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  "title": "How much heat must escape through the floor?",
  "shortTitle": "Internally heated convection flux bounds",
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  "oneLine": "A minimum-principle argument raises the guaranteed heat loss through the base of an internally heated fluid, with different scaling laws for rigid and stress-free plates.",
  "abstract": "For infinite-Prandtl convection in a periodic slab with fixed horizontal periods, a written candidate proves bottom heat-flux lower bounds of order (R log R)^(−1/3) for no-slip plates and R^(−1/2) for stress-free plates. A drift-independent temperature ceiling closes the proof. Numerical prefactors remain estimates; finite-window flow data and finite-range roll scans illustrate, rather than establish, the continuum theorem.",
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    "name": "Bottom heat loss in internally heated infinite-Prandtl convection",
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    {
      "citation": "Arslan and Rojas (2025), New bounds for heat transport in internally heated convection at infinite Prandtl number. Earlier unconditional exponents.",
      "url": "https://doi.org/10.1063/5.0209505",
      "doi": "10.1063/5.0209505"
    },
    {
      "citation": "Chen et al. (2024), Temperature and heat flux bounds of convection driven by non-uniform internal heating. Related conditional profile bound.",
      "url": "https://doi.org/10.1007/s10409-024-23630-x",
      "doi": "10.1007/s10409-024-23630-x"
    },
    {
      "citation": "Sondak, Smith and Waleffe (2015), Optimal heat transport solutions for Rayleigh–Bénard convection. Competing roll optima.",
      "url": "https://doi.org/10.1017/jfm.2015.615",
      "doi": "10.1017/jfm.2015.615"
    },
    {
      "citation": "Wen, Takla, Goluskin and Chini, Steady Rayleigh–Bénard convection: strongly nonlinear high-wavenumber rolls. Three-tenths scaling precedent.",
      "url": "https://arxiv.org/abs/2212.05407",
      "doi": "10.48550/arXiv.2212.05407"
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