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TECHNICAL NOTES

Constructal Placement of High-Conductivity Inserts in a Slab: Optimal Design of “Roughness”

[+] Author and Article Information
M. Neagu, A. Bejan

Department of Mechanical Engineering and Materials Science, Box 90300, Duke University, Durham, NC 27708-0300

J. Heat Transfer 123(6), 1184-1189 (Feb 22, 2001) (6 pages) doi:10.1115/1.1392988 History: Received November 22, 1999; Revised February 22, 2001
Copyright © 2001 by ASME
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References

Bejan, A., 2000, Shape and Structure, from Engineering to Nature, Cambridge University Press, Cambridge, UK.
Bejan, A., 1997, Advanced Engineering Thermodynamics, 2nd ed. chap. 13, John Wiley and Sons, New York.
Bejan,  A., 1997, “Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume,” Int. J. Heat Mass Transf., 40, pp. 799–816.
Bar-Cohen,  A., and Rohsenow,  W. M., 1984, “Thermally Optimum Spacing of Vertical, Natural Convection Cooled, Parallel Plates,” ASME J. Heat Transfer, 106, pp. 116–123.
Peterson,  G. P., and Ortega,  A., 1990, “Thermal Control of Electronic Equipment and Devices,” Adv. Heat Transfer, 20, pp. 181–314.
Knight,  R. W., Goodling,  J. S., and Hall,  D. J., 1991, “Optimal Thermal Design of Forced Convection Heat Sinks—Analytical,” ASME J. Electron. Packag., 113, pp. 313–321.
Anand,  N. K., Kim,  S. H., and Fletcher,  L. S., 1992, “The Effect of Plate Spacing on Free Convection Between Heated Parallel Plates,” ASME J. Heat Transfer, 114, pp. 515–518.
Kakac, S., Yüncü, H., and Hijikata, K., eds., 1994, Cooling of Electronic Systems, Kluwer, Dordrecht, The Netherlands.
Ledezma,  G. A., Bejan,  A., and Errera,  M. R., 1997, “Constructal Tree Networks for Heat Transfer,” J. Appl. Phys., 82, pp. 89–100.
Pozrikidis,  C., 1993, “Unsteady Viscous Flow Over Irregular Boundaries,” J. Fluid Mech., 255, pp. 11–34.
Brady,  M., and Pozrikidis,  C., 1993, “Diffusive Transport Across Irregular and Fractal Walls,” Proc. R. Soc. London, Ser. A, 442, pp. 571–583.
Fyrillas,  M. M., and Pozrikidis,  C., 2001, “Conductive Heat Transport Across Rough Surfaces and Interfaces between Two Conforming Media,” Int. J. Heat Mass Transf., 44, 1789–1801.
FIDAP, Theory Manual, 1993, v. 7, Fluid Dynamics International, Evanston, IL.
Neagu, M., 1999, “Characteristics and Optimization of Composite Systems with Heat Conduction,” Ph.D. thesis, Duke University, Durham, NC.

Figures

Grahic Jump Location
Two-dimensional inserts of high conductivity for cooling a body heated from the side
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Constant-thickness plate inserts that penetrate partially the heated body, and the smallest dimensions cutoff: the minimized global resistance can be reduced by making the plate inserts sufficiently slender.
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Top: The smallest robustness ratio for plate inserts. Middle: The relative penetration length of plate inserts. Bottom: The relative spacing between plate inserts.
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Cylindrical model for the three-dimensional conduction around pin-shaped inserts of high thermal conductivity.
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Top: The smallest robustness ratio for pin inserts. Middle: The relative penetration length of pin inserts. Bottom: The minimized global thermal resistance of systems with optimized plates and pins inserts, using the same amounts and types of conducting materials (k̃,ϕ).
Grahic Jump Location
The minimized global thermal resistance of systems with optimized plates and pins inserts, using the same amounts and types of conducting materials (k̃,ϕ)

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