NATURE INSPIRED OPTIMAL DESIGN OF HEAT CONVEYING NETWORKS FOR ADVANCED FIBER-REINFORCED COMPOSITES

Year 2015, Volume: 1 Issue: 7 - SPECIAL ISSUE 2 Energy Systems and Developments 2015 ICESD 2015 INDIA, - , 01.07.2015

Natalya Kizilova

https://doi.org/10.18186/jte.30823

Abstract

A concept of composite materials reinforced by branching micro or nanotubes optimized for both heat transfer and strength of the material is presented. Numerous examples of reinforcement by branched fibers in cells, tissues and organs of plants and animals are studied. It is shown orientation of the fibers according to principals of the stress tensor at given external load is the main principle of optimal reinforcement in nature. The measurement data obtained on venations of the plant leaves revealed clear dependencies between the diameters, lengths and branching angles that correspond to delivery of the plant sap to live cells of the leaf with minimal energy expenses. The mathematical problem on geometry of asymmetrical loaded branched fibers experienced minimal maximal stress is solved. Heat propagation in the fibers is described by generalized Guyer-Krumhansl equation. It is shown the optimality for the heat propagation, fluid delivery and structural reinforcement are based on the same relations between the diameters, lengths and branching angles. The principle of optimal reinforcement is proposed for technical constructions, advanced composite materials and MEMS devices.

Keywords

Heat transfer, fiber reinforced composites, optimal design, nature inspired solutions, MEMS devices

