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{\rm w}(t, r) = E_1(\frac{r^2}{4 \, t}) = -{\rm Ei} \left( - \frac{r^2}{4 \, t} \right) |
honors the defines a solution planar axial-symmetric diffusion equation:
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| \frac{\partial {\rm w}}{\partial t} = \frac{\partial {\rm w}^2}{\partial^2 r} + \frac{1}{r} \frac{\partial {\rm w}}{\partial r} |
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| {\rm w}(t=0, r) = 0 |
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| {\rm w}(t, r=\infty) = 0 |
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| 0 <= {\rm w}(t, r) < \infty \, , \ \forall (t,r) \in D = \{ t \geq 0, r>0 \}
\subset \mathbb{R} |
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and is widely used in radial mass-heat transfer simulations.
References
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https://www.wolframalpha.com/input/?i=Ei(x)
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