A fractional derivative modeling of heating and cooling of LED luminaires
UNIVERSAL IDENTIFIER: http://hdl.handle.net/11093/1772
EDITED VERSION: https://www.mdpi.com/2227-7390/8/3/362
DOCUMENT TYPE: article
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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