Fourier number

In physics and engineering, the Fourier number (Fo) or Fourier modulus, named after Joseph Fourier, is a dimensionless number that characterizes heat conduction. Conceptually, it is the ratio of the heat conduction rate to the rate of thermal energy storage. It is a "dimensionless" time, which with the Biot number, characterizes transient conduction problems. It is defined as:

:$mbox\{Fo\}\; =\; frac\{alpha\; t\}\{R^2\}$

where:

* "α" is the thermal diffusivity [m²/s]
* "t" is the characteristic time [s]
* R is the length through which conduction occurs [m]

If the number is greater than 0.2, a one term approximation can be used.

For transient mass transfer by diffusion, there is an analogous mass Fourier Number (also denoted Fo) defined as:

:$mbox\{Fo\}\; =\; frac\{D\; t\}\{L^2\}$

where:

* "D" is the Diffusivity
* "t" is the characteristic timescale
* "L" is the length scale of interest

References

* "Fundamentals of Heat and Mass Transfer", Incropera & DeWitt

See also

* Heat equation