Linear and weakly nonlinear triple diffusive convection in a couple stress fluid layer

Abstract

The effect of couple stresses on linear and weakly nonlinear stability of a triply diffusive fluid layer is investigated. Several departures not observed either in singly or doubly diffusive couple stress fluid layer have been identified while analyzing the linear stability of the problem. In contrast to the doubly diffusive couple stress fluid system, oscillatory convection is found to occur even if the diffusivity ratios are greater than unity. The presence of couple stress is to increase the threshold value of solute Rayleigh number beyond which oscillatory convection is preferred. Moreover, disconnected closed oscillatory neutral curves are identified for certain choices of physical parameters indicating the requirement of three critical values of Rayleigh number to specify the linear stability criteria instead of the usual single value. Besides, heart-shaped oscillatory neutral curves are also found to occur in some cases and the effect of couple stress parameter on some of these unusual behaviors is analyzed. A weakly nonlinear stability analysis is performed using modified perturbation technique and the stability of steady bifurcating non-trivial equilibrium solution is discussed. Heat and mass transfer are calculated in terms of Nusselt numbers and the influence of various physical parameters on the same is discussed in detail.