Heat and mass transfer in a saturated porous wedge with impermeable boundaries

Heat and mass transfer in a two-dimensional radial flow of a viscous fluid through a saturated porous wedge-shaped region with confining walls is studied. Similarity transformations are used for the temperature, velocity and pressure, in order to reduce the describing systems to ordinary differential equations with two-point boundary conditions. Both exact and asymptotic solutions are obtained for the velocity and the temperature. It is found that two distinct solutions (jet flow type and slug flow type) exist for a given set of flow parameters. Specific results are presented for small wedge angles. It is shown that symmetric diverging solutions do not exist above a critical Rayleigh number. An application of the theory to the convection of liquid water in a crude model of a fault zone in a geothermally active area is presented.