0
Research Papers: Conduction

Thermal Resistance Approach: An Engineering Tool for Improvement of Conductive Constructal Configurations

[+] Author and Article Information
M. Eslami

School of Mechanical Engineering,
Shiraz University,
Shiraz 71936-16548, Iran
e-mail: meslami@shirazu.ac.ir

K. Jafarpur

School of Mechanical Engineering,
Shiraz University,
Shiraz 71936-16548, Iran

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 28, 2013; final manuscript received April 9, 2014; published online May 9, 2014. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 136(8), 081301 (May 09, 2014) (10 pages) Paper No: HT-13-1602; doi: 10.1115/1.4027459 History: Received November 28, 2013; Revised April 09, 2014

In the last decade, various conductive networks for cooling heat generating bodies have been proposed, analyzed, and optimized. Nevertheless, many of these studies have not been based on an analytical or mathematical formulation of the effective parameters. In this trend, a new geometry is assumed and analyzed (by analytical or numerical methods) hoping to decrease the total thermal resistance of the system. Therefore, the objective of the present paper is to illustrate how to analyze a conductive cooling network and improve it using the analytical procedures based on the general formulation of thermal resistance. As an example, the conventional rectangular elemental volumes with I shaped conductive link is modified to V shaped and pencil shaped designs and optimized analytically. Moreover, general expressions for optimum local thickness and thermal resistance of the links with variable cross section in an arbitrary network are provided. It is shown that improvements up to 50% can be achieved easily by simple geometrical changes if the designer is equipped with a profound knowledge of the important governing parameters.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Bejan, A., 1997, “Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume,” Int. J. Heat Mass Transfer, 40(4), pp. 799–816. [CrossRef]
Ghodoossi, L., and Egrican, N., 2003, “Exact Solution for Cooling of Electronics Using Constructal Theory,” J. Appl. Phys., 93, pp. 4922–4929. [CrossRef]
Gosselin, L., and Bejan, A., 2004, “Constructal Heat Trees at Micro Nano Scales,” J. Appl. Phys., 96, pp. 5852–5859. [CrossRef]
Ghodoosi, L., 2004, “Entropy Generation Rate in Uniform Heat Generating Area Cooled By Conductive Paths: Criterion for Rating the Performance of Constructal Designs,” Energy Convers. Manage., 45(18), pp. 2951–2969. [CrossRef]
Kuddusi, L., and Denton, J. C., 2007, “Analytical Solution for Heat Conduction Problem in Composite Slab and Its Implementation in Constructal Solution for Cooling of Electronics,” Energy Convers. Manage., 48(4), pp. 1089–1105. [CrossRef]
Wu, W., Chen, L., and Sun, F., 2007, “On the “Area to Point” Flow Problem Based on Constructal Theory,” Energy Convers. Manage., 48(1), pp. 101–105. [CrossRef]
Wu, W., Chen, L., and Sun, F., 2007, “Heat-Conduction Optimization Based on Constructal Theory,” Appl. Energy, 84(1), pp. 39–47. [CrossRef]
Zhou, Sh., Chen, L., and Sun, F., 2007, “Optimization of Constructal Volume-Point Conduction With Variable Cross Section Conducting Path,” Energy Convers. Manage., 48(1), pp. 106–111. [CrossRef]
Wei, Sh., Chen, Sh., and Sun, F., 2009, “The Area-Point Constructal Optimization for Discrete Variable Cross Section Conducting Path,” Appl. Energy, 86(7), pp. 1111–1118. [CrossRef]
Tescari, S., Mazet.N., and Neveu, P., 2011, “Constructal Theory Through Thermodynamics of Irreversible Processes Framework,” Energy Convers. Manage., 52(10), pp. 3176–3188. [CrossRef]
Ledezma, G. A., Bejan, A., and Errera, M. R., 1997, “Constructal Tree Networks for Heat Transfer,” J. Appl. Phys., 82(1), pp. 89–100. [CrossRef]
