Numerical analysis of natural convection in an inclined trapezoidal enclosure filled with a porous medium

Abstract

A theoretical study of buoyancy-driven flow and heat transfer in an inclined trapezoidal enclosure filled with a fluid-saturated porous medium heated and cooled from inclined walls has been performed in this paper. The governing non-dimensional equations were solved numerically using a finite-difference method. The effective governing parameters are: the orientation or inclination angle of the trapezoidal enclosure ϕ, which varies between 0° and 180°, the Rayleigh number Ra, which varies between 100 and 1000, the side wall inclination angle θ s and the aspect ratio A. The side wall inclination parameter θ s is chosen as 67°, 72° and 81° and the calculations are tested for two different values of A = 0.5 and 1.0. Streamlines, isotherms, Nusselt number and flow strength are presented for these values of the governing parameters. The obtained results show that inclination angle ϕ is more influential on heat transfer and flow strength than that of the side wall inclination angle θ s . It is also found that a Bénard regime occurs around ϕ = 90 ° , which depends on the inclination of the side wall, Rayleigh number and aspect ratio.