Even though the Biot number and Nusselt number may have similar formulae, they should not be compared at all.

Comparing them is nothing but comparing apples to oranges. The context is completely different in the reason why they are used.

Nusselt number:

Heat transfer is enhanced when the fluid layer moves over a solid surface(convection by fluid) compared to heat transfer when the fluid layer is stationary on the solid surface. (conduction through a fluid)

Biot Number: Biot number is the ratio of conduction resistance within the body to convection resistance at the surface of the body.

Biot number is used to decide if the lumped system analysis can be applied to the heat flow problem where conduction and convection mode of heat transfer is going to take place.

The lumped system approach is used when the Biot number is very very small.

Even though the Biot number and Nusselt number may have similar formulae, they should not be compared at all.

Comparing them is nothing but comparing apples to oranges. The context is completely different in the reason why they are used.

Nusselt number:

Heat transfer is enhanced when the fluid layer moves over a solid surface(convection by fluid) compared to heat transfer when the fluid layer is stationary on the solid surface. (conduction through a fluid)

Biot Number: Biot number is the ratio of conduction resistance within the body to convection resistance at the surface of the body.Biot number is used to decide if the lumped system analysis can be applied to the heat flow problem where conduction and convection mode of heat transfer is going to take place.

The lumped system approach is used when the Biot number is very very small.

(Bi << 0.1)