Flow physics of Prandtl–rheology coupling in non-Newtonian natural convection and entropy generation within a cylindrical annulus

Buoyancy-driven flow of non-Newtonian fluids in annular geometries is relevant to a range of thermal engineering applications. However, the jointly effects of fluid rheology and the Prandtl number on heat transfer and thermodynamic irreversibility in this geometry are still not well characterized. We address this gap through two-dimensional simulations of a power-law fluid undergoing steady laminar buoyancy-driven motion inside a concentric cylindrical annulus held at Ra=104, spanning three rheological states (n=0.6,1.0,1.4) crossed with three thermal-diffusivity regimes (Pr=0.0.026,0.7,10). Circulation patterns, heat transport, and entropy generation are analyzed using a comprehensive set of diagnostics, including stream-function, isotherm, and heat-function contours, along with wall-averaged Nusselt numbers, spatial entropy-generation maps, and the Bejan number. Numerical results show that the effect of Pr depends strongly on the fluid rheology. For the shear-thinning fluid, increasing Pr enhances buoyancy-driven circulation, reduces the thermal boundary-layer thickness, and increasingly confines heat transfer to the heated wall. This shift changes the dominant irreversibility from thermal to fluid-friction entropy generation. In contrast, shear-thickening fluids remain weakly convective, thermally dominated, and only weakly sensitive to the Prandtl number, while Newtonian fluids exhibit an intermediate response. A unified scaling framework is build to connect thermal boundary-layer thickness, the magnitude of heat-transfer enhancement, and irreversibility generation to Ra, Pr, and the power-law index acting together. These outcomes provide a unified physical framework for rationalizing heat transmission and thermodynamic performance for buoyancy-driven flow of shear-dependent fluids.