Diffusion in cylindrically layered materials using the thin-layer method

摘要

The thin-layer method (TLM) is a semi-analytical, numerical tool that has been successfully used in the past for wave motion in layered media. As demonstrated in this paper, it can be applied just as well to diffusive processes. The procedure is presented herein in the context of heat conduction in cylindrically laminated materials, but a similar formulation can be developed also for diffusion processes in bodies consisting of either plane or spherical layers. In essence, the method involves a discretization of the governing equations in the direction of layering together with analytical solutions for one of the remaining directions, or for the variation in time. To this effect, the discrete system of partial differential equations is transformed into the wavenumber- and frequency-domain, and solutions are obtained by a combination of analytical and numerical inverse transforms.