Classical thermodynamics, heat transfer Convective heat transfer Fact

Chilton–Colburn J-factor analogy

Builds on Stanton number Prandtl number Reynolds analogy

Statement

Consider forced flow with free-stream or mean speed $U$ along a surface, with no form drag, so that the drag is skin friction only. Let $C_f$ be the skin friction coefficient, $\mathrm{St}$ the Stanton number and $\Pr$ the Prandtl number. Let $\mathrm{St}_m = h_m / U$ be the mass transfer Stanton number, with mass transfer coefficient $h_m$ . Let $\mathrm{Sc} = \nu / D$ be the Schmidt number, with kinematic viscosity $\nu$ and diffusivity $D$ . The Colburn factors are $j_H = \mathrm{St} \, \Pr^{2/3}$ and $j_D = \mathrm{St}_m \, \mathrm{Sc}^{2/3}$ . For $0.6 < \Pr < 60$ and $0.6 < \mathrm{Sc} < 3000$ , the following hold approximately: $j_H = \frac{C_f}{2}, \qquad j_D = \frac{C_f}{2}.$

Remarks

This is an empirical correlation, not a theorem. For the laminar flat plate it agrees with the Blasius and Pohlhausen results, which give $\mathrm{St}_x \Pr^{2/3} = 0.332 \, \mathrm{Re}_x^{-1/2} = C_{f,x}/2$ . For $\Pr = 1$ it reduces to the Reynolds analogy $\mathrm{St} = C_f / 2$ . For turbulent flow in smooth pipes it holds roughly, which makes friction data a cheap source of heat and mass transfer estimates. On bluff bodies the measured drag includes pressure drag, and the analogy with the total drag coefficient fails.

Going deeper

For a student

The exponent $2/3$ comes from the laminar flat-plate result $\mathrm{Nu}_x \propto \Pr^{1/3}$ , since $\mathrm{St} = \mathrm{Nu} / (\mathrm{Re} \Pr)$ . The analogy extends the Reynolds analogy from $\Pr = 1$ to common liquids and gases. Replacing $\Pr$ by $\mathrm{Sc}$ turns every heat transfer correlation of this form into a mass transfer correlation.

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Heat transfer coefficient concept
Prandtl number concept
Reynolds number concept
Stanton number concept
Thermal boundary layer concept
Reynolds analogy statement
Chilton–Colburn J-factor analogy statement

Tag	`FHSZN0S58C`
URI	`m2://FHSZN0S58C`
Kind	statement, fact
Writing	W0 stub
MSC	80A19, 76R05, 76R50
Status	This copy of the site has no build data. Run `m2 status FHSZN0S58C`.
About	Forced convection
Uses	Stanton number, Prandtl number, Reynolds analogy
Same as	Wikidata Q3879391 Wikipedia Chilton and Colburn J-factor analogy
Changed	3 November 2026

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