Classical thermodynamics, heat transfer Definition

Biot number

Builds on Dimensionless numbers in fluid mechanics Heat transfer coefficient Thermal conductivity

Definition

Let a solid body of thermal conductivity $k > 0$ exchange heat with a fluid through its surface, with heat transfer coefficient $h > 0$ . Let $L > 0$ be a characteristic length of the body. The Biot number is the dimensionless number $\mathrm{Bi} = \frac{h L}{k}.$

Remarks

A common choice of length is $L = V / A$ , the volume of the body divided by its surface area.

Example: a steel ball of radius $r = 0.01$ metres with $k = 50$ , cooled in air with $h = 10$ , in SI units. Then $L = V / A = r / 3$ , so $\mathrm{Bi} = 10 \cdot 0.01 / (3 \cdot 50) \approx 6.7 \cdot 10^{-4}$ , which is far below $0.1$ .

Non-example: the ratio $h L / k_f$ with the conductivity $k_f$ of the fluid instead of the solid is not the Biot number. It is the Nusselt number.

When $\mathrm{Bi} < 0.1$ , the rule of thumb in engineering is that the temperature inside the body is nearly uniform.

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Dimensionless numbers in fluid mechanics concept
Heat transfer coefficient concept
Thermal conductivity concept
Biot number definition

Tag	`6MGFWKBDW8`
URI	`m2://6MGFWKBDW8`
Kind	definition
Writing	W0 stub
MSC	80A19
Defines	Biot number
Uses	Dimensionless numbers in fluid mechanics, Heat transfer coefficient, Thermal conductivity
Changed	3 November 2026

Biot number

Definition

Remarks

Reading path

Further reading

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