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A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires

2020; Multidisciplinary Digital Publishing Institute; Volume: 8; Issue: 3 Linguagem: Inglês

10.3390/math8030362

2227-7390

Eduardo Balvís, Ángel Paredes, Iván Area, Ricardo Bendaña, Alicia V. Carpentier, Humberto Michinel, Sonia Zaragoza,

Heat Transfer and Optimization

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.