Role of Induced Magnetic Field on Transient Natural Convection Flow in a Vertical Channel: The Riemann Sum Approximation Approach
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Department of Mathematics Ahmadu Bello University, Zaria, NIGERIA
Online publication date: 2015-03-11
Publication date: 2015-02-01
International Journal of Applied Mechanics and Engineering 2015;20(1):65-85
This paper investigates the role of induced magnetic field on a transient natural convection flow of an electrically conducting, incompressible and viscous fluid in a vertical channel formed by two infinite vertical parallel plates. The transient flow formation inside the channel is due to sudden asymmetric heating of channel walls. The time dependent momentum, energy and magnetic induction equations are solved semi-analytically using the Laplace transform technique along with the Riemann-sum approximation method. The solutions obtained are validated by comparisons with the closed form solutions obtained for the steady states which have been derived separately and also by the implicit finite difference method. Graphical results for the temperature, velocity, induced magnetic field, current density, and skin-friction based on the semi-analytical solutions are presented and discussed.
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