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.
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e-mail: kpoletkin@ntu.edu.sg
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Steady State Heat Transfer Within a Nanoscale Spatial Domain
Kirill V. Poletkin,
e-mail: kpoletkin@ntu.edu.sg
Kirill V. Poletkin
Division of Thermal and Fluids Engineering, School of Mechanical and Aerospace Engineering, Nanyang Technological University
, 50 Nanyang Avenue, Singapore 639798
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Vladimir Kulish
e-mail: MVVKulish@ntu.edu.sg
Vladimir Kulish
Mem. ASME
Division of Thermal and Fluids Engineering, School of Mechanical and Aerospace Engineering, Nanyang Technological University
, 50 Nanyang Avenue, Singapore 639798
Search for other works by this author on:
Kirill V. Poletkin
Division of Thermal and Fluids Engineering, School of Mechanical and Aerospace Engineering, Nanyang Technological University
, 50 Nanyang Avenue, Singapore 639798
e-mail: kpoletkin@ntu.edu.sg
Vladimir Kulish
Mem. ASME
Division of Thermal and Fluids Engineering, School of Mechanical and Aerospace Engineering, Nanyang Technological University
, 50 Nanyang Avenue, Singapore 639798
e-mail: MVVKulish@ntu.edu.sg
J. Heat Transfer. Jul 2012, 134(7): 074503 (4 pages)
Published Online: May 22, 2012
Article history
Received:
July 3, 2011
Revised:
January 9, 2012
Online:
May 22, 2012
Published:
May 22, 2012
Citation
Poletkin, K. V., and Kulish, V. (May 22, 2012). "Steady State Heat Transfer Within a Nanoscale Spatial Domain." ASME. J. Heat Transfer. July 2012; 134(7): 074503. https://doi.org/10.1115/1.4006160
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