The effect of magnetic field dependent viscosity on thermosolutal convection in ferromagnetic fluid

Abstract

The effect of magnetic field dependent (MFD) viscosity on thermosolutal convection in ferromagnetic fluid is considered for a ferromagnetic fluid layer heated and soluted from below in the presence of a uniform vertical magnetic field. Using the linearized stability theory and the normal mode analysis method, an exact solution is obtained for the case of two free boundaries. For the case of stationary convection, stable solute gradient and MFD viscosity have stabilizing effects on the onset of instability. The magnetization may have destabilizing or stabilizing effect in the presence of MFD viscosity, whereas magnetization has always destabilizing effect in the absence of MFD viscosity. 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 M 1 and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid heated from below in the absence of stable solute gradient. The oscillatory modes are introduced due to the presence of the stable solute gradient, which were non-existent in its absence. A sufficient condition for the non-existence of overstability is also obtained.