Abstract
Abstract The laminar and turbulent regimes of a boundary layer on a flat plate are often represented with separate correlations under the assumption of a distinct “transition Reynolds number.” Average heat coefficients are then calculated by integrating across the “transition point.” Experimental data do not show an abrupt transition, but rather an extended transition region in which turbulence develops. The transition region may be as long as the laminar region. Although this transitional behavior has been known for many decades, few correlations have incorporated it. One attempt was made by Stuart Churchill in 1976. Churchill, however, based his curve fit on some doubtful assumptions about the data sets. In this paper, we develop different approximations through a detailed consideration of multiple data sets for 0.7 ⩽ Pr ⩽ 257, 4000 ⩽ Rex ⩽ 4,300,000, and varying levels of freestream turbulence for smooth, sharp-edged plates at zero pressure gradient. The result we obtain is in good agreement with the available measurements and applies smoothly over the full range of Reynolds number for either a uniform wall temperature or a uniform heat flux boundary condition. Fully turbulent air data are correlated to ±11%. Like Churchill's result, this correlation should be matched to the estimated transition condition of any particular flow. We also review the laminar analytical solutions for a uniform wall heat flux, and point out limitations of the classical Colburn analogy.
Highlights
Simplified treatments of boundary layer heat transfer split the boundary layer into an upstream laminar section and downstream turbulent section
Correlations are formed for these two sections, which are assumed to be separated by a distinct transition Reynolds number
An example is the correlation for average heat transfer coefficient proposed by Whitaker [1]: the heat transfer coefficient is averaged over the length, using results from laminar theory and correlation for turbulent flow
Summary
Simplified treatments of boundary layer heat transfer split the boundary layer into an upstream laminar section and downstream turbulent section. In contrast to Whitaker, Churchill [2] proposed a continuous correlation to predict the local Nusselt number, Nux, from laminar flow, through the transition region, and into the turbulent region. The full statement of Churchill’s equation is given in Appendix A Churchill compared his model to aggregated data for the local and average heat transfer coefficient, with partial agreement. Ur0 from several investigators is the root-mean-square turbulent [10,17,32], and (b) water data from fluctuation Zukauskas and Slanciauskas [26] This fact is important if local values of the heat transfer coefficient are required
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