Radial-spherical coordinates. Transient 1-D.

The Heat Equation for transient 1-D Green's Functions in radial-spherical coordinates is:

$${\frac{1}{r^{2}}} {\frac{\partial }{\partial r}} \left(\vphantom{ r^{2}\frac{\partial G} {\partial r}}\right. {\frac{\partial G}{\partial r}} \left.\vphantom{ r^{2}\frac{\partial G} {\partial r}}\right) {\frac{1}{\alpha }} \delta \prime \delta \tau {\frac{1}{\alpha }} {\frac{\partial G}{\partial t}}$$

The radial-spherical Dirac delta function $\delta$(r - r^$\prime$) has vector arguments and has units of [ meters^-3].