# Fourier Number

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## Fourier number

[‚fu̇r·ē‚ā ‚nəm·bər]*Fo*

_{f }.

*N*

_{Fo }

_{m }.

*N*

_{Fo }

_{h }.

## Fourier Number

one of the similarity criteria of unsteady-state thermal processes. It characterizes the relationship between the rate of change of the thermal conditions in the environment and the rate of variation of the temperature distribution in the system (body) under consideration, and it depends on the size of the body and on its thermal diffusivity.

Sometimes denoted by *Fo*, the Fourier number is defined by the equation *Fo* = *at*/*l*^{2}, where *a* = λ/*pc* is the thermal diffusivity (λ is the thermal conductivity, ρ is the density, and *c* is the specific heat), *l* is the characteristic linear dimension of the body, and *t*_{0} is the characteristic time of change of the external conditions.

Criteria establishing a relationship between the rates of development of different effects are called homochronicity criteria. It follows that the Fourier number is a homochronicity criterion for thermal processes. In the case of thermal processes described by the heat equation, the dimensionless distribution of temperature in a body is represented as a function of dimensionless geometric and thermal similarity criteria, one of which is the Fourier number.

The Fourier number was named for J. Fourier.

S. L. VISHNEVETSKII