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Article

A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires

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ERH-Illumnia, Centro de Iniciativas Empresariais, 32005 Ourense, Spain
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Applied Physics Department, Escola de Enxeñaría Aeronáutica e do Espazo, Universidade de Vigo, 32004 Ourense, Spain
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Applied Mathematics Department, Escola de Enxeñaría Aeronáutica e do Espazo, Universidade de Vigo, 32004 Ourense, Spain
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Materials Engineering Applied Mechanics and Construction Department, Escola de Enxeñaría Aeronáutica e do Espazo, Universiade de Vigo, 32004 Ourense, Spain
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Centro Universitario de la Defensa, 36920 Marín, Spain
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Department of Naval and Industrial Engineering, Escola Politécnica Superior, Universidade da Coruña, 15403 Ferrol, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 362; https://doi.org/10.3390/math8030362
Received: 17 January 2020 / Revised: 27 February 2020 / Accepted: 2 March 2020 / Published: 6 March 2020
In the context of energy efficient lighting, we present a mathematical study of the heating and cooling processes of a common type of luminaires, consisting of a single light-emitting diode source in thermal contact with an aluminum passive heat sink. First, we study stationary temperature distributions by addressing the appropriate system of partial differential equations with a commercial finite element solver. Then, we study the temporal evolution of the temperature of the chip and find that it is well approximated with a fractional derivative generalization of Newton’s cooling law. The mathematical results are compared and shown to largely agree with our laboratory measurements. View Full-Text
Keywords: heat equation; mathematical modeling; cooling law; fractional derivatives heat equation; mathematical modeling; cooling law; fractional derivatives
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MDPI and ACS Style

Balvís, E.; Paredes, A.; Area, I.; Bendaña, R.; Carpentier, A.V.; Michinel, H.; Zaragoza, S. A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires. Mathematics 2020, 8, 362. https://doi.org/10.3390/math8030362

AMA Style

Balvís E, Paredes A, Area I, Bendaña R, Carpentier AV, Michinel H, Zaragoza S. A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires. Mathematics. 2020; 8(3):362. https://doi.org/10.3390/math8030362

Chicago/Turabian Style

Balvís, Eduardo, Angel Paredes, Iván Area, Ricardo Bendaña, Alicia V. Carpentier, Humberto Michinel, and Sonia Zaragoza. 2020. "A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires" Mathematics 8, no. 3: 362. https://doi.org/10.3390/math8030362

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