A unified theory of linear diffusion in multilayered materials

A unified theory of linear diffusion in an n layer finite region and in a two semiinfinite layer region is presented. Very general, possibly discontinuous, interface conditions are proposed for this model of composite material. Analytic solutions for both models are described. It is demonstrated that for particular parametric values, the interface conditions reduce to the well known conditions of perfect thermal contact and linear contact resistance. Likewise, the newly introduced conditions of double contact resistance are subsumed by the general model. The n layer finite region model is solved by reducing the problem to a non standard Sturm-Liouville problem with an appropriately defined inner product which defines the natural norm for this type of problem in laminated materials. The solution is compared to previously obtained solutions of the limiting cases. The uniqueness of the solution is assured through an application of the maximum principle. Two examples are examined. The solution to the problem for two semiinfinite layers is achieved through separation of the problem into two standard one semiinfinite layer problems through an appropriately defined mapping.