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The introduction of solid polymers into a Newtonian solvent inducessignificant modifications in the flow behavior and heat transfercharacteristics of resulting viscoelastic fluids. This study performs acomprehensive numerical investigation on thermal convection within a systemcomprising two concentric horizontal cylinders filled with viscoelastic fluids,with the inner cylinder rotating. The analysis encompasses all three modes ofthermal convection, namely, forced, free, and mixed convection, over a range ofWeissenberg numbers up to 10 and three values of the Richardson number, namely,0, 0.143, and $\infty$, representing forced, mixed, and free convection modesof heat transfer, respectively. In forced convection, the flow field remainsstable, while in free and mixed convection, an increase in the Weissenbergnumber leads to a transition from steady to unsteady periodic, quasi-periodic,and finally, an aperiodic and chaotic behavior. This transition arises due tothe presence of elastic instability and the subsequent appearance of elasticturbulence in viscoelastic fluids with the increasing Weissenberg number.Furthermore, our findings indicate that fluid viscoelasticity has minimalinfluence on heat transfer rates in the cases of forced and free convection.Conversely, heat transfer rates in mixed convection increase with theWeissenberg number. We conduct a detailed analysis of the viscoelastic kineticenergy budget to elucidate this enhancement in the heat transfer rate forviscoelastic fluids. We show that this improved heat transfer results fromkinetic energy transfer from polymer molecules to the flow field, leading toincreased chaotic motion within the system and, eventually, higher heattransfer rates.

Thermal convection of viscoelastic fluids in concentric rotating cylinders: Elastic turbulence and kinetic energy budget analysis