Abstract
We study the electrically conducting fluid stability of magnetohydrodynamic flow between parallel plates by Chebyshev collocation method by applied transverse magnetic field. Temporal growth is obtained by the governing equations. The results show that the dominating factor is the change in shape of the undisturbed velocity profile caused by the magnetic field, which depends only on the Hartmann number. The stability equations is solved by QZ-algorithm to find the eigenvalue problem. The numerical calculation show that Magnetic field with particular magnitude destabilizes Couette flow while other magnitude stabilize the flow. It is also analyzed that Rec decreases rapidly to the minimum value for Hartmann number Ha greater than 3.887 and increases steadily from Hartmann number Ha (>5.559). It is observed that critical Reynolds number Rec is larger as Hartmann number decreases from Ha=3.887. The two critical Reynolds numbers in the elliptic curves are found for different values of Hartmann number.
Highlights
Today applied and fundamental research in engineering and physical science has developed by MHD into a vast field
We considered the linear instability of MHD Couette flow to examine the stability of the basic flow udder the influence of magnetic field on the and the growth of the small disturbances in the flow, The transverse magnetic field effect the stability of plane Couette flow of an electrically conducting fluid between parallel plates
Different values of N1 in Table I indicate the number of terms in the expansion (19) which is required for Rec and kc to converge
Summary
Today applied and fundamental research in engineering and physical science has developed by MHD into a vast field. MHD deals with the flow of electrically conducting fluid which is subject to the magnetic field and/or an electric current driven by an external voltage. Davidson[1] defined that study of MHD is the interactions between moving conducting fluids and magnetic field. Study of the electrically conducting fluids motions and their interactions with magnetic field is known as MHD. Magnetic field influence with man-made and many natural flows. They are routinely used in industry to heat pump, stir (motion in round) and levitate (rising in air) liquid metals. The effect of a constant uniform magnetic field on instability and transition to turbulence of electrically conducting fluids is a subject of growing interest. Most explanations in the effect of a magnetic field on the stability of static situations, being given in terms of the fluid moving through or ‘freezing’ to the field lines Chandrasekhar.[3]
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