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Natural convection of linear entangled polymer in a differentially heated cavity

Published online by Cambridge University Press:  18 July 2025

Bo Guo Open the ORCID record for Bo Guo [Opens in a new window] ,
Rong Liu Open the ORCID record for Rong Liu [Opens in a new window]  and
Xinhui Si Open the ORCID record for Xinhui Si [Opens in a new window]
Bo Guo
Affiliation:
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, PR China
Rong Liu
Affiliation:
School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541004, PR China
Xinhui Si*
Affiliation:
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, PR China
*
Corresponding author: Xinhui Si, sixinhui@sas.ustb.edu.cn
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Abstract

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.

JFM classification

Convection: Convection in cavities Non-Newtonian Flows: Viscoelasticity Nonlinear Dynamical Systems: Bifurcation

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1015 , 25 July 2025 , A32
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© The Author(s), 2025. Published by Cambridge University Press

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