Natural Convection Flow on a Vertical Cylinder with Sinusoidal Temperature Oscillation Under The Effect of Magneto Hydrodynamic

Abstract

       The present work investigates the effect of magneto hydrodynamic (MHD) laminar natural convection flow on a vertical cylinder subjected to sinusoidal temperature oscillation. The governing equations which used are continuity, momentum and energy equations. These equations are transformed to dimensionless equations using vortices-stream function method and the resulting nonlinear system of partial differential equations are then solved numerically using finite difference approximation. A computer program was built to calculate the rate of heat transfer in terms of average Nussle number, velocity distribution as well as temperature distribution for a selection of magneto hydrodynamic parameter range , dimensionless amplitude  and dimensionless time τ΄ (0.2 – 0.8). Numerical solution have been considered for a fluid Prenatal 542 number fixed at (Pr=0.7), Rayleigh number . Generally, the results show that Nu increase as Ra, M and a increase and decrease with τ΄. The effect of Ra and M on the rate of heat transfer is concluded by a correlation. The results are found to be in good agreement compared with the results of [Adams, 1954] for the case of no MHD.