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Multi-physics design of microvascular materials for active cooling applications. (English) Zbl 1225.82089

Microvascular polymeric materials are created by extruding a fugitive ink over a polymeric substrate with tip diameters ranging from a few microns to hundreds of microns. The microvascular materials can be used for active cooling applications. The optimization of the topology of the microvascular network for such applications encompasses a set of objectives that involve several physical phenomena. The energy that drives the flow through the network needs to be minimized in an optimal design. This paper summarizes the authors’ extension of the results presented in [A. M. Aragón, J. K. Wayer, P. H. Geubelle, D. E. Goldberg and S. R. White, Comput. Methods Appl. Mech. Eng. 197, No. 49–50, 4399–4410 (2008; Zbl 1194.74196)] to include the thermal response of the embedded network so that optimized 2D structures can be obtained in the context of active cooling applications. The temperature field can be determined by solving the corresponding partial differential equations in both fluid and solid domains using a multi-objective genetic algorithm. To reduce the computational cost of the conjugate problem some simplifying assumptions that take advantage of the laminar regime of the flow and the high aspect ratio of the microchannels are adopted by the authors.

MSC:

82D60 Statistical mechanics of polymers
82-08 Computational methods (statistical mechanics) (MSC2010)
58E17 Multiobjective variational problems, Pareto optimality, applications to economics, etc.
68T05 Learning and adaptive systems in artificial intelligence
90C29 Multi-objective and goal programming
65Y05 Parallel numerical computation
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Citations:

Zbl 1194.74196
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References:

