IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v15y2022i21p8077-d958644.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/15/21/8077/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/15/21/8077/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Magdalena Piasecka & Kinga Strąk, 2021. "Characteristics of Refrigerant Boiling Heat Transfer in Rectangular Mini-Channels during Various Flow Orientations," Energies, MDPI, vol. 14(16), pages 1-30, August.
    2. Ren, Ting & Ma, Tianzeng & Liu, Sha & Li, Xin, 2022. "Bi-level optimization for the energy conversion efficiency improvement in a photocatalytic-hydrogen-production system," Energy, Elsevier, vol. 253(C).
    3. Piotr Duda, 2023. "Heat Transfer Coefficient Distribution—A Review of Calculation Methods," Energies, MDPI, vol. 16(9), pages 1-21, April.
    4. Tang, Bo & Zhang, Longbin & Liu, Siyu & Bai, Xiaochun & Chen, Guoqing & Shang, Zhiyu, 2024. "Calculation of noise field in main transformer room of indoor substation based on thermal-acoustic coupling," Energy, Elsevier, vol. 297(C).
    5. Boghetti, Roberto & Kämpf, Jérôme H., 2024. "Verification of an open-source Python library for the simulation of district heating networks with complex topologies," Energy, Elsevier, vol. 290(C).
    6. Magdalena Piasecka, 2023. "Heat and Mass Transfer Issues in Mini-Gaps," Energies, MDPI, vol. 16(16), pages 1-6, August.
    7. Magdalena Piasecka & Beata Maciejewska & Artur Piasecki, 2023. "Heat Transfer Calculations during Flow in Mini-Channels with Estimation of Temperature Uncertainty Measurements," Energies, MDPI, vol. 16(3), pages 1-19, January.
    8. Magdalena Piasecka & Sylwia Hożejowska & Anna Pawińska & Dariusz Strąk, 2022. "Heat Transfer Analysis of a Co-Current Heat Exchanger with Two Rectangular Mini-Channels," Energies, MDPI, vol. 15(4), pages 1-19, February.
    9. 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.
    10. Eloy Hontoria & Alejandro López-Belchí & Nolberto Munier & Francisco Vera-García, 2021. "A MCDM Methodology to Determine the Most Critical Variables in the Pressure Drop and Heat Transfer in Minichannels," Energies, MDPI, vol. 14(8), pages 1-13, April.
    11. Magdalena Piasecka & Sylwia Hożejowska & Beata Maciejewska & Anna Pawińska, 2021. "Time-Dependent Heat Transfer Calculations with Trefftz and Picard Methods for Flow Boiling in a Mini-Channel Heat Sink," Energies, MDPI, vol. 14(7), pages 1-24, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:15:y:2022:i:21:p:8077-:d:958644. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.