Effects of Thermal Boundary Conditions on Natural Convection and Entropy Generation in Non-Newtonian Power-Law Fluids

Abstract

This study investigates the role of thermal boundary conditions on natural convection and entropy generation in non-Newtonian power-law fluids confined within a square cavity and a concentric cylindrical annulus. Steady, two-dimensional governing equations based on the incompressible power-law model and the Boussinesq approximation are solved using the Gridap.jl finite element framework. The numerical methodology is validated against benchmark solutions for both Newtonian and non-Newtonian convection, showing good agreement in terms of isotherm fields, streamlines, local Nusselt number distributions, and entropy generation. The effects of fluid rheology and heating mode are examined for shear-thinning, Newtonian, and shear-thickening fluids under uniform and non-uniform thermal boundary conditions. The results show that shear-thinning behavior enhances buoyancy-driven circulation, steepens thermal gradients, and increases heat transfer, whereas shear-thickening behavior suppresses convection and promotes conduction-dominated transport. Thermal boundary conditions are found to play an important role in controlling the intensity and spatial distribution of flow, heat transfer, and irreversibility. In both geometries, uniform heating produces stronger and more distributed convective structures, while non-uniform sinusoidal heating localizes thermal forcing and consistently reduces total entropy generation. An entropy analysis further reveals that viscous dissipation dominates irreversibility in shear-thinning fluids, whereas heat-transfer irreversibility becomes dominant as the power-law index increases. The study demonstrates that appropriate thermal boundary design, together with fluid rheology, provides an effective route for controlling heat transfer and minimizing thermodynamic losses in non-Newtonian convection systems. The source code and metadata are publicly available.