Two-dimensional wall-to-wall optimal heat transport is computed up to Peclet 1e5, showing Nu ~ Pe^0.54, with a conditional upper bound Nu <= C Pe^{6/11} under a separability ansatz.
2019 Exhausting the background approach for bounding the heat transport in rayleigh-b\'enard convection
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Wall-to-wall optimal transport in two dimensions
Two-dimensional wall-to-wall optimal heat transport is computed up to Peclet 1e5, showing Nu ~ Pe^0.54, with a conditional upper bound Nu <= C Pe^{6/11} under a separability ansatz.