Theoretical analysis of a two-dimensional bilayer convection-diffusion-reaction-source problem

TL;DR

This paper provides a comprehensive theoretical analysis of heat transfer in a bilayer system with complex sources, incorporating diffusion, advection, and interfacial resistance, validated through analytical and numerical methods.

Contribution

It introduces an analytical solution and a stable finite difference method for modeling heat transfer in bilayer media with heat sources and interfacial resistance.

Findings

Analytical solutions match numerical simulations.

Interfacial resistance significantly affects temperature distribution.

Model captures complex heat transfer phenomena in layered systems.

Abstract

This work investigates the two-dimensional thermal behavior of a bilayer medium subject to both internal and external heat sources. The model incorporates diffusion, advection, and temperature-dependent volumetric heat generation or absorption in each layer, as well as general convective conditions on the external boundaries. The influence of interfacial thermal resistance between the two materials is also considered. An analytical solution is developed using Fourier-based techniques, and a stable and convergent finite difference method is proposed to analyze particular scenarios. The theoretical results are validated against known solutions and numerical simulations, demonstrating consistency with the expected physical behavior. The findings contribute to a deeper understanding of heat transfer phenomena in layered systems and offer potential insights for optimizing thermal performance in engineering applications involving composite materials.