= Heat current
{title2=$\dot Q$}
A <heat current> is the rate of <heat transfer> across a specified oriented boundary, $\dot Q$, measured in <watts>. For a <heat flux> field $\mathbf q$ and outward unit <normal vector> $\mathbf n$, the outward heat current through a surface is
$$
\dot Q_{\rm out}=\int_A\mathbf q\cdot\mathbf n\,dA.
$$
The sign convention matters: outward and inward currents for the same physical transfer have opposite signs.
A uniform normal <heat flux> $100\ \mathrm{W\,m^{-2}}$ through $0.02\ \mathrm{m^2}$ gives a <heat current> of $2\ \mathrm W$. Maintaining it for $30\ \mathrm s$ transfers $60\ \mathrm J$. In steady one-dimensional <thermal conduction> without internal sources, the current is constant along a bar even if changing cross-sectional <area> makes the local <heat flux> vary. This separates a whole-path transport rate from its concentration over a surface.
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