Editing Heat equation (section)

=== Internal heat generation ===
The function ''u'' above represents temperature of a body. Alternatively, it is sometimes convenient to change units and represent ''u'' as the heat density of a medium. Since heat density is proportional to temperature in a homogeneous medium, the heat equation is still obeyed in the new units.

Suppose that a body obeys the heat equation and, in addition, generates its own heat per unit volume (e.g., in watts/litre - W/L) at a rate given by a known function ''q'' varying in space and time.<ref>Note that the units of ''u'' must be selected in a manner compatible with those of ''q''. Thus instead of being for thermodynamic temperature ([[Kelvin]] - K), units of ''u'' should be J/L.</ref> Then the heat per unit volume ''u'' satisfies an equation
: <math>\frac{1}{\alpha} \frac{\partial u}{\partial t} = \left(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} \right) + \frac{1}{k}q.</math>

For example, a tungsten light bulb filament generates heat, so it would have a positive nonzero value for ''q'' when turned on. While the light is turned off, the value of ''q'' for the tungsten filament would be zero.