# Fourier Number

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## Fourier number

[‚fu̇r·ē‚ā ‚nəm·bər]
(fluid mechanics)
A dimensionless number used in unsteady-state flow problems, equal to the product of the dynamic viscosity and a characteristic time divided by the product of the fluid density and the square of a characteristic length. Symbolized Fof .
(physics)
A dimensionless number used in the study of unsteady-state mass transfer, equal to the product of the diffusion coefficient and a characteristic time divided by the square of a characteristic length. Symbolized NFo m .
(thermodynamics)
A dimensionless number used in the study of unsteady-state heat transfer, equal to the product of the thermal conductivity and a characteristic time, divided by the product of the density, the specific heat at constant pressure, and the distance from the midpoint of the body through which heat is passing to the surface. Symbolized NFo h .
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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/l2, 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 t0 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