Optimal Heat Transport in Rayleigh-Bénard Convection

Abstract

Steady flows that optimize heat transport are obtained for two-dimensional Rayleigh-Bénard convection with no-slip horizontal walls for a variety of Prandtl numbers $Pr$ and Rayleigh number up to $Ra\sim 10^9$. Power law scalings of $Nu\sim R{a}^{\gamma }$ are observed with $\gamma \approx 0.31$, where the Nusselt number $Nu$ is a non-dimensional measure of the vertical heat transport. Any dependence of the scaling exponent on $Pr$ is found to be extremely weak. On the other hand, the presence of two local maxima of $Nu$ with different horizontal wavenumbers at the same $Ra$ leads to the emergence of two different flow structures as candidates for optimizing the heat transport. For $Pr\lesssim 7$, optimal transport is achieved at the smaller maximal wavenumber. In these fluids, the optimal structure is a plume of warm rising fluid which spawns left/right horizontal arms near the top of the channel, leading to downdrafts adjacent to the central updraft. For $Pr>7$ at high-enough Ra, the optimal structure is a single updraft absent significant horizontal structure, and characterized by the larger maximal wavenumber.

29 pages, 16 figures, submitted to the Journal of Fluid Mechanics

References in corpus (5)

• Comparison between two and three dimensional Rayleigh-Bénard convection
• Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection
• Large-scale mean patterns in turbulent convection
• Wall to Wall Optimal Transport
• Heat Transport by Coherent Rayleigh-Bénard Convection

Cited by in corpus (18)

• Roughness as a Route to the Ultimate Regime of Thermal Convection
• Rayleigh-Bénard convection with a melting boundary
• A model of rotating convection in stellar and planetary interiors: I - convective penetration
• Steady Rayleigh--Bénard convection between stress-free boundaries
• Steady Rayleigh--Bénard convection between no-slip boundaries
• Optimal heat transfer enhancement in plane Couette flow
• Learning Closed-form Equations for Subgrid-scale Closures from High-fidelity Data: Promises and Challenges
• On the optimal design of wall-to-wall heat transport
• Coherent Solutions and Transition to Turbulence in Two-Dimensional Rayleigh-Bénard Convection
• Heat transport bounds for a truncated model of Rayleigh-Bénard convection via polynomial optimization
• Analytical bounds on the heat transport in internally heated convection
• Optimal heat transfer and optimal exit times
• Optimal convection cooling flows in general geometries
• Marginally-Stable Thermal Equilibria of Rayleigh-Bénard Convection
• On high Taylor number Taylor vortices
• Bifurcation analysis of two-dimensional Rayleigh--Bénard convection using deflation
• Multi-scale steady solution for Rayleigh-Bénard convection
• Enhancing wall-to-wall heat transport with unsteady flow perturbations