Thermal flows in fractured porous media

We consider the thermal flow problem occuring in a fractured porous medium. The incompressible filtration flow in the porous matrix and the viscous flow in the fractures obey the Boussinesq approximation of the Darcy-Forchheimer law and respectively, the Stokes system. They are coupled by the Saffman's variant of the Beavers-Joseph condition. Existence and uniqueness properties are presented. In the ε-periodic framework, the two-scale homogenized system which governs the asymptotic behaviour (when ε → 0) is found