Abstract
Numerical analysis and analytical solution were performed to study the free convection in transient Couette flow of an electrically conducting fluid confined between two vertical parallel plates. Constant heat flux on the wall with uniform vertical motion in its own plane and periodic temperature on the stationary wall were applied. The dimensionless governing momentum and energy equations are solved numerically using a fully implicit finite difference method. An analytical solution using eigenfunction expansion method is carried out for temperature profile in case of constant plate temperature. Analytical and numerical results converge at a satisfactory degree. The effect of different physical parameters on the transient velocity and temperature, such as Grashof’s number (Gr), magnetic parameter (M), Prandtl number (Pr) and temperature frequency are also studied. It is found that the velocity increases with an increase in Gr and temperature frequency, while it decreases with an increase in Pr and M.
Highlights
Magnetohydrodynamic (MHD) flow of a viscous incompressible electrically conducting fluid has many industrial and engineering applications
The objective of this study is to investigate the transient free convection MHD Couette flow with the presence of both periodic temperature and constant heat flux on walls
The numerical solution using Crank-Niclson technique for velocity and temperature profiles is computed for different values of magnetic parameter, Prandtl number, Grashof number, and temperature frequency
Summary
Magnetohydrodynamic (MHD) flow of a viscous incompressible electrically conducting fluid has many industrial and engineering applications. The effect of the magnetic field on the natural convection flow between two vertical plates under various conditions has been studied extensively. The Laplace transform technique was used to obtain expressions for velocity and temperature fields and their related quantities for the unsteady free convective flow of an incompressible viscous fluid between two vertical parallel plates for impulsive start of one of the plates [1]. The combined effect of natural convection and uniform transverse magnetic field on the Couette flow of an electronically conducting fluid between two parallel plates for impulsive motion of one of the plates was studied in [2], in which expressions for velocity and temperature fields were presented for two different cases, under the assumption of negligible induced magnetic field. Results indicated an increase in the Kelvin forces associated with a thermal boundary layer thickness decrease (higher Reynolds Number)
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