Bilayer one-dimensional Convection-Diffusion-Reaction-Source problem. Analytical and numerical solution
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909364534640640 |
|---|---|
| author | Umbricht, Guillermo Federico Rubio, Diana Tarzia, Domingo Alberto |
| author_facet | Umbricht, Guillermo Federico Rubio, Diana Tarzia, Domingo Alberto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19018 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bilayer one-dimensional Convection-Diffusion-Reaction-Source problem. Analytical and numerical solution Umbricht, Guillermo Federico Rubio, Diana Tarzia, Domingo Alberto Fluid Dynamics Mathematical Physics Analysis of PDEs 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. |
| title | Bilayer one-dimensional Convection-Diffusion-Reaction-Source problem. Analytical and numerical solution |
| topic | Fluid Dynamics Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2410.19018 |