Significant heat-transfer enhancement via polymer additives in two-dimensional sheared convection

Abstract

Heat dissipation is critical in modern engineering and polymer additives offer a potential route to improve fluid-based cooling. We study elasticity-enhanced heat transfer in two-dimensional, thermally stratified Poiseuille flow. At Reynolds numbers italic Re less than or equivalent to 1000 Re ≲ 1000 $\textit{Re} \lesssim 1000$ , we observe two linearly unstable modes: the recently identified elasticity-induced centre mode (Khalid et al. 2021 J. Fluid Mech. 915, A43) and the classical buoyancy-driven convective mode (Kelly 1994 Adv. Appl. Mech. 31, 35–112). Direct numerical simulations show that the centre mode develops into a nonlinear ‘arrowhead’ state but yields negligible heat-transfer enhancement (typically almost equals 0.03 percent sign ≈ 0.03 % $\approx 0.03\,\%$ above the conductive state). By contrast, polymers can enhance the heat flux associated with the convective mode by up to 1100 percent sign 1100 % $1100\,\%$ . The nonlinear convective-mode states are periodic orbits or travelling waves, dominated by hook-like polymer-stress structures that can attach to channel walls. Both unattached and attached hooks act as ‘polymer walls’, steering flow along rather than across them. Unattached hooks deflect fluid vertically around them in the channel interior and reduce flow rate, whereas wall-attached hooks travel more slowly, reorganising the flow into strong counter-rotating rolls and triggering extreme enhancement. The elasto-buoyant nature of these states is confirmed by perturbation kinetic energy budgets, showing that polymer and buoyancy sustain the states synergistically. Wall-attached hooks enable rapid thermal equilibration but impose a large hydraulic penalty, making them suitable for process streams requiring fast temperature adjustment. Unattached hooks provide a more thermally efficient regime for heat transport. These results highlight the potential of elastic fluids for future heat-transfer enhancement technologies.