Free Convection in an Inclined Concentric Annular Square Cavities Filled With Porous Medium and Heated By Non-Uniform Temperature

Abstract

A numerical study of the two-dimensional steady free convection flow in an inclined annulus between two concentric square cavities filled with a porous medium is presented in this paper for the case when the side outer walls are kept with differentially heated temperature while the horizontal outer walls and the inner walls are insulated. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value. The Darcy model is used and the fluid is assumed to be a standard Boussinesq fluid. For the Cartesian coordinate system, the governing equations which were used in stream function form are discretized by using the finite difference method with successive under – relaxation method (SUR) and are solved by Gauss-Siedel iterative method. The upwind scheme was used for the transport terms in the energy conservation equation. The results are presented to demonstrate the streamlines, the isotherms, and the Nusselt number depending on the Rayleigh number ranging from (Ra =10 to 1000), dimension ratio from (Dr = 0.15 to 0.45), and the inclination angle from (= 0o to 45o). Also the effects of the amplitude (=0 to 1) and the wave number (f =0 to 5) of the heated side wall temperature variation on the free convection are investigated. The results show the effect of previous parameters (Ra, Dr,, , and f) on the flow fields and temperature profiles. It also show that the average Nusselt number is a strong function of the Rayleigh number, inclination angle, dimension ratio, and temperature variation. The peak value of the average Nusselt number based on the hot wall temperature is observed to occur at dimension ratio of (0.15), inclination angle of (40.1°), amplitude and wave number (1 & 0.75) for Rayleigh number of (1000).