Oscillatory Porous Medium Ferroconvection in a Viscoelastic Magnetic Fluid with Non-Classical Heat Conduction

Abstract

The classical stability analysis is used to examine the combined effect of viscoelasticity and the second sound on the onset of porous medium ferroconvection. The fluid and solid matrix are assumed to be in local thermal equilibrium. Considering the boundary conditions appropriate for an analytical approach, the critical values pertaining to both stationary and oscillatory instabilities are obtained by means of the normal mode analysis. It is observed that the oscillatory mode of instability is preferred to the stationary mode of instability. It is shown that the oscillatory porous medium ferroconvection is advanced through the magnetic forces, nonlinearity in magnetization, stress relaxation due to viscoelasticity, and the second sound. On the other hand, it is observed that the presence of strain retardation and porous medium delays the onset of oscillatory porous medium ferroconvection. The dual nature of the Prandtl number on the Rayleigh number with respect to the Cattaneo number is also delineated. The effect of various parameters on the size of the convection cell and the frequency of oscillations is also discussed. This problem may have possible implications for technological applications wherein viscoelastic magnetic fluids are involved.

Keywords

• Convection
• Maxwell equations
• Navier-Stokes equations for incompressible viscous fluids
• Porous media
• Viscoelastic fluids
• Ferroconvection