A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires

Eduardo Balvís, Angel Paredes, Iván Area, Ricardo Bendaña, Alicia V. Carpentier, Humberto Michinel and Sonia Zaragoza
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Eduardo Balvís: ERH-Illumnia, Centro de Iniciativas Empresariais, 32005 Ourense, Spain
Angel Paredes: Applied Physics Department, Escola de Enxeñaría Aeronáutica e do Espazo, Universidade de Vigo, 32004 Ourense, Spain
Iván Area: Applied Mathematics Department, Escola de Enxeñaría Aeronáutica e do Espazo, Universidade de Vigo, 32004 Ourense, Spain
Ricardo Bendaña: Materials Engineering Applied Mechanics and Construction Department, Escola de Enxeñaría Aeronáutica e do Espazo, Universiade de Vigo, 32004 Ourense, Spain
Alicia V. Carpentier: Centro Universitario de la Defensa, 36920 Marín, Spain
Humberto Michinel: Applied Physics Department, Escola de Enxeñaría Aeronáutica e do Espazo, Universidade de Vigo, 32004 Ourense, Spain
Sonia Zaragoza: Department of Naval and Industrial Engineering, Escola Politécnica Superior, Universidade da Coruña, 15403 Ferrol, Spain

Mathematics, 2020, vol. 8, issue 3, 1-8

Abstract: 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.

Keywords: heat equation; mathematical modeling; cooling law; fractional derivatives (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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