## 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 *k*^{2}*V* *dxdydz*. But the quantity of heat required to produce a rise of temperature *dV* in unit mass is ...