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A Fractional Single-Phase-Lag Model of Heat Conduction for Describing Propagation of the Maximum Temperature in a Finite Medium

Institute of Mathematics, Czestochowa University of Technology, 21 Armii Krajowej Ave., 42-201 Częstochowa, Poland
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Entropy 2018, 20(11), 876; https://doi.org/10.3390/e20110876
Received: 23 October 2018 / Revised: 9 November 2018 / Accepted: 10 November 2018 / Published: 15 November 2018
(This article belongs to the Section Thermodynamics)
In this paper, an investigation of the maximum temperature propagation in a finite medium is presented. The heat conduction in the medium was modelled by using a single-phase-lag equation with fractional Caputo derivatives. The formulation and solution of the problem concern the heat conduction in a slab, a hollow cylinder, and a hollow sphere, which are subjected to a heat source represented by the Robotnov function and a harmonically varying ambient temperature. The problem with time-dependent Robin and homogenous Neumann boundary conditions has been solved by using an eigenfunction expansion method and the Laplace transform technique. The solution of the heat conduction problem was used for determination of the maximum temperature trajectories. The trajectories and propagation speeds of the temperature maxima in the medium depend on the order of fractional derivatives occurring in the heat conduction model. These dependencies for the heat conduction in the hollow cylinder have been numerically investigated. View Full-Text
Keywords: fractional heat conduction; single-phase-lag model; propagation of the maximum temperature; Caputo derivative; Robotnov function fractional heat conduction; single-phase-lag model; propagation of the maximum temperature; Caputo derivative; Robotnov function
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MDPI and ACS Style

Kukla, S.; Siedlecka, U. A Fractional Single-Phase-Lag Model of Heat Conduction for Describing Propagation of the Maximum Temperature in a Finite Medium. Entropy 2018, 20, 876. https://doi.org/10.3390/e20110876

AMA Style

Kukla S, Siedlecka U. A Fractional Single-Phase-Lag Model of Heat Conduction for Describing Propagation of the Maximum Temperature in a Finite Medium. Entropy. 2018; 20(11):876. https://doi.org/10.3390/e20110876

Chicago/Turabian Style

Kukla, Stanisław, and Urszula Siedlecka. 2018. "A Fractional Single-Phase-Lag Model of Heat Conduction for Describing Propagation of the Maximum Temperature in a Finite Medium" Entropy 20, no. 11: 876. https://doi.org/10.3390/e20110876

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