Multilayer diffusion in a composite medium with imperfect contact
For researchers in heat transfer and applied mathematics, this offers a new analytical approach to a classical problem, but the method is incremental.
This work provides an explicit solution for heat conduction in one-dimensional composite materials with imperfect contact at interfaces, using the Unified Transform Method and numerical computation.
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.