Engineering & Science
Stanton Number (St) & Chilton-Colburn jH Heat-Momentum Analogy Formula
Calculate the dimensionless Stanton Number St = Nu / (Re * Pr) and Chilton-Colburn heat-transfer factor j_H = St * Pr^(2/3) to estimate convective heat transfer directly from Fanning skin-friction drag (j_H ~ f / 2).
Predict convective heat transfer directly from aerodynamic skin-friction drag!
Thomas Stanton, Thomas Chilton, and Allan Colburn unlocked one of transport phenomena’s most powerful engineering shortcuts: because turbulent eddies transport momentum, thermal energy, and chemical species by the exact same mixing mechanism, scaling the Stanton Number St = h / (rho * u * c_p) = Nu / (Re * Pr) by Pr^(2/3) collapses fluids across 0.6 <= Pr <= 60 onto the Chilton-Colburn j-Factor: j_H = St * (Pr ^ (2 / 3)) ~ f_Fanning / 2!
Look at turbulent airflow (Pr = 0.71, Re = 50,000) with measured Nusselt number Nu = 185: the Stanton Number is St = 185 / (50,000 * 0.71) = 0.005211, the Chilton-Colburn factor is j_H = 0.005211 * (0.71 ^ (2/3)) = 0.004147, and the implied Fanning skin-friction factor is f_F = 2 * j_H = 0.00829 (Darcy friction factor f_D = 4 * f_F = 0.0332)—matching smooth-pipe turbulent Moody charts within ~5%!
| Turbulent Transport Metric (Nu = 185, Re = 50,000) | Fluid Prandtl Number Pr | Stanton Number St | Chilton-Colburn Factor jH |
|---|---|---|---|
| Turbulent Air Stream | Pr = 0.71 | 0.005211 | 0.004147 (Fanning f ~ 0.00829) |
| Liquid Water Stream (Nu = 355 at Re = 50k) | Pr = 6.00 | 0.001183 | 0.003907 (Collapsed jH!) |
| Invalid Reynolds or Prandtl <= 0 | Guarded Transport Error | "Invalid Transport Inputs" | Requires Nu > 0, Re > 0, Pr > 0 |
Dimensionless Stanton Number St = Nu / (Re * Pr)
Expresses wall convective heat flux relative to the bulk fluid’s longitudinal advective thermal capacity.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid Transport Inputs", ROUND(B2 / (B3 * B4), 6))Chilton-Colburn Heat-Transfer j-Factor j_H = (Nu / (Re * Pr)) * Pr^(2/3)
Scales St by Pr^(2/3) (~ f_Fanning / 2 across 0.6 <= Pr <= 60).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid Transport Inputs", ROUND((B2 / (B3 * B4)) * (B4 ^ (2 / 3)), 6))Try the example
Use the original values or change them to test your understanding.