...
| LaTeX Math Block |
|---|
|
{\rm w}(t, r) = E_1 \left( \frac{r^2}{4 \, t} \right) = -{\rm Ei} \left( - \frac{r^2}{4 \, t} \right) |
defines a solution of planar axial-symmetric diffusion equation with homogenous initial and boundary conditions:
| LaTeX Math Block |
|---|
| \frac{\partial {\rm w}}{\partial t} = \frac{\partial {\rm w}^2}{\partial^2 r} + \frac{1}{r} \frac{\partial {\rm w}}{\partial r} |
|
| LaTeX Math Block |
|---|
| {\rm w}(t=0, r) = 0 |
|
| LaTeX Math Block |
|---|
| {\rm w}(t, r=\infty) = 0 |
|
| LaTeX Math Block |
|---|
| 0 <= {\rm w}(t, r) < \infty \, , \ \forall (t,r) \in D = \{ t \geq 0, r>0 \}
\subset \mathbb{R} |
|
and is widely used in radial heat-mass transfer simulations.
...
