Fourier Number Calculator

Calculate the dimensionless time used in transient heat-transfer analysis from thermal diffusivity, elapsed time and characteristic length.

Fourier number (Fo)7.2Dimensionless · Fo = αt/L²
InterpretationLarger Fourier number: diffusion has had more time relative to the chosen characteristic length.Its meaning depends on the geometry and transient-conduction solution used next.

Scope: Fourier number is a time-scale ratio. It does not return temperature, heat loss or heating time on its own, and it does not replace the geometry-specific transient solution or boundary condition.

Method and variables

Formula: Fo = αt/L².

  • α — thermal diffusivity
  • t — elapsed time
  • L — characteristic length used by the transient solution

Worked example

For α = 1.2 × 10⁻⁵ m²/s, t = 60 s and L = 0.01 m, Fo = (1.2 × 10⁻⁵ × 60) / 0.01² = 7.2.

How it connects to other tools

Use Biot number to screen the resistance model, then Fourier number to place the event in dimensionless time. The final temperature prediction still needs the right geometry and boundary condition.

Important limits

Fourier number is not a temperature calculation. It does not account for phase change, heat generation, radiation, multilayer construction, property variation or nonuniform boundary conditions.

References

Related tools

Biot Number Calculator · Heat Conduction Calculator · Dimensionless Numbers Calculators

Frequently asked questions

What does Fourier number represent?
It is the ratio of heat diffusion time scale to the time associated with a selected length scale: Fo = αt/L².

Is a larger Fourier number always better?
No. It only indicates that more diffusion time has elapsed relative to the selected length. Whether that is desirable depends on the heating or cooling problem.

How does Fourier number relate to Biot number?
Biot number screens internal versus surface resistance; Fourier number gives the dimensionless time used in transient-conduction solutions.