Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 371, Issue 1990, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsta.2012.0146
Keywords
heat transfer modelling; fractional calculus; partial differential equation
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Funding
- Polish Ministry of Science and Higher Education [4125/B/T02/2009/36]
- Slovak Research and Development Agency [SK-PL-0052-09, VEGA: 1/0729/12, 1/0497/11, 1/0746/11]
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This paper presents the results of modelling 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 a solid material (beam) can be described by an integer order partial differential equation. However, in heterogeneous media, it can be described by a sub- or hyperdiffusion equation which results in a fractional order partial differential equation. Taking into consideration that 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 a new form. This leads to the transfer function that describes the dependency between the heat flux at the beginning of the beam and the temperature at a given distance. This article also presents the experimental results of modelling real plant in the frequency domain based on the obtained transfer function.
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