Natural Convection Heat Transfer from an Isothermal Plate

TL;DR

This paper introduces a novel thermodynamic approach to derive accurate natural convection heat transfer formulas for various plate orientations and shapes, outperforming existing models across a wide range of Rayleigh numbers.

Contribution

It presents a new thermodynamic method for deriving heat transfer formulas that accurately cover upward-facing plates and convex shapes, extending beyond traditional boundary-layer theory.

Findings

Achieves 5.4% RMSRE for upward-facing plates across $1<Ra<10^{12}$.

Outperforms Schulenberg (1985) formula with 3.8% RMSRE on downward-facing plates.

Extends formulas to convex shapes with RMSRE as low as 3.2%.

Abstract

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