A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires
Eduardo Balvís,
Angel Paredes,
Iván Area,
Ricardo Bendaña,
Alicia V. Carpentier,
Humberto Michinel,
Sonia Zaragoza
Affiliations
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
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.
