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Modeling Heat Transfer in Heterogeneous Media Using Fractional Calculus

[+] Author Affiliations
Dominik Sierociuk, Andrzej Dzieliński, Grzegorz Sarwas

Warsaw University of Technology, Warsaw, Poland

Ivo Petras, Igor Podlubny, Tomas Skovranek

Technical University of Kosice, Kosice, Slovakia

Paper No. DETC2011-47374, pp. 143-147; 5 pages
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5480-8
  • Copyright © 2011 by ASME


The paper presents the results of modeling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in solid material (beam) can be described by integer order partial differential equation. However, in heterogeneous media it can be described by sub- or hyperdiffusion equation which results in fractional order partial differential equation. Taking into consideration that the part of the heat flux is dispersed into the neighbouring environment we additionally modify the main relation between heat flux and the temperature, and we obtain in this case the heat transfer equation in the new form. This leads to the transfer function which describes the dependency between the heat flux at the beginning of the beam and the temperature at the given distance. The article also presents the experimental results of modeling real plant in the frequency domain basing on the obtained transfer function.

Copyright © 2011 by ASME



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