The average friction coefficient and Nusselt number are expressed in functional form as

$C_f$=$f_4$ ($Re_L)$ and Nu=$g_3$ ($Re$_L,Pr)

The Nusselt number can be expressed by a simple power-law relation of the form

Nu=C$Re_L^m$ $Pr^n$

Where m and n are constant exponents, and the value of constant C depends on geometry. The Reynolds analogy relates the convection coefficient to the friction coefficient for fluids Pr≈1 and is expresses as

$C_(f,x)$ $Re_L/2$=$Nu_x$ or $C_(f,x)/2$=$St_x$

Where St=$\frac{h}{(ρC_p V)}$=$\frac{Nu}{(Re_L Pr)}$

is the Stanton number.which is also a dimensionless heat transfer coefficient. Reynolds analogy is of limited use because of the restrictions Pr=1 and_$\frac{(∂P^*)}{(∂x^*)}=0$ on it, and it is desirable to have an analogy that is applicable over a wide range of Pr. This is done by adding a Prandtl number correction. The analogy is extended to other Prandtl numbers by the modified Reynolds analogyor Chilton-Colburn analogy,expressed as

$C_(f,x)$ $Re_L/2$=$Nu_x$ $Pr^(-1/3)$

Or

$C_(f,x)/2$=$\frac{h_x}{(ρC_p V)}$ $Pr^(2/3)$≡$j_H$ (0.6 < Pr < 60)

These analogies are also applicable approximately for turbulent flow over a surface, even in the presence of pressure gradients.