Convection-radiation heat transfer in solar heat exchangers filled with a porous medium: Exact and shooting homotopy analysis solution

The case of combined conduction-convection-radiation heat transfer usually occurred in solar thermal usages is the aim of the present study. In this work, the type of combined heat transfer in heat exchangers filled with a fluid saturated cellular porous medium is revisited. It is shown the governing strongly nonlinear differential equation, which has been formulated by performing Darcy-Brinkman equation is exactly solvable. A full discussion and exact analytical solution (Dimensionless temperature distribution) in the implicit form is given for further physical interpretation and it is proved the solution is mathematically unique. The uniqueness of solution is also confirmed by a so-called shooting homotopy analysis method. Furthermore, Effects of porous medium shape parameter (s) and radiation parameters (Tr and λ) on the thermal performance are exactly analyzed.