Effect of dust particles on ferrofluid heated and soluted from below

Abstract

This paper deals with the theoretical investigation of the effect of dust particles on the thermosolutal convection in ferrofluid subjected to a transverse uniform magnetic field. Using linearized stability theory and normal mode analysis, an exact solution is obtained for the case of two free boundaries. For the case of stationary convection, non-buoyancy magnetization and dust particles have a destabilizing effect, whereas stable solute gradient has a stabilizing effect on the onset of instability. The critical wave number and critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of buoyancy magnetic parameter M 1 and results are depicted graphically. It is observed that the critical magnetic thermal Rayleigh number is reduced 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 good for the ferrofluid heated from below in the absence of dust particles and stable solute gradient. The oscillatory modes are introduced due to the presence of the dust particles and stable solute gradient, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained. The paper also reaffirms the qualitative findings of earlier investigations which are, in fact, limiting cases of the present study.