A two-energy equation model for conduction and convection in porous media

A two-energy equation model is proposed for analyzing conduction and convection within porous media in local thermal non-equilibrium. Hsuʹs closure model for the tortuosity effect has been extended to treat not only conduction but also convection in porous media. The two energy equations for the individual phases are combined into a fourth-order ordinary differential equation, so as to treat one-dimensional steady-state problems. Then, the exact solutions are obtained for two fundamental cases, namely, one-dimensional steady conduction in a porous slab with internal heat generation within a solid, and also thermally developing unidirectional flow through a semi-infinite medium.