The thermosolutal instability of axt Oldroydian viscoelastic fluid in porous medium is considered. The effects of uniforrn rotation and unfforra magnetic field, separately, have also been studJed. The stable solute gradient, rotation and magnetic field ate found to have stabilizing effects on the system. The medium permeability has destabilizing effect but in the presence of rotation it has both stabilizing and destabilizing effects depending on the rotation parameter. Th~ magnctic field, rotation and stable solute gradient introduce osciUatory modcs in the system which were non-existent in their absence.

Present study has been conducted to examine the effect of laser surface texturing combined with couple stress fluids on the hydrodynamic lubrication of finite journal bearing in this work. The JFO (Jakobsson, Floberg and Olsson) boundary conditions have been engaged instead ofReynolds boundary conditions to achieve realistic results. Moreover, the results were computed and well-authenticated with the previous published work. It has been observed that load carrying capacity gets increased with couple stresses for smooth journal bearings at different eccentricity ratios. However the increment in load carrying capacity with texture affects only at low eccentricity ratios. The combined effects of texturing with couple stress fluids lower the performance of journal bearing at different eccentricity ratios.

A nonlinear (energy) stability analysis is performed for a magnetized ferrofluid layer heated from below, in the stress-free boundary case. By introducing a suitable generalized energy functional, a rigorous nonlinear stability result is derived for a thermoconvective magnetized ferrofluid. The mathematical emphasis is on how to control the nonlinear terms caused by the magnetic body and inertia forces. It is found that the nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of the linear instability analysis, and thus indicates that the subcritical instabilities are possible. However, it is noted that, in the case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of magnetic parameter, M 3 , on subcritical instability region has also been analysed. It is shown that with the increase of magnetic parameter, M 3 , the subcritical instability region between the two theories decreases quickly. We also demonstrate coupling between the buoyancy and the magnetic forces in the nonlinear energy stability analysis.

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