The Brinkman model for thermosolutal convection in a vertical annular porous layer

A numerical study is carried out on double-diffusive natural convection within a vertical circular porous annulus. Motions are driven by the externally applied constant temperature and concentration differences imposed across the vertical walls of the enclosure. In the formulation of the problem, use is made of the Brinkman extended Darcy model which allows the no-slip boundary condition on a solid wall, to be satisfied. The flow is assumed to be laminar and two dimensional. The density variation is taken into account by the Boussinesq approximation. The control-volume approach is used for solving the governing equations. Solutions for the flow fields, temperature and concentration distributions and Nusselt, Nui and Sherwood, Shi numbers are obtained in terms of the governing parameters of the problem. The effect of both the Darcy number, Da, and the radius ratio, κ, on Nui and Shi is found to be significant. Results for a pure viscous fluid and a Darcy (densely packed) porous medium emerge from the present model as limiting cases.