This paper reports on the multiplicity of steady state solutions and the effect of buoyancy ratio due to both heat and mass transfer on natural convection in a horizontal rectangular cavity filled with a power-law non-Newtonian fluid. The short vertical sides of the cavity are submitted to horizontal thermal and solutal flux densities, while its horizontal walls are impermeable and adiabatic. The problem under consideration is governed by the cavity aspect ratio, A, the Lewis number, Le, the buoyancy ratio, N, the power-law behavior index, n, and the generalized Prandtl, Pr, and thermal Rayleigh, Ra_T, numbers. The equations describing the double-diffusion convection phenomenon are solved numerically using a finite volume method. In the case of a shallow cavity A > > 1, the governing equations are significantly simplified by using the parallel flow approximation, which allows an analytical solution that agrees well with the numerical one. Results expressed in terms of streamlines, isotherms, iso-concentrations, central stream function and average Nusselt and Sherwood numbers are obtained for various values of the governing parameters. The onset and the development of double-diffusive convection, for cooperating and opposing flows, are investigated. The existence of multiple steady state solutions, for a given set of the governing parameters, is demonstrated in the case of opposing double diffusive flow.

本文报道了在充满幂律非牛顿流体的水平矩形空腔中，稳态解的多重性以及由于传热和传质引起的浮力比对自然对流的影响。空腔的短垂直侧面承受水平的热和溶通量密度，而空腔的水平壁则是不透水和绝热的。所考虑的问题由空腔长宽比A，路易斯数Le，浮力比N，幂律行为指数n以及广义Prandtl Pr和热瑞利Ra _T决定。，数字。使用有限体积法对描述双扩散对流现象的方程进行了数值求解。在浅腔A  >> 1的情况下，通过使用平行流近似可以显着简化控制方程，这使得解析解与数值解非常吻合。对于不同的控制参数值，获得了以流线，等温线，等浓度，等浓度，中心流函数以及平均Nusselt和Sherwood数表示的结果。研究了双扩散对流的协同流动和对流的发展。对于给定的一组控制参数，在存在双重扩散流的情况下，证明了多个稳态解的存在。