Effects of MFD viscosity and LTNE on the onset of ferromagnetic convection in a porous medium

The combined effect of magnetic field dependent (MFD) viscosity and a local thermal non-equilibrium (LTNE) on the criterion for the onset of ferromagnetic convection in a ferrofluid saturated horizontal porous layer heated from below in the presence of a uniform vertical magnetic field is studied analytically using linear stability theory. A modified Darcy equation is used to describe the flow in the porous medium and a two-field model for temperature each representing the solid as well as fluid phases separately is used for energy equation. It is demonstrated that the principle of exchange of stability is valid. The results indicate that the onset of ferromagnetic convection is delayed with an increase in the MFD viscosity parameter but shows no influence on the critical wave number. Moreover, the system is found to be more stable when the magnetic forces alone are present. Asymptotic solutions for both small and large values of scaled interphase heat transfer coefficient Ht are presented and compared with those computed numerically. An excellent agreement is obtained between the asymptotic and the numerical results. Besides, the influence of magnetic and LTNE parameters on the stability characteristics of the system is also discussed.