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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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    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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