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A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires

Author

Listed:
  • 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)

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.

Suggested Citation

  • Eduardo Balvís & Angel Paredes & Iván Area & Ricardo Bendaña & Alicia V. Carpentier & Humberto Michinel & Sonia Zaragoza, 2020. "A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires," Mathematics, MDPI, vol. 8(3), pages 1-8, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:362-:d:329577
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    References listed on IDEAS

    as
    1. Jingguo Qu & Lingjian Kong & Jianfei Zhang, 2018. "Experimental Investigation on Flow and Heat Transfer Characteristics of a Needle-Cylinder Type Ionic Wind Generator for LED Cooling," Energies, MDPI, vol. 11(5), pages 1-15, May.
    2. Jang, Daeseok & Yook, Se-Jin & Lee, Kwan-Soo, 2014. "Optimum design of a radial heat sink with a fin-height profile for high-power LED lighting applications," Applied Energy, Elsevier, vol. 116(C), pages 260-268.
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