Double-Diffusive Convection in an Oldroyd-B fluid Layer-Stability of Bifurcating Equilibrium Solutions

The nonlinear stability of stationary and oscillatory double-diffusive convection in an Oldroyd-B fluid layer is investigated using a perturbation method. The cubic Landau equations are derived and based on which the stability of stationary and oscillatory bifurcating solutions in the neighborhood of their critical values is discussed. The boundary between stationary and oscillatory convection demarcated by identifying a codimension-two points in the viscoelastic parameters plane. The bifurcating solution is found to be subcritical depending on the choices of physical parameters. Heat and mass transport are estimated in terms of Nusselt numbers. The effect of Prandtl number is observed only in the case of oscillatory motions and increase in its value is to decrease the heat and mass transfer. Besides, increasing relaxation and retardation parameters is to decrease and increase the amount of heat and mass transfer, respectively in the stationary case, while these parameters found to exhibit an opposing kind of behavior in the case of oscillatory motions.