Multilayer diffusion in a composite medium with imperfect contact
  The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. We find a solution using the Unified Transform Method, due to Fokas and collaborators, applied to interface problems and compute solutions numerically. 
Natalie E. Sheils
math.NA math-ph math.MP