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Many people confuse heat transfer coefficient (htc) based on Reynolds Analogy and htc based on standard wall functions for temperature.
Reynold's analogy relates Nu and Cf - analogy bewteen Cf and Nu.
The Reynolds analogy is:
Cf/2 = St (1)
It assumes Pr = 1.
St = Nu/(Re*Pr) (2)
Nu = htc*L/kf (3)
Re = U*L*density/viscosity (4)
Plugging 2 to 4 into one, we get:
htc = Cf*U*kf*density/(2*viscosity)
htc = Cf * density * U * Cp/2
where Cf is skin friction coef., U is reference velocity, and kf is thermal conductivity of fluid. Note that htc = q"/(Twall - Tref). Now what reference velocity should be used to find htc. Also, when applying this htc, what reference temperature should be used? So, it is not a very useful definition of htc.