Surface heat flux of a cooling plate
= Surface heat flux of a cooling plate
{title2=$q_s(t)=k\Delta T\,[1+2\sum_{n\geq1}e^{-n^2t/\tau_0}]/a$}
For a hot initial plate cooled from above, <Fourier's law> gives the displayed upward <heat flux>. At old ages only the steady value $k\Delta T/a$ remains. At young ages the sum approaches a <Gaussian integral>, giving $q_s\sim k\Delta T/\sqrt{\pi\kappa t}$. This divergence is an idealized sudden surface cooling, not an infinite observed ridge <heat flux>.