Neagu, M., and Bejan, A., 1999, “Constructal-Theory Networks of “Constant” Thermal Resistance,” J. Appl. Phys., 86(2), pp. 1136–1144. [CrossRef]
Neagu, M., and Bejan, A., 1999, “Three-Dimensional Tree Constructs of “Constant” Therm. Resistance,” J. Appl. Phys., 86(12), pp. 7107–7115. [CrossRef]
Almogbel, M., and Bejan, A., 1999, “Conduction Trees With Spacings at the Tips,” Int. J. Heat Mass Transfer, 42(20), pp. 3739–3756. [CrossRef]
Almogbel, M., and Bejan, A., 2001, “Constructal Optimization of Nonuniformly Distributed Tree-Shaped Flow Structures for Conduction,” Int. J. Heat Mass Transfer, 44(22), pp. 4185–4194. [CrossRef]
Rocha, L. A. O., Lorente, S., and Bejan, A., 2002, “Constructal Design for Cooling a Disk-Shaped Area by Conduction,” Int. J. Heat Mass Transfer, 45(8), pp. 1643–1652. [CrossRef]
Ghodoosi, L., and EgricanN., 2004, “Conductive Cooling of Triangular Shaped Electronics Using Constructal Theory,” Energy Convers. Manage., 45(6), pp. 811–828. [CrossRef]
Rocha, L. A. O., Lorente, S., and Bejan, A., 2006, “Constructal Tree Networks With Loops for Cooling a Heat Generating Volume,” Int. J. Heat Mass Transfer, 49(15), pp. 2626–2635. [CrossRef]
Xu, X., Liang, X., and Ren, J., 2007, “Optimization of Heat Conduction Using Combinatorial Optimization Algorithms,” Int. J. Heat Mass Transfer, 50(9), pp. 1675–1682. [CrossRef]
Mathieu-Potvin, F., and Gosselin, L., 2007, “Optimal Conduction Pathways for Cooling a Heat-Generating Body: A Comparison Exercise,” Int. J. Heat Mass Transfer, 50(15), pp. 2996–3006. [CrossRef]
Ding, X., and Yamazaki, K., 2007, “Constructal Design of Cooling Channel in Heat Transfer System by Utilizing Optimality of Branch Systems in Nature,” ASME J Heat Transfer, 129(3), pp. 245–255. [CrossRef]
Boichot, R., Luo, L., and Fan, Y., 2009, “Tree-Network Structure Generation for Heat Conduction by Cellular Automaton,” Energy Convers. Manage., 50(2), pp. 376–386. [CrossRef]
Bai, C., and Wang, L., 2010, “Constructal Allocation of Nanoparticles in Nanofluids,” ASME J. Heat Transfer, 132(5), p. 052404. [CrossRef]
Bai, C., and Wang, L., 2010, “Constructal Structure of Nanofluids,” J. Appl. Phys., 108(7), p. 074317. [CrossRef]
Fan, J., and Wang, L., 2010, “Constructal Design of Nanofluids,” Int. J. Heat Mass Transfer, 53(19), pp. 4238–4247. [CrossRef]
Xiao, Q., Chen, L., and Sun, F., 2011, “Constructal Optimization for ‘Disc-to-Point’ Heat Conduction Without the Premise of Optimized Last-Order Construct,” Int. J. Therm. Sci., 50(6), pp. 1031–1036. [CrossRef]
Marck, G., Harion, J. L., Nemer, M., Russeil, S., and Bougeard, D., 2011, “A New Perspective of Constructal Networks Cooling a Finite-Size Volume Generating Heat,” Energy Convers. Manage., 52(2), pp.1033–1046. [CrossRef]
Song, B., and Guo, Z., 2011, “Robustness in the Volume-to-Point Heat Conduction Optimization Problem,” Int. J. Heat Mass Transfer, 54(21), pp. 4531–4539. [CrossRef]
Lorenzini, G., Biserni, C., and Rocha, L. A. O., 2013, “Constructal Design of X-Shaped Conductive Pathways for Cooling A Heat-Generating Body,” Int. J. Heat Mass Transfer, 58(1), pp. 513–520. [CrossRef]
Lorenzini, G., Biserni, C., and Rocha, L. A. O., 2013, “Constructal Design of Non-Uniform X-Shaped Conductive Pathways for Cooling,” Int. J. Therm. Sci., 71, pp. 140–147. [CrossRef]
Hajmohammadi, M. R., Alizadeh Abianeh, V., Moezzinajafabadi, M., and Daneshi, M., 2013, “Fork-Shaped Highly Conductive Pathways for Maximum Cooling in a Heat Generating Piece,” Appl. Therm. Eng., 61(2), pp. 228–235. [CrossRef]
Chen, L., Feng, H., Xie, Z., and Sun, F., 2013, “Constructal Optimization for ‘Disc-Point’ Heat Conduction at Micro and Nanoscales,” Int. J. Heat Mass Transfer, 67, pp. 704–711. [CrossRef]
