Natural convection in a square porous annulus

The current study is focused to investigate the natural convective heat transfer characteristics in a porous square annulus. Finite element method is used as a tool to simplify the partial differential equations that govern the heat and fluid flow characteristics inside the porous medium. A simple three noded triangular element is used to divide the porous domain into smaller segments known as elements. The algebraic set of equations resulting from the finite element equation are assembled into a global matrix and then solved iteratively to get the solution variables. Thermal equilibrium as well as non equilibrium in porous domain is considered. The effect of various geometric and physical parameters are investigated. The boundary conditions are such that the inner walls of the annulus are heated isothermally to temperature Th, and the outer surfaces are exposed to cool temperature Tc. The width ratio defined as the ratio of hollow portion to the length of the cavity is varied from 0.125 to 0.875. Results are discussed with respect to width ratio, Rayleigh number, radiation parameter and viscous dissipation parameter.