Critical times in multilayer diffusion. Part 1: Exact solutions

While diffusion has been well studied, diffusion across multiple layers, each with different properties, has had less attention. This type of diffusion may arise in heat transport across composite materials or layered biological material. Usually of most interest is a critical time, such as the time for a material to heat up. Here an exact solution is found which is used to numerically demonstrate the critical time behaviour for transport across multiple layers with imperfect contact. This solution illustrates the limitations of traditional averaging methods, which are only good for a large number of layers.