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This study proposes that optimal heat transport in Rayleigh-Bénard convection (heat transfer in fluids between hot and cold plates) is governed by marginal energy stability rather than turbulence intensity alone. Using theoretical analysis of the perturbation-energy balance, the researchers developed a self-consistent model that predicts heat flux scaling as Nu≃0.0245Ra^(1/2) at large Rayleigh numbers, with a characteristic temperature profile featuring conductive layers, logarithmic regions, and a weakly stratified core. Three-dimensional simulations validated that thermal forcing based on this profile maintains high heat flux while suppressing convective motion.
Why it matters
Understanding the fundamental limits of heat transport could improve the design of thermal management systems in industrial applications, from cooling electronics to optimizing energy efficiency in heating and refrigeration systems. The finding that maximum heat transfer can occur without vigorous turbulence challenges conventional assumptions and may enable new approaches to controlling heat flux.
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⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
Abstract: High heat transfer in Rayleigh–B’enard convection is commonly associated with vigorous turbulent motion, but turbulence intensity alone does not explain how a limiting transport state is selected. We propose that such limiting states are organized by marginal energy stability. Starting from the exact perturbation-energy balance, we determine, for a prescribed mean temperature profile, the smallest neutral Rayleigh number over the balance parameter and all admissible disturbances. The corresponding marginal modes are then coupled to the exact mean-temperature equation, producing a self-consistent profile and heat flux. At large $Ra$, the selected branch gives $Nusimeq0.0245Ra^{1/2}$ and develops conductive inner layers, logarithmic-like intermediate regions and a weakly stably stratified core. An equivalent background-field formulation yields the same governing equations and establishes uniqueness of the selected mean profile. Three-dimensional simulations at $10^6le Rale10^8$ show that distributed thermal forcing based on this profile suppresses convective motion while retaining a large wall heat flux.
Source: Optimal heat transport at the edge of energy stability