Convection–radiation heat transfer in solar heat exchangers filled with a porous medium: Homotopy perturbation method versus numerical analysis

The case of combined conduction–convection–radiation heat transfer usually occurred in solar thermal usages is the aim of the present study. This type of combined heat transfer in heat exchangers filled with a fluid saturated cellular porous medium is investigated. The flow is modeled by the Darcy–Brinkman equation. The steady state model of this combined heat transfer is solved semi-analytically based on the homotopy perturbation method (HPM) and numerically based on the finite difference method. No analytical solution has been previously proposed for the problem. Effects of porous medium shape parameter (s) and radiation parameters (Tr and λ) on the thermal performance are analyzed. Furthermore, a discussion on the accuracy and limitations of the HPM in this kind of problems is represented. This study shows that semi-analytical methods (like HPM, VIM, DTM, and HAM) can be used in simulation and prediction of thermal performance of solar energy harvesting systems.