Diffusion in three dimensions different coordinates

The three-dimensional diffusion equation in Cartesian coordinates is 

In spherical coordinates, using x = r sin0 cost)), x = r sin0 sincj), and z = r cos0, then 

Define w = rC in Equation 3-66c then the above equation for three-dimensional diffusion with spherical symmetry is reduced to the same form as Equation 3-10  

The above equation is important and very useful because many solutions obtained for the simple one-dimensional diffusion equation can be applied to the spherical diffusion problem. Below is an example. 

Example 3.5 Consider three-dimensional diffusion in a solid sphere of radius a with spherical geometry (meaning concentration depends only on r with 0 r a). The initial and boundary conditions are 

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