I want to find the analytical solution of a radial diffusion system (1D cylindrical coordinates). Here what is considered is pressure diffusion. The conditions are simple and similar to the following.
Initial P = P0
P(r=infinite) = P0
P (r= 0) = P1 when t > 0
I need the solution of P at any r_i and t.
The flow rate term is unknown.
Could anyone give any suggestion? Thank you.
The closest I know of is page 335 of Carslaw and Jaeger, 2nd edition (section 13.5). I say "closest" because their unsteady solution is from a cylinder of finite radius, i.e. within the domain a
Can you show a snapshot of the diffusion equation? I also hope the diffusion coefficient is constant.
Dear Johnny, this book probably solves what you are looking for:
HEAT CONDUCTION, by DAVID W. HAHN and M. NECATIOZIS¸IK
Juan Manuel Gomba : does it provide the solution that Johnny is looking for, precisely? Hopefully.
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