Biot Number Calculator

This Biot number calculator works out the dimensionless Biot number for a solid body exchanging heat with a surrounding fluid, and tells you whether the simple lumped capacitance model applies. Enter the convective heat transfer coefficient at the surface, the characteristic length of the body, and the thermal conductivity of the material, and the calculator returns the Biot number along with a plain verdict on the modelling assumption. The Biot number, written Bi = h Lc / k, is the ratio of the resistance to heat conduction inside the object to the resistance to heat convection at its surface. When it is small, heat moves through the interior far more easily than it leaves the surface, so the whole body stays at nearly one temperature as it heats or cools, and you can model the transient with a single exponential curve rather than solving the full heat conduction equation. When it is large, the inside cannot keep up with the surface and steep internal temperature gradients form. The usual rule of thumb is that below 0.1 the lumped capacitance model is accurate enough for engineering work. The characteristic length is normally the volume of the body divided by its surface area. The defaults describe a small aluminium part in moderate airflow. Change the inputs to match your own problem, and see the worked example below for the full arithmetic.

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With a Biot number of 0.0125, below 0.1, the lumped capacitance model is valid: internal temperature gradients are small and the object can be treated as a single uniform temperature.

The characteristic length is usually the body volume divided by its surface area. Keep all inputs in SI units so the Biot number stays dimensionless. Estimate only.