Fourier Number Calculator

Enter value and click on calculate. Result will be displayed.
Select calculator :
 
Thermal Diffusivity(α) :
m2/s
Characteristic Time (t) :
s
Characteristic Length (L) :
m
Result:

What is a Fourier Number Calculator?

A Fourier Number Calculator computes the Fourier number (Fo), a dimensionless quantity in heat transfer that characterizes the ratio of heat conduction to heat storage in a material. It helps analyze transient (unsteady) heat conduction problems.

The formula is:

Where:

  • Fo = Fourier number
  • α = Thermal diffusivity (m²/s)
  • t = Time (s)
  • L = Characteristic length (m)

Why is a Fourier Number Calculator Important?

  • Determines how fast heat diffuses through a material
  • Helps in cooling and heating analysis of solids
  • Used in engineering and physics for thermal modeling
  • Essential in food processing, metallurgy, and insulation design

How Does It Work?

  1. Input values for thermal diffusivity (α), time (t), and characteristic length (L).
  2. Apply the formula
  3. Interpret the result:
    • Fo << 1 → Heat has not penetrated deeply (early stage of conduction).
    • Fo > 1 → Material is reaching thermal equilibrium.

Example:
If a metal with α = 1.2 × 10 −5 m²/s, a thickness of 0.01 m, and heated for 100 s, then:

Since Fo > 1, the material is nearing equilibrium.

When is a Fourier Number Calculator Used?

  • Heat treatment of metals (annealing, quenching)
  • Thermal insulation design
  • Food industry (freezing and cooking time estimation)
  • Geothermal and climate studies (heat diffusion in soil and rocks)