MATHEMATICAL MODELING OF OSCILLATORY MHD COUETTE FLOW IN A ROTATING HIGHLY PERMEABLE MEDIUM PERMEATED BY AN OBLIQUE MAGNETIC FIELD

• Published in: Chemical engineering communications 2011-02, Vol.198 (2), p.235-254
• Main Authors: Bég, O. Anwar, Ghosh, S. K., Narahari, M.
• Format: Article
• Language: English
• Subjects: Asymptotic solutions; Channel; Chemical engineering; Darcy number; Fluid dynamics; Hartmann number; Laplace transform method (LTM); Laplace transforms; Magnetic fields; Magnetohydrodynamics (MHD); Mathematical models; Oblique magnetic field; Oscillatory; Permeability; Porosity; Porous medium; Rotation; Secondary flow
• ISSN: 0098-6445; 1563-5201
• DOI: 10.1080/00986445.2010.500165

We study theoretically the incompressible, viscous, oscillatory hydromagnetic Couette flow in a horizontal fluid-saturated highly permeable porous medium parallel-plate channel rotating about an axis perpendicular to the plane of the plates under the action of a uniform magnetic field, B 0 , inclined at an angle θ to the axis of rotation. The flow is generated by the non-torsional oscillation of the lower plate of the channel. The reduced unsteady momentum equations are nondimensionalized with appropriate variables. Exact solutions under specified boundary conditions are obtained using the Laplace transform method (LTM). The flow regime is found to be controlled by a rotational parameter (K 2 ), which is the reciprocal of the Ekman number (Ek), the square of the Hartmann magnetohydrodynamic number (M 2 ), a porous medium permeability parameter (K p ), which is the inverse of the Darcy number (Da), oscillation frequency (ω), dimensionless time (T), and magnetic field inclination (θ). The influence of these parameters on the primary (u 1 ) and secondary (v 1 ) velocity field is presented graphically and studied in detail. Asymptotic behavior of the solutions is also examined for several cases of the square of the Hartmann number, rotation parameter, and oscillation angular frequency. The existence of modified Hartmann boundary layers is also identified. The present study has important applications in MHD (magnetohydrodynamic) energy generator flows, chemical engineering magnetic materials processing, conducting blood flows, and process fluid dynamics.