= Thermal-front retardation in Darcy flow
{title2=$Y=\Gamma\phi X$}
If a thermal front has speed $Y'=\Gamma U$ with $U$ the <Darcy velocity>, while a material front has speed $X'=U/\phi$, their position ratio from coincident initial locations is $Y/X=\Gamma\phi$. Calling a retardation factor the ratio to pore velocity instead would give $Y/X=\Gamma$; these conventions must not be mixed. With cold viscosity $\mu$ and heated viscosity $b\mu$, the displacement's effective viscosity is $\mu_{\rm eff}=\mu[b-(b-1)\Gamma\phi]$. In the pressure resistance the cold layer has length $Y$, the hot injected layer has length $X-Y$, and the displaced layer has length $L-X$.
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