# 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 .

## 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

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References in periodicals archive ?
The maximum normalized temperature rise is calculated as maximum temperature rise with coated wall over temperature rise with uncoated wall and is plotted against the Fourier number for several Biot numbers ranging from 0.3 to 1.84 as shown in Figure 10.
Analysis suggested that for higher Fourier number (lower cycle frequency), relatively low Biot number is required to get maximum temperature rise.
An approximate approach is to refer to a Heisler chart to or to an online calculator to determine the Fourier number (T).
The Fourier number is where ([theta]) and the Bi curve intersect.
To aid in analyzing the behavior of the PCM, an investigation of Biot number and Fourier number is useful.
where [beta] is the radial distance made dimensionless by the BHE depth H, and [[gamma].sub.F] is related to a Fourier number based on the BHE depth [Fo.sub.H]:
The thermal resistance of the ground is a function of time ([tau]) from the initiation of a constant heat rate, bore diameter ([d.sub.b]) and thermal properties ([[alpha].sub.g] = [k.sub.g]/rho[c.sub.p]) expressed in the term Fourier number (Fo = 4[[alpha].sub.g][tau]/[d.sub.b]2).
in bath with extraction solvent) [c.sub.A] concentration of bound kg * [m.sup.-3] component in solid phase [c.sub.p] initial concentration of extracted kg * [m.sup.-3] component in solid phase D effective diffusion coefficient of [m.sup.2] * extracted component from solid phase [s.sup.-1] x Cartesian coordinate (one-dimensional m diffusion) b half thickness of solid phase m [epsilon] porosity of solid phase 1 Na dimensionless volume of extraction 1 solvent [q.sub.n] [n.sup.-th] root of a certain 1 transcendent equation A sorption coefficient 1 S surface of solid phase [m.sup.2] [F.sub.o] Fourier number (i.e.
In the following, we first introduce a simple analysis of microchannel filling based on the Fourier number. This is followed with the use of a hybrid simulation method developed in our laboratory to simulate the injection molding process.
It is seen that the early line and the late line intersects nearly at the same Fourier number of about 17-19, but in an absolute time scale, they represent widely differing values.

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