Editing Biot number (section)

==Definition==
The Biot number is defined as:

:<math>\mathrm{Bi} = \frac{h}{k} L</math>

where:
* <math>{k}</math> is the  [[thermal conductivity]] of the body [W/(m·K)]
* <math>{h}</math> is a convective [[heat transfer coefficient]] [W/(m<sup>2</sup>·K)]
* <math>{L}</math> is a [[characteristic length]] [m] of the geometry considered.

(The Biot number should not be confused with the [[Nusselt number]], which employs the [[thermal conductivity]] of the [[fluid]] rather than that of the body.)


The characteristic length in most relevant problems becomes the heat characteristic length, i.e. the ratio between the body volume and the heated (or cooled) surface of the body:
<math display="block">L = \frac{V}{A_\mathrm{Q}}</math>
Here, the subscript ''Q'', for ''[[heat]]'', is used to denote that the surface to be considered is only the portion of the total surface through which the heat passes. 

The physical significance of Biot number can be understood by imagining the heat flow from a small hot metal sphere suddenly immersed in a pool, to the surrounding fluid. The heat flow experiences two resistances: the first for conduction within the solid metal (which is influenced by both the size and composition of the sphere), and the second for convection at the surface of the sphere. If the thermal resistance of the fluid/sphere interface exceeds that thermal resistance offered by the interior of the metal sphere, the Biot number will be less than one. For systems where it is much less than one, the interior of the sphere may be presumed to be a uniform temperature, although this temperature may be changing with time as heat passes into the sphere from the surface. The equation to describe this change in (relatively uniform) temperature inside the object, is a simple exponential one described by [[Newton's law of cooling]].

In contrast, the metal sphere may be large, so that the characteristic length is large and the Biot number is greater than one. Now, thermal gradients within the sphere become important, even though the sphere material is a good conductor. Equivalently, if the sphere is made of a poorly conducting (thermally insulating) material, such as wood or styrofoam, the interior resistance to heat flow will exceed that of convection at the fluid/sphere boundary, even for a much smaller sphere. In this case, again, the Biot number will be greater than one.