View source for Fourier number

A similitude indicator for non-stationary heat processes. It characterizes the relation between the rate of change of the heat conditions in the surrounding medium and the rate of reconstructing the temperature field inside the system (body) under consideration. It depends on the dimensions of the body and its coefficient of heat conductivity. The Fourier number <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f041/f041080/f0410801.png" /> where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f041/f041080/f0410802.png" /> is the coefficient of thermal conductivity, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f041/f041080/f0410803.png" /> is the heat conductivity, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f041/f041080/f0410804.png" /> is the density, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f041/f041080/f0410805.png" /> is the specific heat, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f041/f041080/f0410806.png" /> is the characteristic linear dimension of the body, and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f041/f041080/f0410807.png" /> is the characteristic time of a change in the exterior conditions.

It is named after J. Fourier.



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====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  L.I. Sedov,   "Similarity and dimensional methods in mechanics" , Infosearch  (1959)  (Translated from Russian)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  G. Birhoff,   "Hydrodynamics, a study in logic, fact and similitude" , Princeton Univ. Press  (1960)</TD></TR></table>