Interaction between forced and natural convection in a thin cylindrical fluid layer at low Prandtl number
arXiv:2401.07306 · doi:10.1017/jfm.2023.922
Abstract
Motivated by nuclear safety issues, we study the heat transfers in a thin cylindrical fluid layer with imposed fluxes at the bottom and top surfaces (not necessarily equal) and a fixed temperature on the sides. We combine direct numerical simulations and a theoretical approach to derive scaling laws for the mean temperature and for the temperature difference between the top and bottom of the system. We find two asymptotic scaling laws depending on the flux ratio between the upper and lower boundaries. The first one is controlled by heat transfer to the side, for which we recover scaling laws characteristic of natural convection. The second one is driven by vertical heat transfers analogous to Rayleigh Benard convection. We show that the system is inherently inhomogeneous, and that the heat transfer results from a superposition of both asymptotic regimes. Keeping in mind nuclear safety models, we also derive a one-dimensional model of the radial temperature profile based on a detailed analysis of the flow structure, hence providing a way to relate this profile to the imposed boundary conditions.
arXiv comment27 pages, 18 Figures
References in corpus (8)
- Scaling in thermal convection: A unifying theory
- A Comparison of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux
- Vertical natural convection: application of the unifying theory of thermal convection
- Resolving the fine-scale structure in turbulent Rayleigh-Benard convection
- Heat Flow and Boundary Heterogeneity in Rotating Convection
- The Effects of Robin Boundary Condition on Thermal Convection in a Rotating Spherical Shell
- Coupled convection and internal gravity waves excited in water around its density maximum at 4°C
- Bounds for Rayleigh-Bénard convection between free-slip boundaries with an imposed heat flux