= Steady heat conduction through layers
{title2=$\Delta T=q\sum_jL_j/k_j$}
In one-dimensional steady <heat conduction> without internal heat sources, <conservation of energy> gives constant <heat flux> $q=-kT'$. Through a layer of thickness $L_j$ and positive <thermal conductivity> $k_j$, the <temperature> drop is $qL_j/k_j$. If adjoining layers are in perfect <thermal contact>, <temperature> and <heat flux> are continuous at each interface, so summing the layer drops proves the displayed formula. <Temperature> is piecewise linear and its slope may jump when <thermal conductivity> changes.
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