$\begin{array}{l}\frac{\partial (\rho c)}{\partial t}+\frac{1}{r}\frac{\partial}{\partial r}(\rho {\alpha}_{\text{l}}{u}_{r}rc)+\frac{1}{r}\frac{\partial}{\partial \theta}(\rho {\alpha}_{\text{l}}{u}_{\theta}c)+\frac{\partial}{\partial z}(\rho {\alpha}_{\text{l}}{u}_{z}c)=\frac{1}{r}\frac{\partial}{\partial r}\left(r{\alpha}_{\text{l}}{D}_{\text{eff}}\frac{\partial c}{\partial r}\right)+\\ \text{\hspace{1em}}\text{\hspace{1em}}\frac{1}{r}\frac{\partial}{\partial \theta}\left(\frac{{D}_{\text{eff}}}{r}{\alpha}_{\text{l}}\frac{\partial c}{\partial \theta}\right)+\frac{\partial}{\partial z}\left({D}_{\text{eff}}{\alpha}_{\text{l}}\frac{\partial c}{\partial z}\right)\end{array}$

_{eff}is the effective diffusion ...

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