Thermal convection in tilted porous fractures

We study theoretically and experimentally the thermal convection in long tilted fractures filled with a porous material (porous layer) embedded in an impermeable solid and saturated with a fluid. The solid is subjected to a constant, vertical temperature gradient and has thermal conductivity larger than that of the saturated porous layer. We discuss different cases of interest in terms of the fracture aspect ratio and the fracture-to-solid conductivity ratio. Analytical expressions for the temperature and velocity profiles of the flow in the porous layer are worked out for low-Rayleigh-number flows.