Next Article in Journal
Symmetric Conformable Fractional Derivative of Complex Variables
Next Article in Special Issue
Percentile Study of χ Distribution. Application to Response Time Data
Previous Article in Journal
On a Fractional Operator Combining Proportional and Classical Differintegrals
Open AccessArticle

A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires

1
ERH-Illumnia, Centro de Iniciativas Empresariais, 32005 Ourense, Spain
2
Applied Physics Department, Escola de Enxeñaría Aeronáutica e do Espazo, Universidade de Vigo, 32004 Ourense, Spain
3
Applied Mathematics Department, Escola de Enxeñaría Aeronáutica e do Espazo, Universidade de Vigo, 32004 Ourense, Spain
4
Materials Engineering Applied Mechanics and Construction Department, Escola de Enxeñaría Aeronáutica e do Espazo, Universiade de Vigo, 32004 Ourense, Spain
5
Centro Universitario de la Defensa, 36920 Marín, Spain
6
Department of Naval and Industrial Engineering, Escola Politécnica Superior, Universidade da Coruña, 15403 Ferrol, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 362; https://doi.org/10.3390/math8030362
Received: 17 January 2020 / Revised: 27 February 2020 / Accepted: 2 March 2020 / Published: 6 March 2020
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. View Full-Text
Keywords: heat equation; mathematical modeling; cooling law; fractional derivatives heat equation; mathematical modeling; cooling law; fractional derivatives
Show Figures

Figure 1

MDPI and ACS Style

Balvís, E.; Paredes, A.; Area, I.; Bendaña, R.; Carpentier, A.V.; Michinel, H.; Zaragoza, S. A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires. Mathematics 2020, 8, 362. https://doi.org/10.3390/math8030362

AMA Style

Balvís E, Paredes A, Area I, Bendaña R, Carpentier AV, Michinel H, Zaragoza S. A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires. Mathematics. 2020; 8(3):362. https://doi.org/10.3390/math8030362

Chicago/Turabian Style

Balvís, Eduardo; Paredes, Angel; Area, Iván; Bendaña, Ricardo; Carpentier, Alicia V.; Michinel, Humberto; Zaragoza, Sonia. 2020. "A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires" Mathematics 8, no. 3: 362. https://doi.org/10.3390/math8030362

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop