Computational Treatment of MHD Transient Natural Convection Flow in a Vertical Channel Due to Symmetric Heating in Presence of Induced Magnetic Field

Abstract

This paper considers the effect of induced magnetic field on transient hydromagnetic natural convection flow of an incompressible viscous electrically conducting fluid in the presence of transverse magnetic field in a vertical channel formed by electrically non-conducting infinite vertical parallel plates due to symmetric heating of vertical parallel plates. The problem is solved using Laplace transform technique and the inversion of the Laplace domain to the time domain is obtained by Riemann-sum approximation method. In order to verify the accuracy of Riemann-sum approximation method, analytical solution for steady state mathematical model is obtained in closed form. The governing equations are also solved using an implicit finite difference method to confirm the method used in the present problem. During the course of numerical computation an excellent agreement was found between steady state solution obtained exactly and transient solution obtained by implicit finite difference method or Riemann sum approximation method at large values of time. The dimensionless parameters in the flow are extensively discussed with the help of graphs.