Numerical study of natural convection in a vertical cylindrical annulus using a non-Darcy equation

A numerical investigation of transient free convection in a vertical cylindrical annulus filled with a fluid saturated porous medium with the inner wall heated to a uniform temperature, the outer wall cooled to a uniform temperature and maintaining top and bottom boundaries at adiabatic condition, has been carried out. A finite difference implicit method which incorporates upwind differencing for nonlinear convective terms and the successive line over relaxation (SLOR) method for convergence are used to solve the coupled nonlinear governing equations. Heat transfer rate and flow fields are obtained for wide range of Rayleigh numbers Ra ranging from 10(3) to 10(6) Darcy numbers Da ranging from 10(-1), to 10(-3), radii ratio lambda in the range 1 less than or equal to lambda less than or equal to 2, and aspect ratio in the range 1 less than or equal to A less than or equal to 2. The numerical results indicate that the temperature and velocity fields are significantly, modified and the heat transfer rate is decreased as the Darcy number decreases. The temperature and velocity fields are significantly modified by the radii ratio. The rate of heat transfer increases with an increase in radii ratio. At a high Rayleigh number the curvature affect on beat transfer is insignificant. The numerical results further indicate that an increase in viscosity ratio (A) reduces the Nusselt number by enhancing the contribution of the viscous diffusion term.