Non-equilibrium heat transfer in metal-foam solar collector with no-slip boundary condition

Convective heat transfer in solar collectors filled with metal foams is analytically investigated with different methods, including numerical, analytical and fin-analysis methods. The Forchheimer/Brinkman/Darcy models are used to establish momentum equations for metal foams while the local thermal non-equilibrium (LTNE)/local thermal equilibrium (LTE) models are employed for energy equations. Some analytical solutions for velocity and temperature are obtained based on Darcy/Brinkman models with thermal dispersion effect considered. Numerical solution and fin solution are also obtained and compared with the analytical solutions with the pros and cons of different models discussed. Effects of some key parameters on flow and heat transfer are discussed. Present fin solution can provide more accurate estimation compared with the fin solution in the literature. The heat transfer difference between Brinkman model and Darcy model is obvious when the duct scale is small. In addition, the combined fin-LTE model is proposed for effectively evaluating thermal performance of metal foams.