An analytical study of linear and non-linear double diffusive convection with Soret effect in couple stress liquids

• Published in: International journal of thermal sciences 2006-09, Vol.45 (9), p.897-907
• Main Authors: Malashetty, M.S., Gaikwad, S.N., Swamy, Mahantesh
• Format: Article
• Language: English
• Subjects: Buoyancy-driven instability; Convection and heat transfer; Couple stress liquid; Double diffusive convection; Double Fourier series; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Lorenz model; Physics; Soret effect; Turbulent flows, convection, and heat transfer
• ISSN: 1290-0729; 1778-4166
• DOI: 10.1016/j.ijthermalsci.2005.12.005

The double diffusive convection in a two-component couple stress liquid layer with Soret effect is studied using both linear and non-linear stability analyses. The linear theory is based on normal mode technique and the non-linear analysis is based on a minimal representation of double Fourier series. The effect of couple stress parameter, the Soret parameter, the solute Rayleigh number, the Prandtl number and the diffusivity ratio on the stationary, oscillatory and finite amplitude convection are shown graphically. It is found that the effects of couple stress are quite large and the positive Soret number enhances the stability while the negative Soret number enhances the instability. The non-linear theory predicts that, finite amplitude motions are possible only for negative Soret parameter. The transient behaviour of thermal and solute Nusselt numbers has been investigated by solving numerically a fifth order Lorenz model using Runge–Kutta method.