Heat-weighted head speed of a porous plume
= Heat-weighted head speed of a porous plume
{title2=$\dot Z_h\simeq\tfrac23W(Z_h)$}
Truncating the steady <porous thermal plume> profile below a head height and conserving supplied heat gives $\dot Z_h\simeq\int w^2dx/\int wdx=(2/3)W(Z_h)$. Thus $Z_h\propto t^{3/4}$. This is an integral bulk-head estimate, while fastest centreline parcels have characteristic speed $W$; the approximation does not resolve the transient nose.