Overstable Magneto-Thermal Convection in a Viscoelastic Ferromagnetic Fluid Saturating a Porous Medium

Abstract

The thermal stability of an incompressible, electrically conducting non-Newtonian ferromagnetic fluid saturated horizontal porous layer heated from below subjected to a magnetic field is investigated. The rheology of the ferromagnetic fluid is described by Walter’s (model ) for calculating the shear stresses from the velocity gradients. The Darcy law for the non-Newtonian ferromagnetic fluid of the Walter’s (model ) type is used to model the momentum equations. The boundaries are considered to be stress-free. The employed model incorporates the effects of buoyancy magnetization, kinematic viscoelasticity, medium porosity and medium permeability. The linear theory   and normal mode technique are used to reduce the coupled non-linear partial differential equations to linear differential equations and the eigenvalue problem is solved analytically by using trial functions satisfying the boundary conditions in the Galerkin Weighted Residuals method. The criteria for both stationary and oscillatory modes are also derived analytically. Numerical results are computed using the software MATHEMATICA version 5.2 and presented graphically. It is observed that the magnetic field and buoyancy magnetization stabilize, whereas the medium permeability and medium porosity destabilize the physical system for both the cases of stationary and oscillatory motions. It is also found that oscillatory modes are not allowed in the absence of magnetic field and viscoelasticity implying thereby that principle of exchange of stabilities is valid.