Hajmohammadi, M. R., Joneydi Shariatzadeh, O., Moulod, M., and Nourazar, S. S., 2014, “Phi and Psi Shaped Conductive Routes for Improved Cooling in a Heat Generating Piece,” Int. J. Therm. Sci., 77, pp. 66–74. [CrossRef]
Bisemi, C., Rocha, L. A. O., and Bejan, A., 2004, “Inverted Fins: Geometric Optimization of the Intrusion Into a Conducting Wall,” Int. J. Heat Mass Transfer, 47(12), pp. 2577–2586. [CrossRef]
Rocha, L., Lorenzini, E., and Bisemi, C., 2005, “Geometric Optimization of Shapes on the Basis of Bejan's Constructal Theory,” Int. Commun. Heat Mass Transfer, 32(10), pp. 1281–1288. [CrossRef]
Bisemi, C., 2007, “Constructal H-Shaped Cavities According to Bejan's Theory,” Int. J. Heat Mass Transfer, 50(11), pp. 2132–2138. [CrossRef]
Lorenzini, G., and Rocha, L., 2009, “Geometric Optimization of T-Y-Shaped Cavity According to Constructal Design,” Int. J. Heat Mass Transfer, 52(21), pp. 4683–4688. [CrossRef]
Xie, Z., Chen, L., and Sun, F., 2010, “Geometry Optimization of T-Shaped Cavities According to Constructal Theory,” Math. Comput. Med., 52(9), pp. 1538–1546. [CrossRef]
Lorenzini, G., Biserni, C., and Rocha, L. A. O., 2011, “Geometric Optimization of Isothermal Cavities According to Bejan's Theory,” Int. J. Heat Mass Transfer, 54(17), pp. 3868–3873. [CrossRef]
Lorenzini, G., Biserni, C., Isoldi, L. A., Dos Santos, E. D., and Rocha, L. A. O., 2011, “Constructal Design Applied to the Geometric Optimization of Y-Shaped Cavities Embedded in a Conducting Medium,” ASME J. Electron. Packag., 133(4), p. 041008. [CrossRef]
Lorenzini, G., Garcia, F. L., Dos Santos, E. D., and Bisemi, C., 2012, “Constructal Design Applied to the Optimization of Complex Geometries: T-Y-Shaped Cavities With Two Additional Lateral Intrusions Cooled by Convection,” Int. J. Heat Mass Transfer, 55(5), pp. 1505–1512. [CrossRef]
Hajmohammadi, M. R., Poozesh, S., Campo, A., and Nourazar, S. S., 2013, “Valuable Reconsideration in the Constructal Design of Cavities,” Energy Convers. Manag., 66, pp. 33–40. [CrossRef]
Eslami, M., and Jafarpur, K., 2012, “Thermal Resistance in Conductive Constructal Designs of Arbitrary Configuration: A New General Approach,” Energy Convers. Manage., 57, pp. 117–124. [CrossRef]
Eslami, M., and Jafarpur, K., 2012, “Optimal Distribution of Imperfection in Conductive Constructal Designs of Arbitrary Configurations,” J. Appl. Phys., 112(10), p. 104905. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

A rectangular element with V shaped conductive links

Grahic Jump Location
Fig. 1

An I shaped rectangular elemental volume

Grahic Jump Location
Fig. 3

A rectangular element with Y shaped conductive links

Grahic Jump Location
Fig. 9

A general arbitrary link with variable cross section

Grahic Jump Location
Fig. 7

A pencil shaped tree with x/L = 0.5 and two probable points with maximum temperature

Grahic Jump Location
Fig. 8

The optimum distribution of an infinite number of infinitesimal links

Grahic Jump Location
Fig. 4

A first order construct with V shaped elements

Grahic Jump Location
Fig. 5

A rectangular element with pencil shaped conductive links

Grahic Jump Location
Fig. 6

Equation (27) has a flat minimum near x/L≈0.8

Grahic Jump Location
Fig. 12

A pencil shaped network with variable cross section

Grahic Jump Location
Fig. 13

(a) The present pencil shaped design developed analytically; (b) optimization results of Xu et al. [19] for a fixed rectangle by simulated annealing algorithm

Grahic Jump Location
Fig. 10

A general network with links of variable and constant thickness

Grahic Jump Location
Fig. 11

A V shaped tree with optimum local thickness

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In