= Heat release rate
{title2=$\dot Q$}
<Heat release rate> is the rate at which a process releases <energy> as <heat>, commonly used to characterize combustion. It has the dimensions of <power> and is measured in <watts>, with $1\,\mathrm{W}=1\,\mathrm{J\,s^{-1}}$. Using $Q_{\rm rel}(t)$ for cumulative released <energy>,
$$
\dot Q(t)=\frac{dQ_{\rm rel}}{dt},\qquad
Q_{\rm rel}(t_2)-Q_{\rm rel}(t_1)=\int_{t_1}^{t_2}\dot Q(t)\,dt.
$$
The <heat release rate> is the height of the curve; total released <energy> is its area.
For a synthetic fire whose <heat release rate> rises linearly from zero to $100\,\mathrm{kW}$ in $60\,\mathrm{s}$ and falls linearly to zero over the next $60\,\mathrm{s}$, the area is a triangle:
$$
Q_{\rm rel}=\tfrac12(120\,\mathrm{s})(100\,\mathrm{kW})
=6000\,\mathrm{kJ}=6\,\mathrm{MJ}.
$$
A second fire with a smaller peak but longer duration can release more total <energy>. A peak value alone therefore cannot describe the full event.
A fuel-based estimate multiplies fuel <mass flow rate> by the effective released <energy> per unit <mass>, under stated assumptions about composition and combustion. For a deliberately stipulated effective value $20\,\mathrm{MJ\,kg^{-1}}$ and fuel rate $0.02\,\mathrm{kg\,s^{-1}}$, the estimate is $400\,\mathrm{kW}$. In <oxygen consumption calorimetry>, measured gas flow and <oxygen> depletion instead provide an estimate of <heat release rate>. NIST uses independently metered reference burners to compare these two inference routes.<Natural Gas Confirmation Burner by NIST>[Research Overview, fuel-consumption heat input and confirmation of oxygen-consumption calorimetry]{ref}
A fire's <heat release rate> differs from the <heat transfer> received by one nearby surface or from the <temperature> of its exhaust. Released <energy> can leave by several paths, while a receiving object can store <internal energy> as well as lose <heat>. Even a gas-based calorimeter needs a defined measurement boundary, capture conditions and time response. The NIST National Fire Research Laboratory provides an example of using exhaust collection to quantify large-fire <heat release rate>.<National Fire Research Laboratory by NIST>[Facility description, large-fire calorimetry and exhaust systems]{ref}
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