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Heat Conduction with Krylov Subspace Method Using FEniCSx

Author

Listed:
  • Varun Kumar

    (Department of Mechanical Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bangalore 560035, India)

  • K. Chandan

    (Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bangalore 560035, India)

  • K. V. Nagaraja

    (Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bangalore 560035, India)

  • M. V. Reddy

    (Nouveau Monde Graphite, Montreal, QC G2E 2G9, Canada)

Abstract

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.

Suggested Citation

  • Varun Kumar & K. Chandan & K. V. Nagaraja & M. V. Reddy, 2022. "Heat Conduction with Krylov Subspace Method Using FEniCSx," Energies, MDPI, vol. 15(21), pages 1-16, October.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:21:p:8077-:d:958644
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    References listed on IDEAS

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    1. Magdalena Piasecka & Beata Maciejewska & Paweł Łabędzki, 2020. "Heat Transfer Coefficient Determination during FC-72 Flow in a Minichannel Heat Sink Using the Trefftz Functions and ADINA Software," Energies, MDPI, vol. 13(24), pages 1-25, December.
    2. Smitha, T.V. & Nagaraja, K.V., 2019. "An efficient automated higher-order finite element computation technique using parabolic arcs for planar and multiply-connected energy problems," Energy, Elsevier, vol. 183(C), pages 996-1011.
    3. Jun He & Ke Wang & Jiangang Li, 2021. "Numerical Analysis of the Convective Heat Transfer Coefficient Enhancement of a Pyro-Breaker Utilized in Superconducting Fusion Facilities," Energies, MDPI, vol. 14(22), pages 1-11, November.
    4. Prashant Singh, 2022. "Errors Incurred in Local Convective Heat Transfer Coefficients Obtained through Transient One-Dimensional Semi-Infinite Conduction Modeling: A Computational Heat Transfer Study," Energies, MDPI, vol. 15(19), pages 1-20, September.
    5. Libor Kudela & Radomír Chýlek & Jiří Pospíšil, 2020. "Efficient Integration of Machine Learning into District Heating Predictive Models," Energies, MDPI, vol. 13(23), pages 1-12, December.
    6. Anastasios Moumtzakis & Stamatis Zoras & Vasilis Evagelopoulos & Argyro Dimoudi, 2022. "Experimental Investigation of Thermal Bridges and Heat Transfer through Window Frame Elements at Achieving Energy Saving," Energies, MDPI, vol. 15(14), pages 1-14, July.
    7. Smitha, T.V. & Nagaraja, K.V., 2019. "Application of automated cubic-order mesh generation for efficient energy transfer using parabolic arcs for microwave problems," Energy, Elsevier, vol. 168(C), pages 1104-1118.
    8. Chao Gao & Yang Liu & Ruquan You & Haiwang Li, 2022. "Theoretical and Numerical Study on Thermal Insulation Performance of Thermal Barrier Coatings," Energies, MDPI, vol. 15(19), pages 1-14, September.
    9. Yi Luo & Liehui Zhang & Yin Feng & Yulong Zhao, 2020. "Three-Dimensional Streamline Tracing Method over Tetrahedral Domains," Energies, MDPI, vol. 13(22), pages 1-19, November.
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    Cited by:

    1. Issa Omle & Ali Habeeb Askar & Endre Kovács & Betti Bolló, 2023. "Comparison of the Performance of New and Traditional Numerical Methods for Long-Term Simulations of Heat Transfer in Walls with Thermal Bridges," Energies, MDPI, vol. 16(12), pages 1-27, June.

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