Fourier number

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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

[edit] References

  • Fundamentals of Heat and Mass Transfer, Incropera & DeWitt
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[edit] See also