Stability of Magnetohydrodynamic Flow over a Stretching Sheet
The linear stability of two-dimensional flow of a viscous electrically conducting fluid permeated by a uniform transverse magnetic field over a flat porous deformable sheet is investigated when the sheet is stretched in its own plane with an outward velocity proportional to the distance from a point on it. Since the flow has curved streamlines as in a stagnation point flow, its stability is examined with respect to three-dimensional disturbances in the form of Taylor-Gortler vortices. Using a numerical method, the differential equations governing stability are integrated for various values of the suction(R) and magnetic(M) parameter. It is shown that the flow is stable for all values of R, M and non-zero values of the dimensionless wave number \(\overline\alpha \) Further for fixed \(\overline\alpha \) and R, the decay rate of the disturbances increases with M. This study is likely to be relevant to certain metallurgical processes where a magnetic field is used to control the rate of cooling of a stretching sheet by drawing it through a coolant.
KeywordsLinear Stability Incompressible Viscous Fluid Stagnation Point Flow Dimensionless Wave Number Magnetohydrodynamic Flow
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