Bilayer one-dimensional Convection-Diffusion-Reaction-Source problem. Analytical and numerical solution

TL;DR

This paper provides an analytical and numerical study of a two-layer one-dimensional heat transfer problem involving diffusion, advection, internal heat sources, and interface resistance, enhancing understanding and design of multilayer systems.

Contribution

It introduces explicit analytical solutions and a convergent finite difference scheme for a complex two-layer heat transfer model with internal heat sources and interface resistance.

Findings

Analytical solutions align with previous results.

Numerical simulations confirm physical coherence.

The work advances theoretical understanding of multilayer heat transfer.

Abstract

This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due to external sources. Additionally, the thermal resistance at the interface between the materials is considered. The situation of interest is modeled mathematically, explicit analytical solutions are found using Fourier techniques, and a convergent finite difference scheme is formulated to simulate specific cases. The solution is consistent with previous results. A numerical example is included that shows coherence between the obtained results and the physics of the problem. The conclusions drawn in this work expand the theoretical understanding of two-layer heat transfer and may also contribute to improving the thermal design of multilayer engineering systems.