NUMERICAL INVESTIGATION OF THE MAGNETIC FIELD EFFECTS ON NATURAL CONVECTION WITHIN A POROUS HORIZONTAL CYLINDRICAL ANNULUS

Abstract

A numerical study is performed to investigate the magnetic field effects on steady laminar natural convection heat transfer between two concentric horizontal cylinders filled with a porous medium. The inner cylinder surface is maintained at a hot temperature (Th), while the outer cylinder surface is at a cold temperature (Tc). The external magnetic field is applied parallel to the gravity. A non-Darcian model is used to simulate the flow in the porous medium. The governing equations in a body-fitted coordinate system were solved numerically using the finite difference method. Numerical results have covered a wide range of the modified Rayleigh number (25 ≤ Ra∗ ≤ 800) and the Hartmann number (0 ≤ Ha ≤ 10). The porosity of porous medium, Prandtl number, and Darcy number were taken as, 0.8, 0.7, and 3.2 × 10−6, respectively. The obtained results are depicted in terms of the streamlines, isotherms, and local and average Nusselt numbers, which show significant effects of Hartmann number and modified Rayleigh number on the fluid flow and temperature distribution inside the annulus. Also, it was found that the increase of magnetic field cause a reduction in the average Nusselt number, which leads to increasing in the thermal insulation.