A Numerical Method for a Heat Conduction Model in a Double-Pane Window
In this article, we propose a one-dimensional heat conduction model for a double-pane window with a temperature-jump boundary condition and a thermal lagging interfacial effect condition between layers. We construct a second-order accurate finite difference scheme to solve the heat conduction proble...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-08-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/11/8/422 |
| _version_ | 1797439491099590656 |
|---|---|
| author | Aníbal Coronel Fernando Huancas Esperanza Lozada Alex Tello |
| author_facet | Aníbal Coronel Fernando Huancas Esperanza Lozada Alex Tello |
| author_sort | Aníbal Coronel |
| collection | DOAJ |
| description | In this article, we propose a one-dimensional heat conduction model for a double-pane window with a temperature-jump boundary condition and a thermal lagging interfacial effect condition between layers. We construct a second-order accurate finite difference scheme to solve the heat conduction problem. The designed scheme is mainly based on approximations satisfying the facts that all inner grid points has second-order temporal and spatial truncation errors, while at the boundary points and at inter-facial points has second-order temporal truncation error and first-order spatial truncation error, respectively. We prove that the finite difference scheme introduced is unconditionally stable, convergent, and has a rate of convergence two in space and time for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mo>∞</mo></msub></semantics></math></inline-formula>-norm. Moreover, we give a numerical example to confirm our theoretical results. |
| first_indexed | 2024-03-09T11:54:01Z |
| format | Article |
| id | doaj.art-a6bf40ebe1854e50a5c66ebbff148f59 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T11:54:01Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-a6bf40ebe1854e50a5c66ebbff148f592023-11-30T23:11:33ZengMDPI AGAxioms2075-16802022-08-0111842210.3390/axioms11080422A Numerical Method for a Heat Conduction Model in a Double-Pane WindowAníbal Coronel0Fernando Huancas1Esperanza Lozada2Alex Tello3Departamento de Ciencias Básicas—Centro de Ciencias Exactas CCE-UBB, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán 3780000, ChileDepartamento de Matemática, Facultad de Ciencias Naturales, Matemáticas y del Medio Ambiente, Universidad Tecnológica Metropolitana, Las Palmeras 3360, Ñuñoa-Santiago 7750000, ChileDepartamento de Ciencias Básicas—Centro de Ciencias Exactas CCE-UBB, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán 3780000, ChileDepartamento de Ciencias Básicas—Centro de Ciencias Exactas CCE-UBB, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán 3780000, ChileIn this article, we propose a one-dimensional heat conduction model for a double-pane window with a temperature-jump boundary condition and a thermal lagging interfacial effect condition between layers. We construct a second-order accurate finite difference scheme to solve the heat conduction problem. The designed scheme is mainly based on approximations satisfying the facts that all inner grid points has second-order temporal and spatial truncation errors, while at the boundary points and at inter-facial points has second-order temporal truncation error and first-order spatial truncation error, respectively. We prove that the finite difference scheme introduced is unconditionally stable, convergent, and has a rate of convergence two in space and time for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mo>∞</mo></msub></semantics></math></inline-formula>-norm. Moreover, we give a numerical example to confirm our theoretical results.https://www.mdpi.com/2075-1680/11/8/422heat conductiondouble-panefinite difference methodunconditional numerical method |
| spellingShingle | Aníbal Coronel Fernando Huancas Esperanza Lozada Alex Tello A Numerical Method for a Heat Conduction Model in a Double-Pane Window Axioms heat conduction double-pane finite difference method unconditional numerical method |
| title | A Numerical Method for a Heat Conduction Model in a Double-Pane Window |
| title_full | A Numerical Method for a Heat Conduction Model in a Double-Pane Window |
| title_fullStr | A Numerical Method for a Heat Conduction Model in a Double-Pane Window |
| title_full_unstemmed | A Numerical Method for a Heat Conduction Model in a Double-Pane Window |
| title_short | A Numerical Method for a Heat Conduction Model in a Double-Pane Window |
| title_sort | numerical method for a heat conduction model in a double pane window |
| topic | heat conduction double-pane finite difference method unconditional numerical method |
| url | https://www.mdpi.com/2075-1680/11/8/422 |
| work_keys_str_mv | AT anibalcoronel anumericalmethodforaheatconductionmodelinadoublepanewindow AT fernandohuancas anumericalmethodforaheatconductionmodelinadoublepanewindow AT esperanzalozada anumericalmethodforaheatconductionmodelinadoublepanewindow AT alextello anumericalmethodforaheatconductionmodelinadoublepanewindow AT anibalcoronel numericalmethodforaheatconductionmodelinadoublepanewindow AT fernandohuancas numericalmethodforaheatconductionmodelinadoublepanewindow AT esperanzalozada numericalmethodforaheatconductionmodelinadoublepanewindow AT alextello numericalmethodforaheatconductionmodelinadoublepanewindow |