Heat transfer in flat-plate boundary layers: a correlation for laminar, transitional, and turbulent flow

Proposed correlation, Eq. (9), compared to constant heat flux data of Blair for three levels of free stream turbulence.
J.H. Lienhard V, “Heat transfer in flat-plate boundary layers: a correlation for laminar, transitional, and turbulent flow,” J. Heat Transfer, online 31 March 2020, 142(6):061805, June 2020. (doi: Open access) (presentation) (one-page summary) (DSpace)
Exterior conduction shape factors from interior conduction shape factors
Shape factors for steady heat conduction enable quick and highly simplified calculations of heat transfer rates within bodies having a combination of isothermal and adiabatic boundary conditions. Many shape factors have been tabulated, and most undergraduate heat transfer books cover their derivation and use. However, the analytical determination of shape factors for any but the simplest configurations can quickly come to involve complicated mathematics, and, for that reason, it is desirable to extend the available results as far as possible. In this paper, we show that known shape factors for the interior of two-dimensional objects are identical to the corresponding shape factors for the exterior of those objects. The canonical case of the interior and exterior of a disk is examined first. Then, conformal mapping is used to relate known configurations for squares and rectangles to the solutions for the disk. Both a geometrical and a mathematical argument are introduced to show that shape factors are invariant under conformal mapping. Finally, the general case is demonstrated using Green’s functions. In addition, the “Yin-Yang” phenomenon for conduction shape factors is explained as a rotation of the unit disk prior to conformal mapping.
J.H. Lienhard V, “Exterior shape factors from interior shape factors,” J. Heat Transfer, online 20 Feb. 2019, 141(6):061301, June 2019. (OPEN ACCESS) (preprint) (presentation)
Accurate linearization of non-gray radiation heat exchange

The internal emissivity based on mean temperature is in good agreement with the exact heat exchange for even extremely non-gray surfaces.
J.H. Lienhard V, “Linearization of Non-gray Radiation Exchange: The Internal Fractional Function Reconsidered,” J. Heat Transfer, online 3 Dec. 2018, 141(5):052701, May 2019. (OPEN ACCESS) (preprint) (presentation)