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r_{wf} < r \leq r_e

\frac{\partial p}{\partial t}= \chi \left[ \frac{\partial^2 p}{\partial r^2} + \frac{1}{r} \frac{\partial p}{\partial r} \right]

\left[ \frac{\partial p}{\partial r} \right]_{r=r_e} = 0

\left[ r\frac{\partial p(t,r)}{\partial r} \right]_{r \rightarrow= r_w} = \frac{q_t}{2 \pi \sigma}

p_{wf}(t)= p(t, r_w) - S \cdot r_w \, \frac{\partial p(t,r)}{\partial r} \Bigg|_{r=r_w}