Natural Convection Heat Transfer From an Isothermal Plate

Abstract Currently, natural convection heat transfer from horizontal, upward-facing plates is known only within expected measurement uncertainties at the Rayleigh numbers (Ra) which have been measured. This investigation derives from theory a comprehensive formula which predicts natural convection heat transfer from unobstructed, upward-facing, isothermal plates. The union of four peer-reviewed data-sets spanning 1 < Ra < 1012 has 5.4% root-mean-squared relative error (RMSRE) versus this new heat transfer formula. This novel theory is based on the thermodynamic constraints on heat-engine efficiency. It derives a formula nearly identical to Churchill and Chu (1975) for vertical plates at 1 < Ra < 1012 . The formula it derives for downward-facing plates has 3.8% RMSRE on four peer-reviewed data-sets spanning 106 < Ra < 1012 ; this is an improvement compared with 4.6% RMSRE of the Schulenberg (1985) formula on the same data. This investigation introduces harmonic mean as the characteristic-length metric for vertical and downward-facing plates, extending these rectangular plate formulas to other convex shapes. It achieves 3.8% RMSRE on vertical disk convection measurements from Hassani and Hollands (1987) and 3.2% from Kobus and Wedekind (1995). Building on the work of Fujii and Imura (1972) and Raithby and Hollands (1998), the three orthogonal plate formulas are combined to calculate the heat transfer at any plate inclination, achieving 4.7% RMSRE on the inclined plate measurements from Fujii and Imura.