Natural convection of linear entangled polymer in a differentially heated cavity

This paper numerically investigates the heat transport and bifurcation of natural convection in a differentially heated cavity filled with entangled polymer solution combined with the boundary layer and kinetic energy budget analysis. The polymers are described by the Rolie-Poly model, which effectively captures the rheological response of entangled polymers. The results indicate that the competition between its shear-thinning and elasticity dominates the flow structures and heat transfer rate. The addition of polymers tends to enhance the heat transfer as the polymer viscosity ratio ( $\beta$ ) decreases or the relaxation time ratio ( $\xi$ ) increases. The amount of heat transfer enhancement (HTE) behaves non-monotonically, which first increases significantly and then remains almost constant or decreases slightly with the Weissenberg number ( $Wi$ ). The critical $Wi$ gradually increases with the increasing $\xi$ , where the maximum HTE reaches approximately $64.9\,\%$ at $\beta = 0.1$ . It is interesting that even at low Rayleigh numbers, the flow transitions from laminar to periodic flows in scenarios with strong elasticity. The bifurcation is subcritical and exhibits a typical hysteresis loop. Then, the bifurcation routes driven by inertia and elasticity are examined by direct numerical simulations. These results are illustrated by time histories, Fourier spectra analysis and spatial structures observed at varying time intervals. The kinetic energy budget indicates that the stretch of the polymers leads to great energy exchange between polymers and flow structures, which plays a crucial role in the hysteresis phenomenon. This dynamic behaviour contributes to the strongly self-sustained and self-enhancing processes in the flow.