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A fractional derivative modeling of heating and cooling of LED luminaires

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A fractional derivative modeling of heating and cooling of LED luminaires

Balvís Outeiriño, Eduardo; Paredes Galán, Ángel; Area Carracedo, Iván Carlos; Bendaña Jácome, Ricardo Javier; Vázquez Carpentier, Alicia; Michinel Álvarez, Humberto Javier; Zaragoza, Sonia
 
DATE : 2020-03-06
UNIVERSAL IDENTIFIER : http://hdl.handle.net/11093/1772
UNESCO SUBJECT : 2209.08 Iluminación ; 3307 Tecnología Electrónica ; 12 Matemáticas
DOCUMENT TYPE : article

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.

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