COMPUTATION OF NATURAL CONVECTION IN A POROUS PARALLELOGRAMMIC ENCLOSURE WITH A MAGNETIC FIELD

Abstract

Detailed numerical calculations are presented in this paper for natural convection in a porous parallelogrammicenclosure with a magnetic field. The inclined walls are maintained isothermally at different temperatures. The top andbottom horizontal straight walls are kept adiabatic. To simplify the effort in matching the grid mesh with the inclinedwalls of the parallelogrammic region/geometry, the computational domain is mapped onto a rectangular shape using anon-linear axis transformation. Transport equations are modeled by a stream-vorticity formulation then expressed in thenew coordinate system and solved numerically by a finite difference method. Based upon the numerical predictions, wefound the convection modes within the enclosure depended upon the Rayleigh number and the inclination angle. As thevalue of magnetic field is made larger, the strength of the heat transfer is progressively suppressed. Tuning theinclination angle decreases the heat transfer performance.

Keywords

• Darcy’s law
• natural convection
• numerical method
• Porous media