Diffusion into a hollow cylinder
Abstract
A completely general solution to the problem of diffusion into a hollow cylinder was obtained. When one of the dimensions of the cylinder, either length or radius, is large compared to the other, one of the two infinite series of this solution converges slowly and is not suitable for practical application. For these situations two alternate solutions, utilizing rapidly converging series, were obtained. Both the concentration distribution and the total uptake as functions of time are considered. A number of specializations are used to show that the solutions are reducible to the cases of a finite solid cylinder, an infinite solid cylinder, an infinite plate, and an infinite hollow cylinder. Finally, several examples are given to show the efficacy of these solutions.
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