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

• The convection–radiation heat transfer in porous filled heat exchangers is studied.
• The Nu number and dimensionless temperature are obtained and discussed.
• The radiative conductivity can enhance the heat transfer rate up to ten times.
• Applicability of HPM is shown via a comparison with numerical analysis.
• It's practical in solar collectors, energy storing packed beds, sun-spaces and etc.

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.