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EN
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.
EN
The unsteady Couette flow in a channel formed by two vertical parallel plates is investigated in the presence of internal heat generation/absorption. The flow is set up due to time dependent motion of one of the plates coupled with asymmetric heating of the infinite vertical parallel plates. Analytical solutions of the resulting partial differential equations are obtained using the Laplace transforms technique. The numerical values obtained from the analytical expressions for temperature, velocity, Nusselt number, skin-friction and mass flux are presented graphically to study the flow behaviour in the presence of the governing parameters. It is interesting to note that in the absence of convection currents (Gr=0) the flow is dependent only on the motion of one of the channel plates. The influence of the heat generation/absorption parameter on the rate of heat transfer on one plate is the exact opposite of the influence on the other plate while its influence on the skin-friction is identical on both plates. In the presence of external cooling, the mass flux diverges as time increases, while it converges to zero in the case of external heating.
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