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Finite element and network electrical simulation of rotating magnetofluid flow in nonlinear porous media with inclined magnetic field and Hall currents. (English) Zbl 1458.76063

Summary: A mathematical model is presented for viscous hydromagnetic flow through a hybrid non-Darcy porous media rotating generator. The system is simulated as steady, incompressible flow through a nonlinear porous regime intercalated between parallel plates of the generator in a rotating frame of reference in the presence of a strong, inclined magnetic field A pressure gradient term is included which is a function of the longitudinal coordinate. The general equations for rotating viscous magnetohydrodynamic flow are presented and neglecting convective acceleration effects, the two-dimensional viscous flow equations are derived incorporating current density components, porous media drag effects, Lorentz drag force components and Hall current effects. Using an appropriate group of dimensionless variables, the momentum equations for primary and secondary flow are rendered nondimensional and shown to be controlled by six physical parameters-Hartmann number (Ha), Hall current parameter (Nh), Darcy number (Da), Forchheimer number (Fs), Ekman number (Ek) and dimensionless pressure gradient parameter (Np), in addition to one geometric parameter-the orientation of the applied magnetic field (\(\theta\)). Several special cases are extracted from the general model, including the non-porous case studied earlier by S. K. Ghosh and I. Pop [“An analytical approach to MHD plasma behaviour of a rotating environment in the presence of an inclined magnetic field as compared to excitation frequency”, Int. J. Appl. Mech. Enging. 11, No. 4, 845–856 (2006)]. A numerical solution is presented to the nonlinear coupled ordinary differential equations using both the Network Simulation Method and Finite Element Method, achieving excellent agreement. Additionally very good agreement is also obtained with the earlier analytical solutions of [loc. cit.] for selected Ha, Ek and Nh values. We examine in detail the effects of magnetic field, rotation, Hall current, bulk porous matrix drag, second order porous impedance, pressure gradient and magnetic field inclination on primary and secondary velocity distributions and also frictional shear stresses at the plates. Primary velocity is seen to decrease with an increase in Hall current parameter (Nh) with the converse observed for the secondary velocity.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76E06 Convection in hydrodynamic stability
76S05 Flows in porous media; filtration; seepage
76W05 Magnetohydrodynamics and electrohydrodynamics
76U05 General theory of rotating fluids
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