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Micro/Nanoscale Heat Transfer

A New Spectral-Finite Volume Approach in Non-Fourier Heat Conduction Problems With Periodic Surface Disturbances

[+] Author and Article Information
Masoud Kharati Koopaee, Amir Omidvar

Department of Mechanical and Aerospace Engineering,  Shiraz University of Technology, Shiraz 71557-13876, Irankharati@sutech.ac.ir

J. Heat Transfer 134(6), 062403 (May 08, 2012) (7 pages) doi:10.1115/1.4006036 History: Received May 08, 2011; Revised October 09, 2011; Published May 08, 2012; Online May 08, 2012

In this study, a simple spectral-finite volume approach for hyperbolic heat conduction problems under periodic surface temperature is presented. In this approach, by choosing only three frequencies from a continuum frequency spectrum of the periodic temperature field, the time dependent governing equation is transformed into the steady state one in the frequency domain. Then, using the finite volume technique, temperature field in the frequency domain for each wave number is obtained. Finally, by transforming back the result to the time domain, the temperature field in the time domain would be obtained. This new method has been validated against some published results and a good agreement has been found. Despite the simplicity of the present method, it is able to accurately predict the temperature distribution in the periodic steady state portion of non-Fourier heat conduction problems subjected to periodic surface temperature.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 8

Nondimensional temperature distribution in the slab at different sections and times. (a) y = 0.5 mm, (b) y = 0.75 mm. Exact solution [22] (solid lines), t = 0 (solid circle), t = T/4 (open circle), t = T/2 (solid square), t = 3 T/4 (open square).

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Figure 9

Contour of temperature distribution in the slab at different times (a) t = 0, (b) t = T/4, (c) t = T/2, (d) t = 3 T/4

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Figure 4

Nondimensional temperature versus nondimensional time for different values of beta. Numerical results of Ref. [35] (solid lines), present method (open circle).

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Figure 5

Six different sections used for numerical results presentation

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Figure 6

Comparison of numerical results using three grid densities and exact results for section y = 0.167 mm at different times

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Figure 7

Nondimensional temperature distribution in the slab at different sections and times. (a) x = 0.25 mm (b) x = 0.5 mm, (c) x = 0.75 mm. Exact solution [22] (solid lines), t = 0 (solid circle), t = T/4 (open circle), t = T/2 (solid square), t = 3 T/4 (open square).

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Figure 1

Cell (i,j) in a general curvilinear system

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Figure 2

Auxiliary control volume for approximating ∂ T⌢k∂ x and ∂ T⌢k∂ y on the upper side of cell (i,j)

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Figure 3

Model of fin used as first test case [35]

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