Analytical and Numerical Study of a Convection-Diffusion-Reaction-Source Problem in Multilayered Materials

TL;DR

This paper provides an analytical and numerical analysis of heat transfer in multilayer materials, incorporating diffusion, advection, internal heat sources, and interface contact resistance, with solutions applicable to complex multilayer systems.

Contribution

It extends previous two-layer models to m-layer systems, offering explicit analytical solutions and a finite difference scheme for multilayer heat transfer analysis.

Findings

Analytical solutions match previous results for two-layer systems.

Numerical simulations confirm physical coherence of the model.

Generalization to multiple layers enhances understanding of multilayer heat transfer.

Abstract

In this work, a thermal energy transfer problem in a one-dimensional multilayer body is theoretically analyzed, considering diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, as well as heat generation due to external sources. Additionally, the thermal contact resistance at the interfaces between each pair of materials is taken into account. The problem is mathematically modeled, and explicit analytical solutions are derived using Fourier techniques. A convergent finite difference scheme is also formulated to simulate specific cases. The solution is consistent with previous results. A numerical example is provided, demonstrating the coherence between the obtained results and the physical behavior of the problem. This work was recently published for a two-layer body; the generalization to m-layer bodies allows for conclusions that enhance the theoretical understanding of heat transfer in multilayer materials and may contribute to improving the thermal design of multilayer engineering systems.