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Research Papers: Micro/Nanoscale Heat Transfer

Boundary Conditions and Evolution of Ballistic Heat Transport

[+] Author and Article Information
F. X. Alvarez1

Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia, Spainxavier.alvarez@uab.cat

D. Jou

Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia, Spain; Institut d’Estudis Catalans, Carme 47, 08001 Barcelona, Catalonia, Spaindavid.jou@uab.es

1

Corresponding author.

J. Heat Transfer 132(1), 012404 (Nov 04, 2009) (6 pages) doi:10.1115/1.3156785 History: Received November 07, 2008; Revised April 10, 2009; Published November 04, 2009; Online November 04, 2009

We analyze the effects of boundary conditions on the evolution of ballistic heat transport in four theoretical models and propose that a Fourier equation with an effective size-dependent thermal conductivity is a good candidate for the description of ballistic transport when boundary conditions are suitably imposed.

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Figures

Grahic Jump Location
Figure 1

1 Plots showing temperature profiles at different nondimensionalized times for different flow regimes depending on its Knudsen number. Profiles are obtained following Eq. 21 with boundary conditions 19,25 at the x=1 and x=0 ends, respectively, with T0i=1 and T1i=0. Thermal conductivity is given by Eq. 11.

Grahic Jump Location
Figure 2

Plots showing temperature profiles at different nondimensionalized times for different flow regimes depending on its Knudsen number for ballistic-diffusive equation. Profiles are obtained following Eq. 18 with boundary conditions 19 at the x=1 and x=0 ends with T0i=1 and T1i=0.

Grahic Jump Location
Figure 3

Plots showing temperature profiles at different nondimensionalized times for different flow regimes depending on its Knudsen number for EPRT equation. Profiles are obtained following Eq. 15 with boundary conditions 16,17 at the x=1 and x=0 ends with Th=1 and Tc=0.

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