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XVIII.—The Equation of Conduction of Heat

Published online by Cambridge University Press:  15 September 2014

Marion C. Gray
Marion C. Gray
Affiliation:
University of Edinburgh Bryn Mawr College, Pa
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Extract

The differential equation of the conduction of heat in ordinary three-dimensional space is generally written in the form

where v denotes the temperature of the medium at time t. For a medium in which the temperature varies only in one direction, e.g. an infinite cylinder with the temperature varying along the axis, the equation is

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Type
Proceedings
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Proceedings of the Royal Society of Edinburgh , Volume 45 , Issue 3 , 1926 , pp. 230 - 244
Copyright
Copyright © Royal Society of Edinburgh 1926

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References

page 231 note * Forsyth, Theory of Differential Equations, part iv, vol. vi, pp, 107–109.

page 231 note † Fourier, Théorie Analytique de la Chaleur.

page 234 note * Poincaré, Théorie Analytique de la Chaleur, chap. vii.