What is the insight that lead to the ColburnChilton analogy

What is the insight that lead to the Colburn-Chilton analogy and what advantage does it have over the Reynold\'s analogy as a methodology for solving mass transfer problems?

Solution

Chilton–Colburn J-factor analogy is a successful and widely used analogy between heat, momentum, and mass transfer. The basic mechanisms and mathematics of heat, mass, and momentum transport are essentially the same. Among many analogies (like Reynolds analogy, Prandtl–Taylor analogy) developed to directly relate heat transfercoefficients, mass transfer coefficients, and friction factors Chilton and Colburn J-factor analogy proved to be the most accurate.

For = const. it reduces to the popular form of Stanton number (St) increasing with increasing Re, whereas for variable it reduces to St increasing with decreasing Re. Consequently, the Chilton-Colburn analogy of St•Pr^2/3 increasing with increasing c_f is qualitatively valid whenever the Reynolds’ analogy is valid. Thus, Reynolds analogy is valid for flows that are close to developed. But colborn chilton analogy is valid for all fully developed turbulent flow in conduits with Re > 10000, 0.7 < Pr < 160, and tubes where L/d > 60.