Could anyone tell me that where can I find an analytical solution of diffusion equation (PDE) with 1D zero flux boundary at outlet? I need this for calculating rock permeability from pressure diffusion.
I have found there are some literatures giving solution in a semi-inifinite domain. What I want to get is an analytical solution in a finite domain with at x=0, c =C0 and at x =L, flux = 0.
Thank you.
The following "Classic" books can help you for sure:
1- As said above by Pascale: Conduction of heat in solids by Carslaw and Jaeger.
2- The mathematics of diffusion by John Crank.
3- Cannon JR (2008) The one-dimensional heat equation, encyclopedia of mathematics and its applications. Cambridge University Press, Cambridge.
4- van Genuchten MT, Alves WJ (1982), Analytical solutions of the one-dimensional convective–dispersive solute transport equation. U.S. Department of Agriculture, Technical, Bulletin No. 1661, p 151.
5- A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary/Partial/Nonlinear Differential Equations, 2nd Edition, Chapman & Hall/CRC Press, Boca Raton, 2003
(Last one is a series of books, not one single volume)
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