Editing Nusselt number (section)

==Context==
An understanding of convection boundary layers is necessary to understand convective heat transfer between a surface and a fluid flowing past it. A thermal boundary layer develops if the fluid free stream temperature and the surface temperatures differ. A temperature profile exists due to the energy exchange resulting from this temperature difference.
[[Image:Thermal Boundary Layer.jpg|400px|thumb|Thermal Boundary Layer]]

The heat transfer rate can be written using [[Newton's law of cooling]] as

:<math>Q_y=hA\left( T_s-T_\infty \right)</math>,

where ''h'' is the [[heat transfer coefficient]] and ''A'' is the heat transfer surface area. Because heat transfer at the surface is by conduction, the same quantity can be expressed in terms of the [[thermal conductivity]] ''k'':

:<math>Q_y=-kA\frac{\partial }{\partial y}\left. \left( T-T_s \right) \right|_{y=0}</math>.

These two terms are equal; thus

:<math>-kA\frac{\partial }{\partial y}\left. \left( T-T_s \right) \right|_{y=0}=hA\left( T_s-T_\infty \right)</math>.

Rearranging,

:<math>\frac{h}{k}=\frac{\left. \frac{\partial \left( T_s-T \right)}{\partial y} \right|_{y=0}}{\left( T_s-T_\infty \right)}</math>.

Multiplying by a representative length ''L'' gives a dimensionless expression:

:<math>\frac{hL}{k}=\frac{\left. \frac{\partial \left( T_s-T \right)}{\partial y} \right|_{y=0}}{\frac{\left( T_s-T_\infty \right)}{L}}</math>.

The right-hand side is now the ratio of the temperature gradient at the surface to the reference temperature gradient, while the left-hand side is similar to the Biot modulus. This becomes the ratio of conductive thermal resistance to the convective thermal resistance of the fluid, otherwise known as the Nusselt number, Nu.

:<math>\mathrm{Nu} = \frac{h}{k/L} = \frac{hL}{k}</math>.