Technical Briefs

Steady State Heat Transfer Within a Nanoscale Spatial Domain

[+] Author and Article Information
Kirill V. Poletkin, Vladimir Kulish1

 Division of Thermal and Fluids Engineering, School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798kpoletkin@ntu.edu.sg


Corresponding authors.

J. Heat Transfer 134(7), 074503 (May 22, 2012) (4 pages) doi:10.1115/1.4006160 History: Received July 03, 2011; Revised January 09, 2012; Published May 22, 2012; Online May 22, 2012

In this paper, we study the steady state heat transfer process within a spatial domain of the transporting medium whose length is of the same order as the distance traveled by thermal waves. In this study, the thermal conductivity is defined as a function of a spatial variable. This is achieved by analyzing an effective thermal diffusivity that is used to match the transient temperature behavior in the case of heat wave propagation by the result obtained from the Fourier theory. Then, combining the defined size-dependent thermal conductivity with Fourier’s law allows us to study the behavior of the heat flux at nanoscale and predict that a decrease of the size of the transporting medium leads to an increase of the heat transfer coefficient which reaches its finite maximal value, contrary to the infinite value predicted by the classical theory. The upper limit value of the heat transfer coefficient is proportional to the ratio of the bulk value of the thermal conductivity to the characteristic length of thermal waves in the transporting medium.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 2

(Solid line) The curve of the size-dependent thermal conductivity of Si thin film at 300 K is prediction from Eq. 13. The symbols are experimental results: the triangles, squares, and rhombus cited from Refs. [21], [22], and [23], respectively.

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Figure 3

Statement of the problem

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Figure 4

Dependence of the heat transfer coefficient on the logarithmic-scale spatial variable in dimensionless form

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Figure 1

Dependence of the thermal conductivity on the logarithmic-scale spatial variable in dimensionless form: ηmax  = 1.53 and k¯max=1.38



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