References

• -
• Fung, Y.C., 1981. Biomechanics: Mechanical Properties
• of Living Tissues. NY: Springer-Verlag. 2.
• Kizilova, N.N. and Posdniak, L.O., 2005. Biophysical
• mechanisms of long-distance transport of liquids and
• signaling in high plants. Biophysical Bulletin, 15(1), p.99- 103. 3.
• Murray, C.D., 1926. The physiological principle of
• minimum work. I. The vascular system and the cost of
• blood volume. Proc. Nat. Acad. Sci. USA, 12, pp.207-214. 4.
• Murray, C.D., 1926. The physiological principle of
• minimum work applied to the angle of branching of
• arteries. J. Gen. Physiol., 9, pp. 835–841. 5.
• Rosen, R., 1967. Optimality Principles in Biology. NY: Plenum Press. 6.
• Weibel, E.R., 1963. Morphometry of the human lung. NY:Academic. 7.
• La Barbera, M., 1990. Principles of design of fluid
• transport systems in zoology. Science, 1000, pp. 249-252. 8.
• Kizilova, N. and Popova, N., 1999. Study on
• transportation systems of plant leaves. Probl. Bionics, 51, pp. 71-79. 9.
• McCulloh, K.A., Sperry, J.S. and Adler, F.R., 2003.
• Water transport in plants obeys Murray’s law, Nature, Vol. 421, pp.939-942.
• Kizilova, N., 2008. Common Constructal Principles in Design of Transportation Networks in Plants and Animals. In: A.Bejan, G.Grazzini, eds. Shape and Thermodynamics. Florence: Florence Univ. Press. pp. 1-12.
• Zaragoza, C., Márquez, S. and Saura, M., 2012. Endothelial mechanosensors of shear stress as regulators of atherogenesis. Curr Opin Lipidol., 23, pp. 446-52.
• Chernousko, F.L., 1977. Optimal structure of branching pipelines. Appl. Mathem. Mech, 41, pp.376-83.
• Kizilova, N., 2005. Hydraulic Properties of Branching Pipelines with Permeable Walls. Intern. J. Fluid Mech.Res., 32, pp.98-109.
• Kizilova, N., 2004. Computational approach to optimal transport network construction in biomechanics. Lecture Notes in Computer Sci., 3044, pp.476-85.
• Leelavanichkul, S. and Cherkaev, A., 2004. Why grain in tree’s trunks spiral: mechanical perspective. Struct. Multidisc. Optimiz., 28, pp.127–135.
• S.C. Cowin, ed., 1989. Bone Mechanics, Boca Raton; CRC Press.
• Kizilova, N., 2012. Mathematical modelling of biological growth and tissue engineering. In: R. Bedzinski, and M. Petrtyl, eds. Current trends in development of implantable tissue structures, Warsaw: IBB Press, pp.18- 27.
• Fukada, E. and Yasuda, I., 1957. On the piezoelectric effect in bone. J. Phys. Soc. Japan. 12, pp.1158-1162. and 19. Avdeev, Yu.A. Regirer, S.A., 1985. Electromechanical properties of bone tissue. In: Modern problems of biomechanics. Riga; Zinatne, 2, pp.101-131.
• Langer, K.. 1861. Zur Anatomie und Physiologie der Haut. Über die Spaltbarkeit der Cutis. Sitzungsbericht der Mathematisch-naturwissenschaftlichen Classe der Wiener Kaiserlichen Academie der Wissenschaften Abt., pp.44-54.
• Kramer, E.M., 2002. A mathematical model of pattern formation in the vascular cambium of trees. J. Theor. Biol. 216, pp. 147-159.
• Holzapfel, G.A., Gasser, Th.C. and Ogden, R.W., 2006. A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models. J. Elasticity, 61, pp. 1-48.
• Birk, D.E., Southern, J.F., Zycband, E.I., et al., 1989. Collagen fibril bundles: a branching assembly unit in tendon morphogenesis. Development, 107, pp.437-443.
• Brownfield, D.G., Venugopalan, G., Lo, A., et al., 2013. Patterned collagen fibers orient branching mammary epithelium through distinct signaling modules. Curr. Biol., 23, pp.703-709.
• Kizilova, N., 2011. Geometrical regularities and mechanical properties of branching actin structures. In: Nanobiophysics, Kharkov:IM Press, pp.141-146.
• Schwendener, S., 1874. Das mechanische Prinzip in anatomische Bau der Monokotylen mit verleichenden Ausblicken auf die übringen Pfanzenklassen, Leipzig.
• Schwendener, S., 1878. Die mechanische theorie der blattstellungen, Leipzig.
• Honda, H., 1978. Tree branch angle: maximizing effective leaf area, Science, 199, pp. 888-889.
• Niklas, K.J. and Spatz, H.-Ch., 2004. Growth and hydraulic (not mechanical) constraints govern the scaling of tree height and mass. Proc. Nat. Acad. USA., 101, pp. 15661–3.
• Yarin, A.L., Kataphinan, W. and Renekera, D.H., 2005. Branching in electrospinning of nanofibers. J. Appl. Phys. 98, p.064501.
• Gevorkyan, A., Shter, G.E., Shmueli, Y., et al., 2014. Branching effect and morphology control in electrospun PbZr0.52Ti0.48O3 nanofibers. J. Mater. Res., 29(16), pp. 1721-9.
• Aggarwal, D., Matthew, H.W.T., 2009. Branched chitosans II: Effects of branching on degradation, protein adsorption and cell growth properties. Acta Biomaterialia, 5, pp. 1575–81
• Boskovic, B.O., Stolojan, V., Zeze, D.A., et al., 2004. Branched carbon nanofiber network synthesis at room temperature using radio frequency supported microwave plasmas. J. Appl. Phys., 96(6), pp. 3443-6.
• Heyning, O.T., Bernier, P., Glerup, M., 2005. A low cost method for the direct synthesis of highly Y-branched nanotubes. Chemical Phys. Lett., 409, pp. 43–47.
• Alvarez, F.X., Jou, D. and Sellitto, A., 2009. Phonon hydrodynamics and phonon-boundary scattering in nanosystems. J.Appl.Phys., 105(1), p.014317.
• Zamir, M. and Medeiros, J.A., 1982. Arterial branching in man and monkey. J. Gen. Physiol., 79, pp.353–360.
• O’Reilly, O.M. and Tresierras, T.N., 2011. On the static equilibria of branched elastic rods. Intern. J. Engin. Sci., 49, pp. 212–27.
• Kizilova, N., 2004. Optimization of branching pipelines on basis of design principles in Nature. In: Proc. of the ECCM Congress on Computational Methods in Applied Sciences, Finland, 1, pp.237-48.
• Heyning, O.T., Bernier, P. and Glerup, M., 2005. A low cost method for the direct synthesis of highly Y-branched nanotubes. Chemical Phys. Lett., 409, pp. 43–47.
• Osvatha, Z., Koosa, A.A., Horvatha, Z.E., et al., 2003. STM observation of asymmetrical Y-branched carbon nanotubes and nano-knees produced by the arc discharge method. Materials Sci. Engin., 23, pp. 561–4.
• Mohapatra, S.K., Misra, M., Mahajan, V.K. and Raja, K.S., 2008. Synthesis of Y-branched TiO2 nanotubes. Materials Letters, 62, pp. 1772–4.
• Gothard, N., Daraio, C., Gaillard, J., et al., 2004. Controlled Growth of Y-Junction Nanotubes Using Ti- Doped Vapor Catalyst. Nano Letters, 4, pp. 213-7.