Multilayer diffusion in a composite medium with imperfect contact

TL;DR

This paper provides an explicit solution for heat conduction in one-dimensional composite materials with imperfect contact, using the Unified Transform Method, and demonstrates numerical computation of the solutions.

Contribution

It introduces a novel application of the Unified Transform Method to solve heat conduction problems with unknown interface conditions in composite media.

Findings

Explicit solutions for heat conduction in composite media are derived.

Numerical solutions demonstrate the method's effectiveness.

The approach handles unknown interface conditions without prescribed temperature or flux.

Abstract

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.