Linear and Weakly Nonlinear Double-Diffusive Magnetoconvection in a Non-Newtonian Fluid Layer

Abstract

The linear and weakly nonlinear stability of a doubly diffusive electrically conducting non-Newtonian couple stress fluid layer in the presence of a uniform vertical magnetic field is investigated. The system behaves like a triply diffusive one with the magnetic field as a third diffusing component. Several remarkable departures from those of doubly diffusive couple stress fluid systems are recognized and the implications of couple stresses on the same are explored. By performing the linear stability analysis, it has been recognized that (i) oscillatory convection occurs even if the diffusivity ratios are greater than unity, (ii) the bottom-heavy solute gradient in the presence of magnetic field, as well as magnetic field in the presence of bottom-heavy solute gradient, destabilize the system under certain conditions, (iii) disconnected closed oscillatory neutral curves occur for certain choices of physical parameters indicating the necessity of three critical values of thermal Rayleigh number to specify the linear stability criteria instead of the usual single value. A weakly nonlinear stability analysis has been performed using modified perturbation theory and the steady bifurcating equilibrium solution is found to be subcritical in some parameter space. Heat and mass transports are calculated in terms of Nusselt numbers and the influence of physical parameters on the same is discussed in detail.