Abstract
Using recently developed boundary-layer equations for turbulent Rayleigh-B\'enard convection that take into account fluctuations and buoyancy, we derive analytical results for heat flux scaling dependencies in low- and high-Prandtl-number limits. Our theoretical results are supported by direct numerical simulation data, and further reveal a surprising close resemblance of the heat flux scaling dependencies in turbulent Rayleigh-B\'enard and steady forced convection. This finding resolves the paradox of the apparent applicability of the scaling results in steady forced convection even though the boundary layer theory in that case is not applicable to turbulent Rayleigh-B\'enard convection.
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