Numerical solutions to natural convection in a channel with porous walls under a transverse magnetic field

The problems of fully developed natural convection flow in a porous channel under transverse magnetic field are discussed, and a combination of both linear and quadratic density temperature variations is used to express the body force term as a buoyancy term. A finite difference scheme is used to transform the equations of motion and energy into a set of nonlinear algebraic equations, which are then solved by the usual iterative method. It is found that an increase in Hartmann number is followed by a decrease in both velocity and temperature throughout the width of the channel. For large positive suction Reynolds numbers, the plane of maximum velocity is pulled towards the lower wall while that of maximum temperature is shifted toward the upper wall. For small suction Reynolds numbers, the lower wall is cooled and the upper wall is heated, while the situation is reversed for large numbers.