# Fourier Number

Written by Jerry Ratzlaff. Posted in Dimensionless Numbers

Fourier number is a dimensionless number 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.

## FORMULA

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

Where:

$$Fo$$ = Fourier number

$$\alpha$$ = thermal diffusivity

$$t$$ = time

$$l$$ = characteristic length

Solve for:

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

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

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