The effect of magnetic-field-dependent viscosity and rotation on ferrothermohaline convection saturating a porous medium in the presence of dust particles

Abstract

This paper deals with the theoretical investigation of the combined effect of magnetic-field-dependent (MFD) viscosity and rotation on ferrothermohaline convection saturating a porous medium in the presence of dust particles subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained using a linearized stability theory and the normal mode analysis method. For the case of stationary convection, dust particles always have a destabilizing effect, whereas rotation, stable solute gradient and magnetic-field-dependent viscosity always have a stabilizing effect on the onset of convection. In the absence of rotation, the destabilizing effect of medium permeability is depicted, but in the presence of rotation, medium permeability may have a destabilizing or a stabilizing effect on the onset of convection. In the absence of MFD viscosity, the destabilizing effect of non-buoyancy magnetization is depicted, but in the presence of MFD viscosity, non-buoyancy magnetization may have a destabilizing or a stabilizing effect on the onset of convection. The critical wave number and critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of magnetic parameter M1 and results are depicted graphically. 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, stable solute gradient and rotation. The oscillatory modes are introduced due to the presence of the dust particles, stable solute gradient and rotation, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.