Numerical investigation of viscoelastic thermal convection in entangled polymer solutions: Elliptical cylinder effects within a square enclosure

This study numerically explores natural convection heat transfer of linear entangled polymer solutions in a square cavity with an elliptical cylinder, using the Rolie-Poly model to describe the solution's rheological properties. It analyzes how geometry and fluid rheology jointly affect flow and heat transfer, finding that both exert significant impacts. In the stable convection, the elliptical cylinder with an axial length ratio of 1:2 has the highest heat transfer efficiency. The rotation effect is significant, and the heat transfer efficiency is the worst at 45° and the best when placed vertically. At Ra=106, the cylinder with an axial ratio of 1 performs well, and increasing the rotation angle of elliptical cylinders further enhances heat transfer. The Weissenberg number (Wi) has a nonlinear effect on the average Nusselt number (Nu), with Nu almost unchanged when Wi>25. Lower polymer viscosity ratio (β) reduces flow stability but improves heat transfer. When the relaxation-time ratio exceeds the threshold value (ξ=5), Nu oscillates periodically, caused by model asymmetry and shear-thinning effect. Here, the shear-thinning effect dominates the flow-field evolution, reducing viscous dissipation, lowering system instability threshold, and inducing oscillations. This study provides a novel design insight for optimizing viscoelastic thermal convection in cavity-column structures for industrial applications.