• The paper investigated double-diffusive convection of a shear-thinning fluid. • All parameters of the Carreau model influence the convective flows. • When Ra T very high, the Carreau and power-law models give almost the same results. • The results of scale analysis and numerical solution are in good agreement. We study heat and mass transfers by natural convection for shear-thinning non-Newtonian binary fluids confined in a square cavity. Thermal and solutal boundary conditions of the Dirichlet type are applied on the vertical walls of the cavity while the horizontal ones are assumed adiabatic and impermeable. We used the rheological Carreau model, adequate for many non-Newtonian fluids to characterize the shear-thinning behavior. The first part from this study is devoted to the numerical solution of the governing equations, and the effect of the governing parameters, namely, the thermal Rayleigh number Ra T , Prandtl number Pr , Lewis number Le , buoyancy ratio N and the various parameters of Carreau model. Numerical calculations are also carried out by considering the same problem on the basis of the power-law model, and a comparison of the results predicted by the two rheological models is performed. In the second part, a scale analysis is proposed to obtain correlations giving the heat and mass transfers. The results of this approach are validated numerically and a good agreement is found between the two methods.