Fractional Order Model of the Two Dimensional Heat Transfer Process

Krzysztof Oprzędkiewicz, Wojciech Mitkowski and Maciej Rosół
Additional contact information
Krzysztof Oprzędkiewicz: Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30 023 Krakow, Poland
Wojciech Mitkowski: Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30 023 Krakow, Poland
Maciej Rosół: Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30 023 Krakow, Poland

Energies, 2021, vol. 14, issue 19, 1-16

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.

Keywords: fractional order systems; two dimensional heat transfer; fractional order state equation; Caputo operator; thermal camera (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/1996-1073/14/19/6371/pdf (application/pdf)
https://www.mdpi.com/1996-1073/14/19/6371/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jeners:v:14:y:2021:i:19:p:6371-:d:650260

Access Statistics for this article

Energies is currently edited by Ms. Agatha Cao

More articles in Energies from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().