Interplay of shear-dependent rheology and buoyancy forces in non-newtonian heat transfer

This study explore the fundamental mechanism governing buoyancy-driven flow and heat transfer of a shear-dependent non-Newtonian fluid modeled by Reiner–Philippoff (RPP) constitutive relation in an open-ended cavity with permeable horizontal surfaces. A finite element framework is implemented to solve the weak formulation of the coupled momentum and energy equations on a triangular mesh, using an implicit scheme for the linear terms and a semi-implicit approach for the transport terms. The study highlights the interplay between thermal gradients, shear-thinning and shear-thickening rheology, and buoyancy forces, demonstrating how non-Newtonian viscosity alterations influence convective transport, thermal boundary layers, and velocity profiles. The results reveal that higher Grashof numbers make upward flow motion much stronger and improve convective heat transmission. On the other hand, strong shear-rate dependencies cause localized changes in flow structure and thermal stratification. This study offers new insights into the physics of shear-dependent buoyancy-driven convection in open domains, contributing to a better understanding and modeling of non-Newtonian fluid systems which are important for engineering and industrial heat transfer applications including solar thermal receivers, electronic cooling, polymer extrusion, food processing, fire safety, and energy-efficient building designs.