Temperature-dependent viscosity impact on entropy generation and Rayleigh-Benard thermosolutal convection for non-Newtonian binary fluids

Abstract This work presents a comprehensive study of natural thermosolutal convection in a square cavity filled with a non-Newtonian power-law fluid with temperature-dependent viscosity. Such configurations are relevant to several engineering and geophysical applications, where the optimization of coupled thermal and solutal transport under complex rheological behavior is of major interest. The novelty of the present work lies in the simultaneous consideration of three key physical features: non-Newtonian behavior, exponential thermo-viscous dependence, and double-diffusive convection, within a unified framework that also includes entropy generation analysis. The governing equations are solved numerically to examine the effects of the thermal Rayleigh number, behavior index, viscosity variation parameter, and buoyancy ratio on the flow structure, heat and mass transfer, and irreversibilities. The results show that increasing the thermo-viscosity parameter markedly enhances convection near the heated wall from 9.733 to 19.842 for n = 0.6, highlighting the much stronger thermo-viscous sensitivity of shear-thinning fluids and the associated enhancement of heat and mass transfer. In addition, thermo-dependence significantly lowers the onset threshold of convection: at n = 1, the critical thermal Rayleigh number decreases from about 430 for m = 0 to about 100 for m = 3, corresponding to a reduction of nearly 77%. More generally, the highest threshold is observed for ( n = 1.4, m = 0) with Ra Tc ≈ 495, whereas the lowest one is obtained for ( n = 0.6, m = 3) with Ra Tc ≈55, representing an overall reduction of about 89%. However, shear-thickening behavior retards the flow circulation and reduces the transfer efficiency. Entropy analysis shows that thermal and solutal irreversibilities dominate Newtonian and shear-thickening fluids, while viscous dissipation becomes the dominant source of entropy generation in shear-thinning regimes under strong thermo-dependence; in this case, the total entropy generation increases from 8.875 to 34.256, while the Bejan number decreases from 0.312 to 0.104, indicating a shift toward viscous-dissipation-dominated irreversibility. The Bejan number distributions further highlight the spatial competition between diffusive and frictional entropy mechanisms. The study reports novel findings on the combined influence of thermal and rheological effects on double-diffusive convection and valuable insights on the design and optimization of novel thermal systems employing non-Newtonian working fluids.