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Research Papers: Conduction

Flux Limiters in Radial Heat Transport in Silicon Nanolayers

[+] Author and Article Information
A. Sellitto

Department of Mathematics, Computer Science
and Economics,
University of Basilicata,
Campus Macchia Romana,
Potenza 85100, Italy
e-mail: ant.sellitto@gmail.com

V. A. Cimmelli

Department of Mathematics, Computer Science
and Economics,
University of Basilicata,
Campus Macchia Romana,
Potenza 85100, Italy
e-mail: vito.cimmelli@unibas.it

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 14, 2013; final manuscript received March 8, 2014; published online April 10, 2014. Assoc. Editor: Robert D. Tzou.

J. Heat Transfer 136(7), 071301 (Apr 10, 2014) (6 pages) Paper No: HT-13-1351; doi: 10.1115/1.4027183 History: Received July 14, 2013; Revised March 08, 2014

By using the thermomass-theory approach, the temperature in a thin layer heated by a hot spot is derived in steady states. It is shown that an anomalous temperature profile, which seems to be at odds with the fundamental laws of continuum physics, may occur. The compatibility of this situation with second law of thermodynamics is analyzed in view of the concept of flux limiter.

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Figures

Grahic Jump Location
Fig. 1

Thin layer heated by a very small heat source which produces a hot circular zone. The hot spot is supplied with a constant amount of heat Q0 per unit time. The radius of the hot spot is r0 and its thickness is h. Abroad this zone, the local heat flux q propagates radially away from the source, as it is shown in the figure zoom.

Grahic Jump Location
Fig. 2

Temperature behavior as a function of the radial distance Δr = r − r0 from the hot spot in a silicon thin layer: theoretical prediction arising from Eq. (18). The hot-spot temperature is T0 = 300 K, the supplied heat per unit time is Q0 = 5 × 10–4 W, the height of the layer is h = 50 × 10–9 m, and the hot-spot radius is r0 = 50 × 10–9 m.

Grahic Jump Location
Fig. 3

Temperature behavior as a function of the radial distance Δr = r − r0 from the hot spot in a silicon thin layer: theoretical prediction arising from Eq. (18). The hot-spot temperature is T0 = 300 K, the supplied heat per unit time is Q0 = 5 × 10–5 W, the height of the layer is h = 50 × 10–9 m, and the hot-spot radius is r0 = 2 × 10–9 m.

Grahic Jump Location
Fig. 4

Local heat flux q = Γ/r and threshold heat flux qtr = 2γcv3T02r/(λρ), as a function of the radial distance Δr = r − r0 from the hot spot, in comparison. The layer is made of silicon. The hot spot temperature is T0 = 300 K, the supplied heat per unit time is Q0 = 5 × 10–5 W, the height of the layer is h = 50 × 10–9 m, and the hot-spot radius is r0 = 2 × 10–9 m.

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