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Methods of Mathematical Physics, Third Edition by Bertha Jeffreys, Harold Jeffreys

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Chapter 20CONDUCTION OF HEAT IN ONE AND THREE DIMENSIONS

Then cold, and hot, and moist, and dry,In order to their stations leap.

JOHN DRYDEN, Song for St Cecilia’s day

20·01. Equation of heat conduction.

The rate of transmission of heat across a surface by conduction is equal to –k∂v/∂n per unit area, where V is the temperature, k a constant of the material called the thermal conductivity, and dn an element of the normal to the surface. Hence we can show easily that in a uniform material the rate of flow of heat into an element of volume dxdydz is kimage2V dxdydz. But the quantity of heat required to produce a rise of temperature dV in unit mass is ...

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