Nusselt Number - Derivation

Derivation

The Nusselt number may be obtained by a non dimensional analysis of the Fourier's law since it is equal to the dimensionless temperature gradient at the surface:

, where q is the heat flux, k is the thermal conductivity and T the fluid temperature.

Indeed if:, and

we arrive at :

then we define :

so the equation become :

By integrating over the surface of the body:

, where