Heat Conduction with Krylov Subspace Method Using FEniCSx
The study of heat transfer deals with the determination of the rate of heat energy transfer from one system to another driven by a temperature gradient. It can be observed in many natural phenomena and is often the fundamental principle behind several engineering systems. Heat transfer analysis is n...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/15/21/8077 |
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| author | Varun Kumar K. Chandan K. V. Nagaraja M. V. Reddy |
| author_facet | Varun Kumar K. Chandan K. V. Nagaraja M. V. Reddy |
| author_sort | Varun Kumar |
| collection | DOAJ |
| description | The study of heat transfer deals with the determination of the rate of heat energy transfer from one system to another driven by a temperature gradient. It can be observed in many natural phenomena and is often the fundamental principle behind several engineering systems. Heat transfer analysis is necessary while designing any product. The most common numerical method used to analyze heat transfer is the finite element method. This paper uses the finite element method to demonstrate steady and transient heat conduction in a three-dimensional bracket. The goal here was to determine the temperature distribution and rate of heat flow in the solid. This is crucial in designing machine elements as they are subjected to various thermal loads during operation and also due to fluctuations in the surrounding environmental conditions. The temperature significantly affects stress, displacements, and volumetric strains. Thus, to analyze thermal stresses induced in a machine element, it is necessary to find the temperature field first. The thermal analysis was performed using the open-source package FEniCSx on Python. The program was run using a preconditioned Krylov subspace method for higher-order function spaces. The Krylov subspace solver drastically reduces computational time. The time taken for the execution of each order was recorded and presented. |
| first_indexed | 2024-03-09T19:06:15Z |
| format | Article |
| id | doaj.art-3b59b1486f844120baa05a99815a2200 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-09T19:06:15Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-3b59b1486f844120baa05a99815a22002023-11-24T04:31:29ZengMDPI AGEnergies1996-10732022-10-011521807710.3390/en15218077Heat Conduction with Krylov Subspace Method Using FEniCSxVarun Kumar0K. Chandan1K. V. Nagaraja2M. V. Reddy3Department of Mechanical Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bangalore 560035, IndiaDepartment of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bangalore 560035, IndiaDepartment of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bangalore 560035, IndiaNouveau Monde Graphite, Montreal, QC G2E 2G9, CanadaThe study of heat transfer deals with the determination of the rate of heat energy transfer from one system to another driven by a temperature gradient. It can be observed in many natural phenomena and is often the fundamental principle behind several engineering systems. Heat transfer analysis is necessary while designing any product. The most common numerical method used to analyze heat transfer is the finite element method. This paper uses the finite element method to demonstrate steady and transient heat conduction in a three-dimensional bracket. The goal here was to determine the temperature distribution and rate of heat flow in the solid. This is crucial in designing machine elements as they are subjected to various thermal loads during operation and also due to fluctuations in the surrounding environmental conditions. The temperature significantly affects stress, displacements, and volumetric strains. Thus, to analyze thermal stresses induced in a machine element, it is necessary to find the temperature field first. The thermal analysis was performed using the open-source package FEniCSx on Python. The program was run using a preconditioned Krylov subspace method for higher-order function spaces. The Krylov subspace solver drastically reduces computational time. The time taken for the execution of each order was recorded and presented.https://www.mdpi.com/1996-1073/15/21/8077heat conductionfinite element methodsteady state conductiontransient conductionFEniCSxhigher-order function space |
| spellingShingle | Varun Kumar K. Chandan K. V. Nagaraja M. V. Reddy Heat Conduction with Krylov Subspace Method Using FEniCSx Energies heat conduction finite element method steady state conduction transient conduction FEniCSx higher-order function space |
| title | Heat Conduction with Krylov Subspace Method Using FEniCSx |
| title_full | Heat Conduction with Krylov Subspace Method Using FEniCSx |
| title_fullStr | Heat Conduction with Krylov Subspace Method Using FEniCSx |
| title_full_unstemmed | Heat Conduction with Krylov Subspace Method Using FEniCSx |
| title_short | Heat Conduction with Krylov Subspace Method Using FEniCSx |
| title_sort | heat conduction with krylov subspace method using fenicsx |
| topic | heat conduction finite element method steady state conduction transient conduction FEniCSx higher-order function space |
| url | https://www.mdpi.com/1996-1073/15/21/8077 |
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