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## Main Question or Discussion Point

I have the following diffusion equation

[tex]

\frac{\partial^{2}c}{\partial r^{2}} + \frac{2}{r}\frac{\partial c}{\partial r} = \frac{1}{\alpha}\frac{\partial c}{\partial t}

[/tex]

where [tex]\alpha[/tex] is the diffusivity. The solution progresses in a finite domain where [tex]0 < r < b[/tex], with initial condition

[tex] c(r,0) = g(r) [/tex]

and the boundary conditions

[tex]

c(b,t) = 1

[/tex]

[tex]

c(0,t) = 0

[/tex]

How will I proceed with this using the separation of variables?

I think the time-dependent part is straight forward after separation of variables. But how will I deal with the spatial part where Bessel functions have to be dealt with?

Thanks.

[tex]

\frac{\partial^{2}c}{\partial r^{2}} + \frac{2}{r}\frac{\partial c}{\partial r} = \frac{1}{\alpha}\frac{\partial c}{\partial t}

[/tex]

where [tex]\alpha[/tex] is the diffusivity. The solution progresses in a finite domain where [tex]0 < r < b[/tex], with initial condition

[tex] c(r,0) = g(r) [/tex]

and the boundary conditions

[tex]

c(b,t) = 1

[/tex]

[tex]

c(0,t) = 0

[/tex]

How will I proceed with this using the separation of variables?

I think the time-dependent part is straight forward after separation of variables. But how will I deal with the spatial part where Bessel functions have to be dealt with?

Thanks.

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