A linearized approximation was developed for the stress-induced diffusion model which described H transport in planar and cylindrical membranes. The linearized version of the stress-induced diffusion model was suitable for closed-form solution, and yielded quantitative predictions of the short-term behavior of the permeation flux for both planar and cylindrical structures.

Stress-Induced Diffusion of Hydrogen in Metallic Membranes - Cylindrical versus Planar Formulation – II. A.Adrover, M.Giona, L.Capobianco, P.Tripodi, V.Violante: Journal of Alloys and Compounds, 2003, 358[1-2], 157-67