Definition of the Biot Number
Definition
The heat transfer coefficient $h$ of a solid object multiplied by the characteristic length $L$ and divided by the thermal conductivity $k$ is a dimensionless number called the Biot number. $$ \mathrm{Bi} := {{h L} \over k} $$
Explanation
The characteristic length is often defined as the ratio of the object’s volume $V$ to its surface area $A$, i.e. $L = V / A$; however, in the following discussion we will simplify by imagining the object has the shape of a sphere.
A common assumed scenario when discussing the Biot number is dropping a heated sphere into cold water and letting it cool. A large Biot number means that $h$ is large, so according to Newton’s law of cooling there is a large heat flux from the sphere’s surface due to convection — in other words, it cools rapidly.
Here, the Biot number can be used as an indicator of how uniform the object’s temperature is. If $h$ is fixed, one way to make the Biot number small is to make $L$ small — in other words, to reduce the size of the sphere. In the extreme case, if $L \approx 0$, the sphere becomes so small that the temperature of the surface and the interior of the sphere are nearly uniform.
Another way for the Biot number to be small is for $k$ to increase. Because $k$ is the object’s thermal conductivity, a small Biot number implies heat spreads rapidly within the object, so again the surface and the interior of the sphere are nearly at the same temperature.