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Entropy 2018, 20(9), 685; https://doi.org/10.3390/e20090685

Constructal Optimization for Cooling a Non-Uniform Heat Generating Radial-Pattern Disc by Conduction

1,2,3
,
1,2,3
,
1,2,3,* and 1,2,3
1
Institute of Thermal Science and Power Engineering, Naval University of Engineering, Wuhan 430033, China
2
Military Key Laboratory for Naval Ship Power Engineering, Naval University of Engineering, Wuhan 430033, China
3
College of Power Engineering, Naval University of Engineering, Wuhan 430033, China
*
Author to whom correspondence should be addressed.
Received: 4 August 2018 / Revised: 29 August 2018 / Accepted: 5 September 2018 / Published: 7 September 2018
(This article belongs to the Section Thermodynamics)
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Abstract

A heat conduction model in a radial-pattern disc by considering non-uniform heat generation (NUHG) is established in this paper. A series of high conductivity channels (HCCs) are attached on the rim of the disc and extended to its center. Constructal optimizations of the discs with constant and variable cross-sectional HCCs are carried out, respectively, and their maximum temperature differences (MTDs) are minimized based on analytical method and finite element method. Besides, the influences of the NUHG coefficient, HCC number and width coefficient on the optimal results are studied. The results indicate that the deviation of the optimal constructs obtained from the analytical method and finite element method are comparatively slight. When the NUHG coefficient is equal to 10, the minimum MTD of the disc with 25 constant cross-sectional HCCs is specifically reduced by 48.8% compared to that with 10 HCCs. As a result, the heat conduction performance (HCP) of the disc can be efficiently improved by properly increasing the number of HCCs. The minimum MTD of the disc with variable cross-sectional HCC is decreased by 15.0% when the width coefficient is changed from 1 to 4. Therefore, the geometry of variable cross-sectional HCC can be applied in the constructal design of the disc to a better heat transfer performance. The constructal results obtained by investigating the non-uniform heat generating case in this paper can contribute to the design of practical electronic device to a better heat transfer performance. View Full-Text
Keywords: constructal theory; radial-pattern disc; non-uniform heat generation; minimum maximum temperature difference; variable cross-section; generalized thermodynamic optimization constructal theory; radial-pattern disc; non-uniform heat generation; minimum maximum temperature difference; variable cross-section; generalized thermodynamic optimization
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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You, J.; Feng, H.; Chen, L.; Xie, Z. Constructal Optimization for Cooling a Non-Uniform Heat Generating Radial-Pattern Disc by Conduction. Entropy 2018, 20, 685.

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