Natural convection of dilute polymer solution in a differentially heated square cavity with different thermal boundary conditions

This study numerically investigates the effects of different top and bottom thermal boundary conditions on the flow state and heat transport in viscoelastic natural convection. The polymer solution is described by the FENE-P model in a two-dimensional differentially heated cavity. Four types of thermal boundary conditions are considered: adiabatic, linear, constant, and sinusoidal. Results are presented through comparative analyses of flow structures and heat transfer. Compared to their Newtonian counterparts, viscoelastic convection exhibits enhanced heat transfer performance in all four types of cavities. At the Rayleigh number (Ra)=104 and polymer viscosity ratio (β)<0.5, heat transfer is more efficient in viscoelastic convection within adiabatic cavities than in sinusoidal cavities, in contrast to Newtonian trends. At Ra=103, heat conduction dominates, and the flow structures remain similar across all cavities. As Ra increases to 106, the influence of convection becomes significant. Sinusoidal boundaries suppress small-scale vortices and promote the development of large-scale circulations, particularly at Weissenberg number (Wi)=100. In the linear, constant, and sinusoidal cavities, the average Nusselt number (Nu) increases with Ra more slowly than in the adiabatic case. At Ra=106, the Nusselt number is the highest in the adiabatic cavity. Kinetic energy analyses indicate that the transition from conduction to convection occurs later in linear, constant, and sinusoidal cavities. Moreover, the slower growth of viscous dissipation in the adiabatic cavities allows more energy to be retained for convective motion, resulting in higher heat transfer efficiency. These findings underscore the importance of boundary condition design for optimizing heat transfer in viscoelastic fluid applications and fill the gap in understanding viscoelastic natural convection under realistic boundary conditions.