Question: How to solve this 2D Axisymmetric Diffusion PDE?

Dear Maple Users,

I appreciate your help with the previous 1D PDE problem that I posted.

Now I have another 2D axisymmetric diffusion PDE, looking for u(r,z,t), no variation in the theta direction:

PDE: u'_t = alpha*(u"_r + (1/r)*u'_r + u"_z); a < r < b, 0 < z < L, 0 < t < infinity

BC1: u| _{z = L} = Psi_s

BC2: -alpha*u'_z| _{z = 0} = 0

BC3: -alpha*u'_r| _{r = a} = 0

BC4: -alpha*u'_r| _{r = b} = flux_b

IC: u(r,z,0) = (z/L)*Psi_s

a, b, L, alpha, Psi_s, flux_b are given.

My attempt at a solution is attached, following the solution path that you provided for the previous 1D PDE problem.

2D_CCS_PDE_Sol.mw

I have run into an error message that I am unable to resolve. I would greatly appreciate your taking a look at this.

Perhaps, there is no closed form solution to this problem and a numerical solution may have to be attempted.

Please advise. Thanks.

Joseph Thodiyil