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The equation for an infinite cylinder with the radius rm is given by [2]
and for a sphere with the radius rm
where
(3.35)
(3.36)
(3.37)
In the range of F0 > 1, only the first term of these equations is significant. Therefore, for
the heating or cooling time we obtain [2]
Plate:
Cylinder:
Sphere:
(3.38)
(3.39)
(3.40)
The solutions of Equation 3.32 to Equation 3.37 are presented in a semi-logarithmic
plot in Figure 3.9, in which the temperature ratio 0^ = (Tw - Tb)/(TW - Ta) is shown
as a function of the Fourier number F0.
Not considering small Fourier numbers, these plots are straight lines approximated by
Equation 3.38 to Equation 3.40.
If the time tk is based on the centre line temperature Th instead of the average temperature
fb, we get [3]
(3.41)
Analogous to Figure 3.9, the ratio 0^ with the centre line temperature Tb at time tk is
plotted in Figure 3.10 over the Fourier number for bodies of different geometry [4].