Heat-Mass Analogy:
Because the Nu and Sh equations are derived from these analogous governing equations, one can directly swap the Nu and Sh and the Pr and Sc numbers to convert these equations between mass and heat.
In many situations, such as flow over a flat plate, the Nu and Sh numbers are functions of the Pr and Sc numbers to some coefficient . Therefore, one can directly calculate these numbers from one another using:
Where   can be used in most cases, which comes from the analytical solution for the Nusselt Number for laminar flow over a flat plate. For best accuracy, n should be adjusted where correlations have a different exponent.
We can take this further by substituting into this equation the definitions of the heat transfer coefficient, mass transfer coefficient, and Lewis number, yielding:
For fully developed turbulent flow, with n=1/3, this becomes the Chilton–Colburn J-factor analogy. Said analogy also relates viscous forces and heat transfer, like the Reynolds analogy.