= Integral exponential profile for porous wall convection
{title2=$f(\eta)\simeq2^{2/3}(1-e^{-\eta/2^{1/3}})$}
Assume an exponentially decreasing <temperature> profile while imposing wall heat flux, impermeability and the exact integrated heat budget. For $f=C(1-e^{-\eta/d})$, the wall condition gives $C=d^2$ and $\int(f')^2d\eta=1$ gives $d^3=2$. This yields the displayed integral approximation and discharge $\int wdy\simeq2^{2/3}\kappa z/\delta$. It satisfies the boundary conditions and exact flux budget, but not the differential equation pointwise; its mass-flux coefficient is approximate.
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