Transient MHD Natural Convection between Two Vertical Walls Heated/Cooled Asymmetrically

Abstract

The present paper analyses a closed form solution for the transient free convective flow of a viscous and incompressible fluid between two vertical walls as a result of asymmetric heating or cooling of the walls. The convection currents between the walls occur due to a change in the temperature of the walls to that of the temperature of the fluid. The Laplace transform method has been used to find the solutions for the velocity and temperature fields by solving the governing partial differential equations. The numerical values obtained from the analytical solution show that the flow is initially in the downward direction near the cooled wall for negative values of the buoyancy force distribution parameter. The temperature field of both the air and water gradually decreases and becomes negative near the cooled wall for all negative values of the buoyancy force distribution parameter. The transient solution approaches a steady state when the non-dimensional time becomes comparable with the actual Prandtl number.