Mixed convection of a viscoplastic fluid with a variable yield stress in a lid-driven cavity

Abstract

This study is a numerical investigation on heat and momentum transfer in viscoplastic fluids that exhibit a variable yield stress. Viscoplastic fluids are recognized for transitioning from solid to liquid under flow-induced shear-rate. However, these materials exhibit intricate rheological behaviors beyond this fundamental characteristic, often linked to thixotropy. Thixotropy delineates reversible, time-dependent alterations in a fluid's viscosity at a specific shear-rate. The temporal changes in viscosity stem from variations in the fluid's microstructure, responsive to the induced shear-rate. When subjected to shear, the fluid's microstructure breaks down into smaller units, countered by Brownian motion, resulting in a rearrangement of the microstructure due to attractive forces between microconstituents. These microstructural variations are thus reversible. Notably, these changes affect not only viscosity but also the yield stress of the fluid, categorizing it as a non-ideal yield-stress fluid with yield-stress variations linked to microstructure, termed isotropic hardening. This study aims to explore how variations in yield-stress fluid microstructure impact heat and momentum transfer. As a starting point, this study considers the lid-driven cavity flow with differentially heated walls in the presence of an external magnetic field. Addressing the yield-stress fluid microstructure variations involves utilizing the Houska–Papanastasiou model, a regularized model capturing thixotropy and isotropic hardening. The resulting governing equations are made dimensionless and numerically solved through the finite-element method. The findings indicate that a more pronounced breakdown of the fluid's microstructure correlates with a higher Nusselt number at the hot wall. Additionally, variations in fluid microstructure influence both the size and location of unyielded zones.