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.