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Similarity solutions of a MHD boundary-layer flow past a continuous moving surface. (English) Zbl 1213.76234
Summary: This note deals with a theoretical and numerical analysis of multiple similarity solutions of the two-dimensional MHD boundary-layer flow over a permeable surface, with a power law stretching velocity, in the presence of a magnetic field $B$ applied normally to the surface. We have taken the free stream velocity to vary as ${x}^{m}$, where $x$ is the coordinate along the plate measured from the leading edge and $m$ is a constant. The magnetic field $B$ is assumed to be proportional to ${x}^{\frac{m-1}{2}}$. The problem depends on the power law exponent and the magnetic parameter $M$ or the Stewart number. It is shown, under certain circumstance, that the problem has an infinite number of solutions.
##### MSC:
 76W05 Magnetohydrodynamics and electrohydrodynamics 76D10 Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids) 76M55 Dimensional analysis and similarity (fluid mechanics)