A nonlinear stability analysis for magnetized ferrofluid heated from below in the presence of couple stresses for combination of different bounding surfaces

Abstract

This work aims to inspect the impact of couple stress forces on the convective stability of magnetized ferrofluid for different combinations of bounding surfaces. Both linear and nonlinear analyses are conducted to obtain eigenvalue problems. Normal mode analysis is used for linear analysis, while the energy method is used for nonlinear analysis, and a generalized energy functional is introduced. For solving eigenvalue problems, the Galerkin method is employed. It is found that the Rayleigh numbers for the two analyses did not match, suggesting the existence of a subcritical instability region. Furthermore, it is observed that the subcritical instability region decreased as the magnetic parameter increased, whereas an increase in the couple stress parameter increased the subcritical instability region. For this analysis, three different combinations of bounding surfaces are considered. It is also observed that fluid confined in the rigid–rigid bounding surface is more thermally stable, which is suitable for convection in ferrofluid.