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XVIII.—The Equation of Conduction of Heat

  • Marion C. Gray (a1) (a2)

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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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.

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