Modelling the Effect of Hartmann Number on Transient Period, Viscous Dissipation and Joule Heating in a Transient MHD Flow over a Flat Plate Moving at a Constant Velocity
B. M. Nyamai *
Department of Mathematics and Physics, Moi University, P.O.Box 3900, Eldoret, Kenya.
*Author to whom correspondence should be addressed.
Abstract
This study is designed to investigate the effect of Hartmann number on transient period, Joule heating and viscous dissipation in an incompressible MHD (Magneto-Hydrodynamics) flow over a flat plate moving at a constant velocity. The governing momentum equation is non-dimensionalized and solved by the Laplace transform technique. The solution is decomposed into transient part and steady state part and then the effect of Hartmann number on transient period concerning velocity and its two related quantities (Joule heating and viscous dissipation) is analyzed. It was found out that when Hartmann number is increased the transient period is shortened and it was the same for the three quantities. In addition, the steady state solutions for both Joule heating and viscous heating were found to be equal. Even though velocity decreases when the Hartmann number is increased, the opposite was discovered for both Joule heating and viscous heating. Graphical analysis indicated that transient period changes considerably if Hartmann number is between 0 and 2. This study will find use in those industrial areas where magnetic fields are used to control liquid / molten metals in open channels.
Keywords: MHD, Hartmann number, transient period, Joule and Viscous dissipation