Fourier number

Remarks

The substitution $\tau = \alpha t / L^2$ and $\xi = x / L$ turns the heat equation $\partial_t T = \alpha \Delta_x T$ into $\partial_\tau T = \Delta_\xi T$. So $\mathrm{Fo}$ is the time variable of the dimensionless heat equation.

Example: a steel plate with $\alpha = 1.2 \cdot 10^{-5}$ square metres per second and half-thickness $L = 0.01$ metres, after $t = 10$ seconds. Then $\mathrm{Fo} = 1.2 \cdot 10^{-5} \cdot 10 / 10^{-4} = 1.2$.

Non-example: $\alpha t / L$ is not the Fourier number; it has the unit of a length, so it is not dimensionless.