Biot Number Calculator

Calculate the Biot number to screen whether internal temperature gradients in a solid are likely to matter during convection-driven heating or cooling.

Biot number (Bi)0.0167Dimensionless · Bi = hLc/ks
InterpretationBi ≤ 0.1: internal conduction resistance is often small enough for a lumped-capacitance first approximation.Use Lc = volume / exposed surface area when that definition applies.

Scope: the usual Bi ≤ 0.1 rule is a first screening criterion, not a design approval. Geometry, boundary condition, property variation and the actual definition of characteristic length still matter.

Method and variables

Formula: Bi = hLc/ks.

  • h — convection heat-transfer coefficient
  • Lc — characteristic length
  • ks — thermal conductivity of the solid

Worked example

A solid with h = 25 W/(m²·K), Lc = 0.01 m and ks = 15 W/(m·K) has Bi = 0.0167. This is below 0.1, so a lumped-capacitance estimate may be a reasonable first approximation.

How it connects to other tools

Use Biot number before a transient lumped-capacitance analysis. Fourier number then describes the dimensionless elapsed time in that analysis.

Important limits

The Bi ≤ 0.1 rule is not universal validation. Nonuniform convection, multilayer parts, strongly temperature-dependent properties, radiation, internal heat generation and complex geometry can require a more detailed model.

References

Related tools

Heat Conduction Calculator · Prandtl Number Calculator · Dimensionless Numbers Calculators

Frequently asked questions

What does the Biot number compare?
It compares a solid's internal conduction resistance with its surface convection resistance: Bi = hLc/ks.

What does Bi less than 0.1 mean?
It is a common first criterion for treating a body as approximately uniform in temperature in a lumped-capacitance analysis, subject to the geometry and boundary conditions.

What is characteristic length?
For many transient-conduction applications it is the body volume divided by the exposed surface area. The correct definition depends on the model and geometry.