The effect of magnetic-field-dependent viscosity on ferroconvection in a porous medium in the presence of dust particles

Abstract

This paper deals with the theoretical investigation of the effect of magnetic-field-dependent (MFD) viscosity on the thermal convection in ferromagnetic fluid saturating a porous medium in the presence of dust particles. For a flat ferromagnetic fluid layer contained between two free boundaries, the exact solution is obtained using a linear stability analysis. For the case of stationary convection, medium permeability and dust particles always have a destabilizing effect whereas the MFD viscosity has a stabilizing effect on the onset of convection. In the absence of MFD viscosity, the destabilizing effect of magnetization is depicted but in the presence of MFD viscosity, magnetization may have a destabilizing or stabilizing effect on the onset of convection. The critical wave number and critical magnetic thermal Rayleigh number for the onset of stationary convection are also determined numerically for sufficiently large values of buoyancy magnetization parameter M1. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. It is observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid saturating a porous medium heated from below in the absence of dust particles. The oscillatory modes are introduced due to the presence of the dust particles, which were nonexistent in their absence. A sufficient condition for the nonexistence of overstability is also obtained.