In this paper, we propose a general methodology by which a universal temperature profile, derived by matching temperature gradients in the overlap region of the wall layer and the core layer, that is valid for high Rayleigh number flows, can be recast into a correlation for the Nusselt number. We then evaluate its adequacy for three types of flows: (a) fully developed flows (e.g., the infinite channel), (b) developing flows (e.g., the vertical flat plate boundary layer), and (c) complex flows (e.g., Rayleigh-Bénard convection and the differentially heated square cavity). The correlation for the Nusselt number, in general, contains a logarithmic term, usually missing in earlier studies, with which we are able to match existing direct numerical simulations or experimental data very well for both fully developed and complex flows.
Nusselt Number Correlations for Turbulent Natural Convection Flows Using Asymptotic Analysis of the Near-Wall Region
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Balaji, C., Hölling, M., and Herwig, H. (December 1, 2006). "Nusselt Number Correlations for Turbulent Natural Convection Flows Using Asymptotic Analysis of the Near-Wall Region." ASME. J. Heat Transfer. August 2007; 129(8): 1100–1105. https://doi.org/10.1115/1.2737485
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