= Taylor dispersion in a parabolic porous-layer velocity profile
{c}
{title2=$D_{\rm eff}=D+U^2h^2/(210D)$}
For <interstitial velocity> $u=6U\xi(1-\xi)$, $\xi=z/h$, reflecting transverse walls and molecular <diffusion> $D$, solve $D\chi''=u-U$ with zero mean and zero normal derivative. One solution is $\chi=(Uh^2/D)(\xi^3-\xi^4/2-\xi^2/2+1/60)$. Averaging the <advection-diffusion equation> gives enhancement $-\overline{(u-U)\chi}=D\overline{(\chi')^2}=U^2h^2/(210D)$. The approximation requires transverse equilibration and slowly varying longitudinal concentration.
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