Time-Fractional Fourier Law in a finite hollow cylinder under Gaussian-distributed heat flux
Kielce University of Technology, Faculty of Mechatronics and Mechanical Engineering, Department of Mechanical Technology and Metrology, Aleja Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland
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Published online: 4 June 2018
This paper presents the solution of the theoretical model of heat conduction based on timefractional Fourier equation for a finite hollow cylinder treated with heat flux on one of the front surfaces. A derivative of fractional order in the Caputo sense was applied to record the temperature derivative in time. The distributions of temperature fields in the hollow cylinder were determined with the use of Fourier-Bessel series, as surface functions of two variables (r, θ) . The distributions of temperature fields were determined using analytical methods and applying integral transformation methods. The Laplace transform with reference to time, the Fourier finite cosine transform with reference to axial coordinate z and Marchi-Zgrablich transform for radial coordinate r. The fractional heat conduction equation was analysed for 0 < α ≤ 2
© The Authors, published by EDP Sciences, 2018
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