Abstract
In this chapter, we will return to the local scale and present a fundamental approach for shape optimization. This numerical approach is based on the so-called cellular automaton (CA) algorithm, capable of treating a class of optimization problems that we encounter in heat and mass transfer. Two examples will be illustrated to demonstrate the procedure of CA approach: (1) how to organize a finite quantity of high conductivity material in order to efficiently drain heat from a heat generating surface to a sink and (2) how to optimize the shape of fluid path with a finite void volume that connects a source to one or several outlet ports, with the purpose of flow equidistribution and pressure drop minimization. The shape optimization by CA procedure generally leads to the creation of multi-scale arborescent geometries that commonly exist in nature, with consequently intensified heat and mass transfer.
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References
Bejan A (1997) Constructal-theory network of conducting paths for cooling a heat generating volume. Int J Heat Mass Transf 40:799–816
Bejan A, Tondeur D (1998) Equipartition, optimal allocation, and the constructal approach to predicting organization in nature. Rev Gen Therm 37:165–180
Boichot R, Deseure J (2008) Interconnect design optimization of sofc using a cellular automation and cfd tools. In: Fundamentals and developments of fuel cells (FDFC) conference, Nancy, France
Boichot R, Luo L (2010) A simple cellular automaton algorithm to optimize heat transfer in complex configurations. Int J Exergy 7:51–64
Boichot R, Luo L, Fan Y (2009) Tree-network structure generation for heat conduction by cellular automaton. Energy Convers Manage 50:376–386
Borrvall T, Petersson J (2003) Topology optimization of fluids in stokes flow. Int J Numer Methods Fluids 41:77–107
Chen L (2012) Progress in study on constructal theory and its applications. Sci China Ser E: Technol Sci 55:802–820
Chen S, Doolen G (1998) Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech 30:329–364
Cheng X, Li Z, Guo Z (2003) Constructs of highly effective heat transport paths by bionic optimization. Sci China Ser E: Technol Sci 46:296–302
Evgrafov A (2005a) The limits of porous materials in the topology optimization of stokes flows. Appl Math Optim 52:263–277
Evgrafov A (2005b) Topology optimization of slightly compressible fluids. Z Angew Math Mech 86:46–62
Evgrafov A, Pingen G, Maute K (2006) Topology optimization of fluid problems by the lattice Boltzmann method. Solid Mech Appl 137:559–568
Fan Z, Zhou X, Luo L, Yuan W (2008a) Experimental investigation of the flow distribution of a 2-dimensional constructal distributor. Exp Therm Fluid Sci 33:77–83
Fan Y, Boichot R, Goldin T, Luo L (2008b) Flow distribution property of the constructal distributor and heat transfer intensification in a mini heat exchanger. AIChE J 54:2796–2808
Gersborg-Hansen A, Sigmund O, Haber RB (2005) Topology optimization of channel flow problems. Struct Multidisc Optim 30:181–192
Ghodoossi L (2004) Conceptual study on constructal theory. Energy Convers Manage 45:1379–1395
Ghodoossi L, Egrican N (2004) Conductive cooling of triangular shaped electronics using constructal theory. Energy Convers Manage 45:811–828
Gosselin L, Tye-Gingras M, Mathieu-Potvin F (2009) Review of utilization of genetic algorithms in heat transfer problems. Int J Heat Mass Transf 52:2169–2188
Klimetzek FR, Paterson J, Moos O (2006) Autoduct: Topology optimization for fluid flow. In: Proceedings of Konferenz fur Angewandte Optimierung, Karlsruhe
Kuddusi L, Denton JC (2007) Analytical solution for heat conduction problem in composite slab and its implementation in constructal solution for cooling of electronics. Energy Convers Manage 48:1089–1105
Kuddusi L, Egrican N. (2008) A critical review of constructal theory. Energy Convers Manage 49:1283–1294
Lorenzini G, Oliveira Rocha LA (2006) Constructal design of y-shaped assembly of fins. Int J Heat Mass Transf 49:4552–4557
Luo L, Fan Y, Zhang W, Yuan X, Midoux N (2007) Integration of constructal distributors to a mini crossflow heat exchanger and their assembly configuration optimization. Chem Eng Sci 62:3605–3619
Mathieu-Potvin F, Gosselin L (2007) Optimal conduction pathways for cooling a heat-generating body: a comparison exercise. Int J Heat Mass Transf 50:2996–3006
Moos O, Klimetzek FR, Rossmann R (2004) Bionic optimization of air-guiding systems. In: Proceedings of SAE 2004 world congress and exhibition, Detroit, USA, pp 95–100
Pingen G, Evgrafov A, Maute K (2007) Topology optimization of flow domains using the lattice Boltzmann method. Struct Multi Optim 34:507–524
Rocha LAO, Lorente S, Bejan A (2002) Constructal design for cooling a disc-shaped area by conduction. Int J Heat Mass Transf 45:1643–1652
Wang L, Fan Y, Luo L (2010) Heuristic optimality criterion algorithm for shape design of fluid flow. J Comput Phys 229:8031–8044
Wei S, Chen L, Sun F (2009) The area-point constructal optimization for discrete variable cross-section conducting path. Appl Energy 86:1111–1118
Wu W, Chen L, Sun F (2007) On the “area to point” flow problem based on constructal theory. Energy Convers Manage 48:101–105
Xia Z, Cheng X, Li Z, Guo Z (2004) Bionic optimization of heat transport paths for heat conduction problems. J Enhanced Heat Transf 11:119–131
Xu X, Liang X, Ren J (2007) Optimization of heat conduction using combinatorial optimization algorithms. Int J Heat Mass Transf 50:1675–1682
Zhang Y, Liu S (2008) Design of conducting paths based on topology optimization. Heat Mass Transf 44:1217–1227
Zhou S, Chen L, Sun F (2007) Optimization of constructal volume-point conduction with variable cross section conducting path. Energy Convers Manage 48:106–111
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Boichot, R., Wang, L., Luo, L., Fan, Y. (2013). Cellular Automaton Methods for Heat and Mass Transfer Intensification. In: Luo, L. (eds) Heat and Mass Transfer Intensification and Shape Optimization. Springer, London. https://doi.org/10.1007/978-1-4471-4742-8_6
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DOI: https://doi.org/10.1007/978-1-4471-4742-8_6
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