Abstract
Steady and unsteady flow of a second grade MHD fluid in a porous medium with Hall current effects is studied. Assuming an à priori known vorticity proportional to the stream function up to an additive uniform stream, exact solutions for velocity field are obtained corresponding to different choices of pertinent flow parameters. Graphical results are presented to depict the influence of pertinent flow parameters on the considered MHD flow.
Highlights
MHD flow analysis of differential type fluids have been the subject of numerous experimental, mathematical and numerical studies over the past few decades due to their diverse applications in for example exploration geophysics, hydrology, cooling system designs and MHD generators, see Refs. 1–11 and references therein.The constitutive equations of the differential type fluids, that are non-Newtonian in nature, possess non-linearity both in inertial and viscous parts
Assuming an à priori known vorticity proportional to the stream function up to an additive uniform stream, exact solutions for velocity field are obtained corresponding to different choices of pertinent flow parameters
The fluid is conducting under the application of an applied magnetic field and it flows through a porous medium together with Hall current effects
Summary
MHD flow analysis of differential type fluids have been the subject of numerous experimental, mathematical and numerical studies over the past few decades due to their diverse applications in for example exploration geophysics, hydrology, cooling system designs and MHD generators, see Refs. 1–11 and references therein. Several attempts have been made to find analytic and closed form solutions to velocity field and stream functions for various physical and geometrical configurations. Labropulu[12] considered a specific vorticity, different from that discussed in Ref. 24 and presented both steady as well as unsteady solutions. In prior work, no attempt has been made, at least not to the knowledge of the authors, to resolve both steady and unsteady second grade MHD fluids in porous media using a vorticity proportional to the stream function up to an additive uniform stream depending upon both spatial variables; see (17) below.
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