Fourier Number Calculator
Enter thermal diffusivity, time and characteristic length to compute the dimensionless Fourier number Fo = α·t/L².
Input Data
Results
At a glance:The Fourier number Fo = α·t/L² is a dimensionless time in conduction heat transfer, where α = k/(ρ·c_p) is thermal diffusivity, t is time and L a characteristic length (e.g. slab half-thickness). Fo compares how far heat has diffused (conduction) relative to thermal storage; large Fo means the temperature profile has largely developed (quasi-steady), small Fo means early transient. It appears in the solution of the heat equation (e.g. dimensionless charts for cooling of solids). Together with the Biot number it classifies heating/cooling regimes (lumped vs distributed).
Formula
Fourier number: Fo = α·t/L²
α = k/(ρ·c_p)
$$\mathrm{Fo} = \dfrac{\alpha\,t}{L^2}$$How to Use
- Enter thermal diffusivity α (m²/s), time t (s) and characteristic length L (m).
- The calculator returns Fo.
Case Studies
Cooling a slab
α = 1e-5 m²/s, t = 100 s, L = 0.05 m.
Fo = 1e-5×100/0.0025 = 0.4.
Moderate transient; profile still developing.
FAQ
What does a large Fourier number mean?
Heat has had time to diffuse through the body; the temperature field is close to its steady-state shape. Fo ≫ 1 → developed profile; Fo ≪ 1 → early transient near the surface.
How is it used with the Biot number?
Biot Bi = hL/k compares internal to external resistance. With Bi < 0.1 the lumped-capacitance method applies regardless of Fo; otherwise the transient solution depends on both Bi and Fo.
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References
Content review: Calculatorism Editorial Team. Results are for reference only; please refer to the relevant authorities for the official figures.