[1] Hensel, H., Heat and cold, Annual Review of Physiology, 21, 1, 91-116 (1959)
[2] Morgareidge, K. R.; White, F. N., Cutaneous vascular changes during heating and cooling in the galapagos marine iguana, Nature, 223, 587-591 (1969)
[3] Seebacher, F.; Franklin, C. E., Integration of autonomic and local mechanisms in regulating cardiovascular responses to heating and cooling in a reptile (crocodylus porosus), Journal of Comparative Physiology B: Biochemical, Systemic, and Environmental Physiology, 174, 7, 577-585 (2004)
[4] Cooper, T.; Randall, W. C.; Hertzman, A. B., Vascular convection of heat from active muscle to overlying skin, Journal of Applied Physiology, 14, 2, 207-211 (1959), <http://jap.physiology.org/cgi/reprint/14/2/207.pdf>, <http://jap.physiology.org/cgi/content/abstract/14/2/207>
[5] Brengelmann, G., Specialized brain cooling in humans?, FASEB Journal, 7, 12, 1148-1152 (1993), <http://www.fasebj.org/cgi/reprint/7/12/1148.pdf>, <http://www.fasebj.org/cgi/content/abstract/7/12/1148>
[6] Bar-Cohen, Y., Biomimetics – using nature to inspire human innovation, Bioinspiration and Biomimetics, 1, 1, P1 (2006)
[7] Fratzl, P., Biomimetic materials research: what can we really learn from nature’s structural materials?, Journal of The Royal Society Interface, 4, 15, 637-642 (2007), <http://rsif.royalsocietypublishing.org/content/4/15/637.full.pdf+html>, doi:10.1098/rsif.2007.0218, <http://dx.doi.org/10.1098/rsif.2007.0218>
[8] Bhushan, B., Biomimetics: lessons from nature – an overview, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 367, 1893, 1445-1486 (2009), <http://rsta.royalsocietypublishing.org/content/367/1893/1445.full.pdf+html>, doi:10.1098/rsta.2009.0011, <http://dx.doi.org/10.1098/rsta.2009.0011>
[9] J.F.V. Vincent, Biomimetics – a review, in: Proceedings of the Institution of Mechanical Engineers, Part H, Journal of Engineering in Medicine 223.; J.F.V. Vincent, Biomimetics – a review, in: Proceedings of the Institution of Mechanical Engineers, Part H, Journal of Engineering in Medicine 223.
[10] Therriault, D.; White, S. R.; Lewis, J. A., Chaotic mixing in three-dimensional microvascular networks fabricated by direct-write assembly, Nature Materials, 2, 4, 265-271 (2003)
[11] Toohey, K. S.; Sottos, N. R.; Lewis, J. A.; Moore, J. S.; White, S. R., Self-healing materials with microvascular networks, Nature Materials, 6, 8, 581-585 (2007)
[12] B.D. Kozola, L.A. Shipton, V.K. Natrajan, K.T. Christensen, S.R. White, Characterization of active cooling and flow distribution in microvascular polymers, Journal of Intelligent Material Systems and Structures. <http://dx.doi.org/10.1177/1045389X10379662>; B.D. Kozola, L.A. Shipton, V.K. Natrajan, K.T. Christensen, S.R. White, Characterization of active cooling and flow distribution in microvascular polymers, Journal of Intelligent Material Systems and Structures. <http://dx.doi.org/10.1177/1045389X10379662>
[13] Tuckerman, D.; Pease, R., High-performance heat sinking for vlsi, Electron Device Letters, 2, 5, 126-129 (1981)
[14] Weisberg, A.; Bau, H. H.; Zemel, J., Analysis of microchannels for integrated cooling, International Journal of Heat and Mass Transfer, 35, 10, 2465-2474 (1992), doi:10.1016/0017-9310(92)90089-B, <http://dx.doi.org/10.1016/0017-9310(92)90089-B>
[15] Wei, X.; Joshi, Y.; Patterson, M. K., Experimental and numerical study of a stacked microchannel heat sink for liquid cooling of microelectronic devices, Journal of Heat Transfer, 129, 10, 1432-1444 (2007), doi:10.1115/1.2754781, <http://link.aip.org/link/?JHR/129/1432/1>
[16] Wu, P.; Little, W. A., Measurement of the heat transfer characteristics of gas flow in fine channel heat exchangers used for microminiature refrigerators, Cryogenics, 24, 8, 415-420 (1984), doi:10.1016/0011-2275(84)90015-8, <http://www.sciencedirect.com/science/article/B6TWR-48HY7GT-XY/2/2bcd94912b65a130c352fd0bdf205f9e>
[17] Bejan, A.; Lorente, S., Constructal theory of generation of configuration in nature and engineering, Journal of Applied Physics, 100, 4, 041301 (2006)
[18] Bejan, A.; Lorente, S.; Wang, K.-M., Networks of channels for self-healing composite materials, Journal of Applied Physics, 100, 3, 033528 (2006), doi:10.1063/1.2218768, <http://dx.doi.org/10.1063/1.2218768>
[19] Bejan, A.; Lorente, S., Design with Constructal Theory (2008), John Wiley & Sons Inc. · Zbl 1400.92334
[20] Lee, J.; Lorente, S.; Bejan, A., Transient cooling response of smart vascular materials for self-cooling, Journal of Applied Physics, 105, 6, 064904 (2009), doi:10.1063/1.3068323, <http://link.aip.org/link/?JAP/105/064904/1>
