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3 International Journal of Applied Mechanics and Engineering

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Role of sudden application or withdrawal of magnetic field on MHD Couette flow

Jha B. K., Oni M. O.

International Journal of Applied Mechanics and Engineering

2019

Vol. 24, no. 4

92--105

This article investigates the impact of a sudden application or sudden withdrawal of a magnetic field on an unsteady MHD Couette flow formation in a parallel plate channel. The governing momentum equation is derived and solved exactly in Laplace domain using the Laplace transform technique with the necessary initial and boundary conditions to capture the present physical situation for the cases; sudden application or sudden withdrawal of a magnetic field. Due to the complexity of the solution obtained, the Riemann-sum approximation technique is used to transform the Laplace domain to time domain. During the course of graphical and tabular representations, results show that the Hartmann number, time and nature of application of a magnetic field play an important role in the transition from hydrodynamic to magnetohydrodynamic flow and vice-versa. Also, fluid velocity steady-state solution is independent on whether the magnetic field is fixed relative to the moving plate or to the fluid for sudden withdrawal of magnetic field. In addition, the application of a sudden magnetic field leads to a delay in the attainment of steady-state solution.

Unsteady Hartmann two-phase flow: the Riemann-sum approximation approach

Jha B. K., Babila C. T., Isa S.

International Journal of Applied Mechanics and Engineering

2016

Vol. 21, no. 4

891--904

We consider the time dependent Hartmann flow of a conducting fluid in a channel formed by two horizontal parallel plates of infinite extent, there being a layer of a non-conducting fluid between the conducting fluid and the upper channel wall. The flow formation of conducting and non-conducting fluids is coupled by equating the velocity and shear stress at the interface. The unsteady flow formation inside the channel is caused by a sudden change in the pressure gradient. The relevant partial differential equations capturing the present physical situation are transformed into ordinary differential equations using the Laplace transform technique. The ordinary differential equations are then solved analytically and the Riemann-sum approximation method is used to invert the Laplace domain into time domain. The solution obtained is validated by comparisons with the closed form solutions obtained for steady states which have been derived separately and also by the implicit finite difference method. The variation of velocity, mass flow rate and skin-friction on both plates for various physical parameters involved in the problem are reported and discussed with the help of line graphs. It was found that the effect of changes of the electric load parameter is to aid or oppose the flow as compared to the short-circuited case.

Role of induced magnetic field on transient natural convection flow in a vertical channel: The Riemann sum approximation approach

Jha B. K., Sani I.

International Journal of Applied Mechanics and Engineering

2015

Vol. 20, no. 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 Chanel 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 hale 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.