Numerical Study of Non-Darcian Natural Convection Heat Transfer in a Rectangular Enclosure Filled with Porous Medium Saturated with Viscous Fluid

Abstract

A numerical study of non-Darcian natural convection heat transfer in a rectangular enclosure filled with porous medium saturated with viscous fluid was carried out. The effects of medium Rayleigh number, porosity, particle to fluid thermal conductivity ratio, Darcy number and enclosure aspect ratio on heat transfer were examined to demonstrate the ability of using this construction in thermal insulation of buildings walls. A modified Brinkman-Forchheimer-extended Darcy flow model was used and no-slip boundary conditions were imposed for velocity at the walls and the governing equations were expressed in dimensionless stream function, vorticity, and temperature formulation. The resulting algebraic equations obtained from finite difference discritization of vorticity and temperature equations are solved using (ADI) method which uses Three Diagonal Matrix Algorithm (TDMA) in each direction, while that of the stream function equation solved using successive iteration method. The study was done for the range of enclosure aspect ratio ( 2 H / L 30 ) which is in the tall layers region at medium Rayleigh number (5 2000 m Ra ), Darcy number (Da=10-3, 10-4, 10-5 ), porosity ( =0.35, 0.45, 0.55), particle to fluid thermal conductivity (kS/kf=5.77, 38.5, 1385.5).The results showed that the Nusselt number is direct proportional to medium Rayleigh number and porosity and reversely proportional to Darcy number, ratio of particle to fluid thermal conductivity and enclosure aspect ratio. The variables that affect the heat transfer in the above arrangement was correlated in a mathematical equation that account better for their affects on heat transfer which is represented by mean Nusselt number (Nu).

Keywords

• Porous medium
• Rectangular enclosure
• Non-Darcian Natural Convection
• Viscose fluid