[21] Wang, K.-M.; Lorente, S.; Bejan, A., Vascular materials cooled with grids and radial channels, International Journal of Heat and Mass Transfer, 52, 5-6, 1230-1239 (2009), doi:10.1016/j.ijheatmasstransfer.2008.08.027, <http://dx.doi.org/10.1016/j.ijheatmasstransfer.2008.08.027> · Zbl 1157.80374
[22] Wang, K.-M.; Lorente, S.; Bejan, A., Vascular structures for volumetric cooling and mechanical strength, Journal of Applied Physics, 107, 4, 044901 (2010), doi:10.1063/1.3294697, <http://link.aip.org/link/?JAP/107/044901/1>
[23] T. Borrvall, A. Klarbring, J. Petersson, B. Torstenfelt, Topology optimization in fluid mechanics, in: Fifth World Congress on Computational Mechanics, Vienna, Austria, 2002.; T. Borrvall, A. Klarbring, J. Petersson, B. Torstenfelt, Topology optimization in fluid mechanics, in: Fifth World Congress on Computational Mechanics, Vienna, Austria, 2002.
[24] Borrvall, T.; Petersson, J., Topology optimization of fluids in stokes flow, International Journal for Numerical Methods in Fluids, 41, 1, 77-107 (2003), doi:10.1002/fld.426, <http://dx.doi.org/10.1002/fld.426> · Zbl 1025.76007
[25] Klarbring, A.; Petersson, J.; Torstenfelt, B.; Karlsson, M., Topology optimization of flow networks, Computer Methods in Applied Mechanics and Engineering, 192, 35-36, 3909-3932 (2003) · Zbl 1054.76028
[26] Goldberg, D. E., Genetic Algorithms in Search, Optimization, and Machine Learning (1989), Addison-Wesley Publishing Company: Addison-Wesley Publishing Company Massachusetts · Zbl 0721.68056
[27] Goldberg, D. E., The Design of Innovation: Lessons from and for Competent Genetic Algorithms (2002), Kluwer Academic Publishers: Kluwer Academic Publishers Massachusetts · Zbl 1047.68162
[28] Michalewicz, Z.; Dasgupta, D.; Riche, R. G.L.; Schoenauer, M., Evolutionary algorithms for constrained engineering problems, Computers and Industrial Engineering, 30, 4, 851-870 (1996)
[29] Zitzler, E.; Thiele, L., Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach, IEEE Transactions on Evolutionary Computation, 3, 4, 257-271 (1999)
[30] Sbalzarini, I.; Muller, S.; Koumoutsakos, P., Microchannel optimization using multiobjective evolution strategies;;, (Zitzler, E.; Thiele, L.; Deb, K.; Coello Coello, C.; Corne, D., Evolutionary Multi-Criterion Optimization of Lecture Notes in Computer Science, vol. 1993 (2001), Springer: Springer Berlin, Heidelberg), 516-530
[31] Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6, 2, 182-197 (2002)
[32] Aragón, A. M.; Wayer, J. K.; Geubelle, P. H.; Goldberg, D. E.; White, S. R., Design of microvascular flow networks using multi-objective genetic algorithms, Computer Methods in Applied Mechanics and Engineering, 197, 49-50, 4399-4410 (2008) · Zbl 1194.74196
[33] Therriault, D.; Shepherd, R.; White, S.; Lewis, J., Fugitive inks for direct-write assembly of three-dimensional microvascular networks, Advanced Materials, 17, 4, 395-399 (2005)
[34] Natrajan, V.; Christensen, K., Microscopic particle image velocimetry measurements of transition to turbulence in microscale capillaries, Experiments in Fluids, 43, 1, 1-16 (2007)
[35] Langhaar, H. L., Steady flow in the transition length of a straight tube, Journal of Applied Mechanics, 9, A55-A58 (1942)
[36] Brebbia, C. A.; Ferrante, A. J., Computational Hydraulics (1983), Butterworth Heinemann Ltd.: Butterworth Heinemann Ltd. London · Zbl 0502.65067
[37] Kays, W. M.; Crawford, M. E.; Weigand, B., Convective Heat and Mass Transfer (2004), McGraw-Hill
[38] Aragón, A. M.; Duarte, C. A.; Geubelle, P. H., Generalized finite element enrichment functions for discontinuous gradient fields, International Journal for Numerical Methods in Engineering, 82, 2, 242-268 (2010) · Zbl 1188.74051
[39] Belytschko, T.; Gracie, R.; Ventura, G., A review of extended/generalized finite element methods for material modeling, Modelling and Simulation in Materials Science and Engineering, 17, 4, 043001 (2009)
[40] Pareto, V., Manuale di Economia Politica (1906), Piccola Biblioteca Scientifica: Piccola Biblioteca Scientifica Milan, (Translated into English by Ann S. Schwier, Manual of Political Economy, MacMillan, London, 1971)
[41] Cantú-Paz, E.; Goldberg, D. E., Efficient parallel genetic algorithms: theory and practice, Computer Methods in Applied Mechanics and Engineering, 186, 2-4, 221-238 (2000) · Zbl 0978.90106
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