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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

Type
Proceedings
Information
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.