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

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.

Figures (7)

• Figure 1: General scheme of the problem of interest.
• Figure 2: Scheme of intersection of the functions $q(x)$ and $r(x)$. On the left, for case \ref{['case1']}, and on the right, for case \ref{['case2']}.
• Figure 3: Heat source.
• Figure 4: Temperature difference between the layers (interface), $Pb-Material$ (left) and $Material-Fe$ (right) for different materials.
• Figure 5: Temperature for $t=10h$, $Pb-Material$ (left) and $Material-Fe$ (right).

Theorems & Definitions (1)

• Example 1