Natural Convection Heat Transfer from an Isothermal Plate

Using boundary-layer theory, natural convection heat transfer formulas which are accurate over a wide range of Rayleigh numbers ($Ra$) were developed in the 1970s and 1980s for vertical downward-facing plates. A comprehensive formula upward-facing plates remained unsolved because they do not form conventional boundary-layers. From thermodynamic constraints on heat-engine efficiency, novel approach presented here derives from isothermal The union four peer-reviewed data-sets spanning $1<Ra<10^{12}$ has 5.4% root-mean-squared relative error (RMSRE) new formula. Applied to plates, this outperforms Schulenberg (1985) formula's 4.6% RMSRE with 3.8% $10^6<Ra<10^{12}$. introduction harmonic mean as characteristic-length metric extends those rectangular plate other convex shapes, achieving disk Hassani Hollands (1987) 3.2% Kobus Wedekind (1995).