Biot Number Calculator

This Biot number calculator helps you compute the Biot number. What is the Biot number? The Biot number determines how quickly heat transfers from the surface of the body to its interior. The text below explains the physics behind the heat transfer and gives the Biot number formula.

The Biot number helps us answer the following question: How much will the temperature inside a body vary if we heat up a part of its surface?

If the Biot number is small (much less than 1), then the temperature on the surface and interior will be very similar. For the actual conductive or convective heat-transfer rate rather than their relative importance, use the heat transfer calculator.

On the other hand, if the Biot number is large (much larger than 1), there will be a large temperature gradient inside the body.

If we warm the surface of a material, two things happen. First, we warm the surface. The efficiency of this process depends on the heat transfer coefficient. That surface parameter can be calculated separately with the heat transfer coefficient calculator.

Secondly, the heat from the surface starts to flow through the rest of the material, heating the interior. How quickly this happens depends on the thermal conductivity of a material. Check the thermal conductivity calculator to learn more about this phenomenon.

The Biot number compares the efficiency of these two processes.

1. If the heat transfer is more efficient than the thermal conductivity, the surface will warm up quicker than the rest of the body – the Biot number is larger than 1.

2. On the other hand, if the material conducts heat well, then besides warming it up only in one place, its temperature will be pretty uniform – the Biot number is smaller than 1.

The Biot number formula is given by:

where:

• ${\rm Bi}$ – Biot number;
• $L_{\rm c}\ \rm [m]$ – Characteristic length of the material;
• $h\ \rm [W/m^2\! \cdot\! K]$ – Heat transfer coefficient at the material's surface; and
• $k\ \rm [W/m\! \cdot\! K]$ – Thermal conductivity of the material.

We can compute the characteristic length $L_{\rm c}\ \rm [m]$ knowing the volume $V\ \rm [m^3]$ and the area $A\ \rm [m^2]$ of a surface through which the material is heated up (or cooled down):

For example, for a copper pan of water with characteristic length $\small L_{\rm c} = 15\ \rm cm$, the Biot number is $\small \rm Bi = 2.807$. This means that when we heat the pan, there will be a significant difference in temperatures between the water at the bottom and at the top of the pot. If we decrease the amount of water (decrease the characteristic length), the Biot number drops, signaling a more uniform temperature inside the pot.

In the Biot number calculator computations, we took the water thermal conductivity as $\small k = 0.7\ \rm W/m\! \cdot\! K$ and the heat transfer coefficient between copper and water as $\small h = 13.1\ \rm W/m\! \cdot\! K$.