used to identify changes in the convective heat exchange coefficient as a function of position and air temperature at the solar collector outlet.