Biot Number

Biot Number (Eq. 5.9) is a dimensionless parameter. It is a measure of how dramatic the temperature difference across a solid is in comparison to the temperature difference across the boundary undergoing convection.

Where is the convection heat transfer coefficient, is the characteristic length, and is the thermal conductivity coefficient.

Section 5.2 goes says the following:

Biot number provides a measure of the temperature drop in the solid relative to the temperature difference between the solid's surface and the fluid.

From Equation 5.9, it is also evident that the Biot number may be interpreted as a ratio of thermal resistances.

In particular, if Bi ≪ 1, the resistance to conduction within the solid is much less than the resistance to convection across the fluid boundary layer.

It is used in the lumped capacitance method as well as to tell if the fin approximation can be used... I think, idk.

and are conduction and convection resistances as given in thermal circuits.