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Fractional Order Model of the Two Dimensional Heat Transfer Process

Author

Listed:
  • Krzysztof Oprzędkiewicz

    (Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30 023 Krakow, Poland
    These authors contributed equally to this work.)

  • Wojciech Mitkowski

    (Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30 023 Krakow, Poland
    These authors contributed equally to this work.)

  • Maciej Rosół

    (Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30 023 Krakow, Poland
    These authors contributed equally to this work.)

Abstract

In this paper, a new, state space, fractional order model of a heat transfer in two dimensional plate is addressed. The proposed model derives directly from a two dimensional heat transfer equation. It employes the Caputo operator to express the fractional order differences along time. The spectrum decomposition and stability of the model are analysed. The formulae of impluse and step responses of the model are proved. Theoretical results are verified using experimental data from thermal camera. Comparison model vs experiment shows that the proposed fractional model is more accurate in the sense of MSE cost function than integer order model.

Suggested Citation

  • Krzysztof Oprzędkiewicz & Wojciech Mitkowski & Maciej Rosół, 2021. "Fractional Order Model of the Two Dimensional Heat Transfer Process," Energies, MDPI, vol. 14(19), pages 1-16, October.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:19:p:6371-:d:650260
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    References listed on IDEAS

    as
    1. Raseelo J. Moitsheki & Atish Rowjee, 2011. "Steady Heat Transfer through a Two-Dimensional Rectangular Straight Fin," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-13, April.
    2. Sierociuk, Dominik & Skovranek, Tomas & Macias, Michal & Podlubny, Igor & Petras, Ivo & Dzielinski, Andrzej & Ziubinski, Pawel, 2015. "Diffusion process modeling by using fractional-order models," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 2-11.
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    Cited by:

    1. Krzysztof Oprzędkiewicz & Maciej Rosół & Wojciech Mitkowski, 2022. "Modeling of Thermal Traces Using Fractional Order, a Discrete, Memory-Efficient Model," Energies, MDPI, vol. 15(6), pages 1-13, March.

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