The onset of double diffusive convection in a layer of Maxwell viscoelastic fluid in porous medium with cross diffusion effects is studied using linear and nonlinear stability analysis. The previous study has focused on linear stability analysis only. Therefore, in the present study, we have focused on oscillatory convection and nonlinear stability theory. The linear analysis is based on the classical normal mode technique. The expressions for stationary, oscillatory convections are obtained as a function of governing parameters such as solute Rayleigh number, Soret parameter, Dufour parameter and Lewis number and their effects on the stability of a system are shown graphically. The nonlinear analysis is based on the truncated Fourier series which provides the quantification of heat and mass transfer. The transient behavior of Nusselt and Sherwood numbers is studied by solving numerically a fifth order Lorentz type system using Runge-Kutta method.
In this paper, we have investigated the onset of double diffusive convection (DDC) in a couple stress fluid saturated rotating anisotropic porous layer in the presence of Soret and Dufour effects using linear stability analyses which is based on the usual normal mode technique. The onset criteria for both stationary and oscillatory modes obtained analytically. The effects of the Taylor number, mechanical anisotropy parameter, Darcy Prandtl number, solute Rayleigh number, normalized porosity parameter, Soret and Dufour parameters on the stationary and oscillatory convections shown graphically. The effects of couple stresses are quite significant for large values of the non-dimensional parameter and delay the onset of convection. Taylor number has stabilizing effect on double diffusive convection, Dufour number has stabilizing effect in stationary mode while destabilizing in oscillatory mode. The negative Soret parameter stabilizes the system and positive Soret parameter destabilizes the system in the stationary convection, while in the oscillatory convection the negative Soret coefficient destabilize the system and positive Soret coefficient stabilizes the system.
Internal heating on the onset of Darcy-Brinkman convection in a binary viscoelastic fluid-saturated sparsely packed porous layer with Soret effect is studied using linear stability analyses. The Oldroyd-B model is employed to describe the rheological behavior of binary fluid. An extended form of the DarcyOldroyd law incorporating Brinkman's correction and time derivative is used to describe the flow through a porous layer and the Oberbeck-Boussinesq approximation is invoked. The onset criterion for stationary and oscillatory is derived analytically. The effect of internal Rayleigh number, Soret parameter, relaxation and retardation parameters, solute Rayleigh number, Darcy number, Darcy-Prandtl number, normalized porosity, and Lewis number on the stability of a system is investigated and is shown graphically.
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