Optimum bifurcating-tube tree for gas transport

Journal of Fluids Engineering, Transactions of the ASME

Volumn 127, Issue 3, 2005, Pages 550-553

  Liu, Tianshu ^a  

^a Western Michigan University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENGINEERING ANALYSIS; GAS DIFFUSION; GAS TRANSPORT; STRUCTURE STABILITY;

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); CONCENTRATION (PROCESS); DIFFUSION; HEAT CONVECTION; MASS TRANSFER; OPTIMIZATION; PROBLEM SOLVING;

ENERGY TRANSFER;

EID: 22944433499     PISSN: 00982202     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1899168     Document Type: Article

References (18)

1. Weibel, E. R., and Gomez, D. M., 1962, "Architecture of the Human Lung," Science, 137, pp. 577-585.
2. Weibel, E. R., 1963, Morphometry of the Human Lung, Academic, New York.
3. Murray, C. D., 1926, "The Physiological Principle of Minimum Work," Proc. Natl. Acad. Sci. U.S.A., 12, pp. 207-214.
4. Horsfield, K., and Cumming, G., 1967, "Angles of Branching and Diameters of Branches in the Human Bronchial Tree," Bull, Math. Biophys., 29, pp. 245-259.
5. Horsfield, K., Dart, G., Olson, D. E., Filley, G. F., and Cumming, G., 1971, "Models of the Human Bronchial Tree," J. Appl. Physiol., 31, pp. 201-217.
6. Horsfield, K., 1990, "Diameters, Generations, and Orders of Branches in the Bronchial Tree," J. Appl. Physiol., 68, pp. 457-461.
7. Wilson, T. A., 1967, "Design of the Bronchial Tree," Nature (London), 18, pp. 668-669.
8. West, B. J., Bhargava, V., and Goldberger, A. L., 1986, "Beyond the Principle of Similitude: Renormalization in the Bronchial Tree," J. Appl. Physiol., 60, pp. 1089-1097.
9. West, B. J., and Goldberger, A. L., 1987, "Physiology in Fractal Dimensions," Am. Sci., 75, pp. 354-365.
10. Rashevsky, N., 1960, "Mathematical Biophysics - Physico-mathematical Foundation of Biology," Dover, New York, Vol. 2, Chap. XXVI.
11. LaBarbera, M., 1990, "Principles of Design of Fluid Transport Systems in Zoology," Science, 249, pp. 992-1000.
12. LaBarbera, M., 1993, "Optimality in Biological Fluid Transport Systems," In Fluid Dynamics in Biology, Contemporary Mathematics, A. Y. Cheer and C. P. van Dam, eds., American Mathematical Society, Providence, RI, Vol. 141, pp. 565-586.
13. Mandelbrot, B. B., 1982, The Fractal Geometry of Nature, Freeman, New York, Chaps. 12 and 17.
14. McMahon, T., 1973, "Size and Shape in Biology," Science 179, pp. 1201-1204.
15. Timoshenko, S., and Goodier, N., 1951, "Theory of Elasticity (2nd ed.)," McGraw-Hill, New York.
16. Zamir, M., 1976, "Optimality Principles in Arterial Branching," J. Theor. Biol., 62, pp. 227-251.
17. Uylings, H. B. M., 1977, "Optimization of Diameters and Bifurcation Angles in Lung and Vascular Tree Structures," Bull. Math. Biol., 39, pp. 509-520.
18. Roy, A. G., and Woldenberg, M. J., 1982, "A Generalization of the Optimal Models of Arterial Branching," Bull. Math. Biol., 44, pp. 349-360.