Q kA

dT dx

The heat flux is dependent upon the area across which energy flows and the temperature gradient at that plane. The coefficient of proportionality is a material property, called thermal conductivity k. This relationship always applies, both for steady and transient cases. If the gradient can be found at any point and time, the heat flux density, Q/A can be calculated.

Conduction Equation. The control volume approach from thermodynamics can be applied to give an energy balance which we call the conduction equation. For brevity we omit the details of this development; see Refs. 2 and 3 for these derivations. The result is

This equation gives the temperature distribution in space and time, G is a heat-generation term, caused by chemical, electrical, or nuclear effects in the control volume. Equation I.4 can be written

pC dT

k dT

0 0

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