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On exact solution of unsteady MHD flow of a viscous fluid in an orthogonal rheometer. (English) Zbl 1304.35568
Summary: This paper studies the unsteady MHD flow of a viscous fluid in which each point of the parallel planes are subject to the non-torsional oscillations in their own planes. The streamlines at any given time are concentric circles. Exact solutions are obtained and the loci \(\Gamma\) of the centres of these concentric circles are discussed. It is shown that the motion so obtained gives three infinite sets of exact solutions in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks. These solutions reduce to a single unique solution when symmetric solutions are looked for. Some interesting special cases are also obtained from these solutions.
MSC:
35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
76U05 General theory of rotating fluids
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