Heat conduction in fractal tree-like branched networks

International Journal of Heat and Mass Transfer

Volumn 49, Issue 19-20, 2006, Pages 3746-3751

  Xu, Peng ^a   Yu, Boming ^a   Yun, Meijuan ^a   Zou, Mingqing ^a  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Constructal; Effective thermal conductivity; Fractal tree like branched networks; Thermal electrical analogy

Indexed keywords

COMPUTATIONAL GEOMETRY; FRACTALS; LAMINAR FLOW; THERMAL CONDUCTIVITY; TREES (MATHEMATICS); TURBULENT FLOW;

CONSTRUCTAL; EFFECTIVE THERMAL CONDUCTIVITY; FRACTAL TREE-LIKE BRANCHED NETWORKS; THERMAL-ELECTRICAL ANALOGY;

HEAT CONDUCTION;

COMPUTATIONAL GEOMETRY; FRACTALS; HEAT CONDUCTION; LAMINAR FLOW; THERMAL CONDUCTIVITY; TREES (MATHEMATICS); TURBULENT FLOW;

EID: 33745348782     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2006.01.033     Document Type: Article

References (26)

1. Mauroy B., Filoche M., Andrade Jr. J.S., and Sapoval B. Interplay between geometry and flow distribution in an airway tree. Phys. Rev. Lett. 90 (2003) 148101
2. Majumdar A., Alencar A.M., Buldyrev S.V., Hantos Z., Stanley H.E., and Suki B. Characterization of the branching structure of the lung from "macroscopic" pressure-volume measurements. Phys. Rev. Lett. 87 (2001) 058102
3. Kitaoka H., Takaki R., and Suki B. A three-dimension model of the human airway tree. J. Appl. Physiol. 87 (1999) 2207-2217
4. Albert R., and Baraba'si A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74 (2002) 47-97
5. Dorogovtsev S.N., and Mendes J.F.F. Evolution of Networks: From Biological Nets to the Internet and the WWW (2003), Oxford University, Oxford
6. Amaral L.A.N., and Ottino J.M. Complex networks. Eur. Phys. J. B 38 (2004) 147-162
7. Song C.M., Havlin S., and Makse H.A. Self-similarity of complex networks. Nature 433 (2005) 392-395
8. B.B. Mandelbrot, The Fractal Geometry of Nature, New York, 1982.
9. West G.B., Brown J.H., and Enquist B.J. A general model for the origin of allometric scaling laws in biology. Science 276 (1997) 122-126
10. Brown J.H., West G.B., and Enquist B.J. Scaling in Biology (2000), Oxford University, UK
11. Chen Y.P., and Cheng P. Heat transfer and pressure drop in fractal tree-like microchannel nets. Int. J. Heat Mass Transfer 45 (2002) 2643-2648
12. Tondeur D., and Luo L. Design and scaling laws of ramified fluid distributors by the constructal approach. Chem. Eng. Sci. 59 (2004) 1799-1812
13. Bejan A. Shape and Structure, from Engineering to Nature (2000), Cambridge University, UK
14. Murray C.D. The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc. Natl. Acad. Sci. USA 12 (1926) 207-214
15. Bejan A. Constructal theory: from thermodynamic and geometric optimization to predicting shape in nature. Energy Convers. Manage. 39 (1998) 1705-1718
16. Bejan A. Constructal-theory network of conducting paths for cooling a heat generating volume. Int. J. Heat Mass Transfer 40 (1997) 799-816
17. Bejan A. The tree of convective heat streams: its thermal insulation function and the predicted 3/4-power relation between body heat loss and body size. Int. J. Heat Mass Transfer 44 (2001) 699-704
18. Kearney M.M. Engineered fractals enhance process applications. Chem. Eng. Prog. 96 (2000) 61-68
19. McCulloh K.A., Sperry J.S., and Adler F.R. Water transfer in plants obeys Murray's law. Nature 421 (2003) 939-942
20. Mauroy B., Filoche M., Weibel E.R., and Sapoval B. An optimal bronchial tree may be dangerous. Nature 427 (2004) 633-636
21. Reis A.H., Miguel A.F., and Aydin M. Constructal theory of flow architecture of the lungs. Med. Phys. 31 (2004) 1135-1140
22. Muralidhar K. Equivalent conductivity of a heterogeneous medium. Int. J. Heat Mass Transfer 33 (1990) 1759-1766
23. Hus C.T., Cheng P., and Wong K.W. A lumped-parameter model for stagnant thermal conductivity of spatially periodic porous media. J. Heat Transfer 117 (1995) 264-269
24. Yu B.M., and Cheng P. Fractal models for the effective thermal conductivity of bi-dispersed porous media. J. Thermophys. Heat Transfer 16 (2002) 22-29
25. Ma Y.T., Yu B.M., Zhang D.M., and Zou M.Q. Fractal geometry model for the effective thermal conductivity of three-phase porous media. J. Appl. Phys. 95 (2004) 6426-6434
26. Bejan A., Dincer I., Lorente S., Miguel A., and Reis A.H. Porous and Complex Flow Structures in Modern Technologies (2004), Springer, New York