Fourier number

A similitude indicator for non-stationary heat processes. It characterizes the relation between the rate of change of the heat conditions in the surrounding medium and the rate of reconstructing the temperature field inside the system (body) under consideration. It depends on the dimensions of the body and its coefficient of heat conductivity. The Fourier number $\mathrm{Fo} = a t_0 / l^2$ where $a = \lambda / \rho c$ is the coefficient of thermal conductivity, $\lambda$ is the heat conductivity, $\rho$ is the density, $c$ is the specific heat, $l$ is the characteristic linear dimension of the body, and $t_0$ is the characteristic time of a change in the exterior conditions.

It is named after J. Fourier.

References

Zbl 0095.20303

[a1]	L.I. Sedov, "Similarity and dimensional methods in mechanics" , Infosearch (1959) (Translated from Russian)
[a2]	G. Birkhoff, "Hydrodynamics, a study in logic, fact and similitude" , Princeton Univ. Press (1960)