Heat generation rate ($\dot{Q}$)

A heat generation rate specifies the power deposited into microscopic thermal degrees of freedom, usually through conversion of electrical, chemical or mechanical energy. Its unit is the watt. The term is used as a source in a thermal energy balance; it does not imply creation of total energy.

A resistor supplied with current $I$ has electrical power $I^{2}R$ converted by Joule heating. If that power is deposited approximately uniformly in a body of volume $V$, the volumetric heat generation rate is $q^{\prime \prime \prime }=I^{2}R/V$. A steady body can export the same total power through heat transfer and retain constant temperature. If it is approximately isolated for a short interval, the deposited energy instead raises its internal energy, giving $C\dot{T}=P$ when its heat capacity is approximately constant.

Thermal power generated per unit volume. Its integral over a region is the region's total heat generation rate.