# Fourier Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

## Fourier Number

Fourier number ( $$Fo$$ ) (dimensionless number) is giving the ratio of heat conduction rate to the rate of thermal energy storage in a solid.  This is mainly used in unsteady state heat transfer.

### Fourier Number FORMULA

$$Fo = \frac{\alpha t}{l^2}$$          $$Fourier \; number \;=\; \frac { difference \; in \; thermal \;\;x\;\; time } { characteristic \; length^2 }$$

Where:

$$Fo$$ = Fourier number

$$\alpha$$ (Greel symbol alpha) = thermal diffusivity

$$t$$ = time

$$l$$ = characteristic length

Solve for:

$$\alpha = \frac{ Fo l^2 }{ t }$$

$$t = \frac{ Fo l^2 }{ \alpha }$$

$$L = \sqrt { \frac{ \alpha t }{ Fo } }$$