Some stability problems of Non-Newtonian Fluids

Abstract

The non-Newtonian fluids are of vital importance due to their diverse applications in modern technology, industries and bio-mechanics. Thus, the analysis of thermal stability and thermosolutal stability of such fluids like Rivlin-Ericksen fluids, couple-stress fluids, ferromagnetic fluids and micropolar fluids are desirable. We have used the two fundamental hypotheses i.e., continuum hypothesis and Newtonian mechanics throughout our study. In the present thesis, the linearized stability theory and normal mode analysis have been used to study the effects of various important parameters like suspended particles, compressibility, rotation, magnetic field, Hall currents, solute gradient, variable gravity, porous medium, micropolar coefficient, coupling parameter, micropolar heat conduction parameter etc. on various stability problems of hydrodynamic and hydromagnetic systems of non-Newtonian fluids. The thermal stability of a layer of Rivlin-Ericksen fluid heated and soluted from below in porous medium is considered to include the effect of suspended particles in the presence of uniform magnetic field, uniform rotation and variable gravity field. It is found that, for stationary convection, suspended particles have destabilizing effect, solute gradient has stabilizing effect whereas magnetic field, permeability and rotation have stabilizing/destabilizing effect under certain conditions. The principle of exchange of stabilities is satisfied in the absence of magnetic field, rotation and stable solute gradient. The presence of these parameters introduces oscillatory modes into the system.