The equations of heat conduction

Abstract

The Fourier equation of heat conduction (1.1) has already been introduced. This equation is for one-dimensional heat flow, and may be written in a more general form:

$$$$

((2.1))

where Q_n is the rate of heat conduction in the n-direction, and ∂t/∂n is the temperature gradient in that direction. The partial derivative is used since there may exist temperature gradients in other directions. One-dimensional conduction does not often occur in practice since a body would have to be either perfectly insulated at its edges or so large that conduction would be one-dimensional at the centre.