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Constructal Design Associated with Genetic Algorithm to Maximize the Performance of H-Shaped Isothermal Cavities

  • Emanuel da Silva Dias Estrada
  • Elizaldo Domingues dos Santos
  • Liércio André Isoldi
  • Luiz Alberto Oliveira Rocha
Chapter

Abstract

The constructal design method associated with the genetic algorithm is used to optimize the geometry of a H-shaped cavity that intrudes into a solid conducting wall. The objective is to minimize the maximum excess temperature between the solid and the cavity. Internal heat generation is distributed uniformly throughout the solid wall. The cavity surface is isothermal, while the solid wall has adiabatic conditions on the outer surface. There are six degrees of freedom which are free to vary. The H-cavity is optimized completely, i.e. it is optimized with respect to all its degrees of freedom. The ratio between the volume of the H-shaped cavity and the total volume (ϕ) is a problem constraint, which is evaluated here. Numerical results show that the optimal H-shaped configuration is the one that distributes better the hot spots in agreement with the optimal imperfections principle. The H-shaped cavity has its worst performance when the ratio between its height and length is set equal to two. The performance improves as this ratio is larger or smaller than two. An important finding is that the dimensionless maximum excess temperature calculated for the best H-shaped cavity with ratio between the height and the length of the cavity equal to 0.1 is approximately only 30% of the maximum excess temperature calculated for the elemental C-shaped cavity under the same thermal conditions.

Notes

Acknowledgements

Professors Elizaldo D. dos Santos, Liércio A. Isoldi and Luiz A.O. Rocha acknowledge the sponsorship from CNPq—Conselho Nacional de Desenvolvimento Científico e Tecnológico. Professor Emanuel S. D. Estrada acknowledges the financial support from CAPES—Coordenação de Aperfeiçoamento de Pessoal de Nível Superior.

References

  1. 1.
    Bejan, A.: Shape and Structure, from Engineering to Nature. Cambridge University Press, New York (2000)zbMATHGoogle Scholar
  2. 2.
    Bejan, A.: The Physics of Life: The Evolution of Everything. St. Martins Press, New York City (2016)Google Scholar
  3. 3.
    Bejan, A., Almogbel, M.: Constructal T-shaped fins. Int. J. Heat Mass Transf. 43(12), 2101–2115 (2000). http://dx.doi.org/10.1016/S0017-9310(99)00283-5 CrossRefGoogle Scholar
  4. 4.
    Bejan, A., Lorente, S.: Design with Constructal Theory. Wiley, Hoboken (2008)CrossRefGoogle Scholar
  5. 5.
    Bejan, A., Zane, J.P.: Design in Nature: How the Constructal Law Governs Evolution in Biology, Physics, Technology, and Social Organization, 1st edn. Doubleday, New York (2012)Google Scholar
  6. 6.
    Bello-Ochende, T., Meyer, J., Bejan, A.: Constructal multi-scale pin–fins. Int. J. Heat Mass Transf. 53(13–14), 2773–2779 (2010). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.02.021 CrossRefGoogle Scholar
  7. 7.
    Biserni, C., Rocha, L.A.O., Bejan, A.: Inverted fins: geometric optimization of the intrusion into a conducting wall. Int. J. Heat Mass Transf. 47(12–13), 2577–2586 (2004). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2003.12.018 CrossRefGoogle Scholar
  8. 8.
    Biserni, C., Rocha, L.A.O., Stanescu, G., Lorenzini, E.: Constructal H-shaped cavities according to Bejan’s theory. Int. J. Heat Mass Transf. 50(11–12), 2132–2138 (2007). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2006.11.006 CrossRefGoogle Scholar
  9. 9.
    COMSOL multiphysics: COMSOL multiphysics reference manual (2014). www.comsol.com
  10. 10.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning, 1st edn. Addison-Wesley Longman Publishing Co., Inc., Boston (1989)zbMATHGoogle Scholar
  11. 11.
    Gonzales, G., Estrada, E.S.D., Emmendorfer, L., Isoldi, L., Xie, G., Rocha, L., Santos, E. D.: A comparison of simulated annealing schedules for constructal design of complex cavities intruded into conductive walls with internal heat generation. Energy 93, 372–382 (2015). http://dx.doi.org/10.1016/j.energy.2015.09.058 CrossRefGoogle Scholar
  12. 12.
    Hajmohammadi, M.R., Poozesh, S., Nourazar, S.S.: Constructal design of multiple heat sources in a square-shaped fin. Proc. Inst. Mech. Eng. E: J. Process Mech. Eng. 226, 324–336 (2012). http://dx.doi.org/10.1177/0954408912447720 CrossRefGoogle Scholar
  13. 13.
    Hajmohammadi, M.R., Poozesh, S., Campo, A., Nourazar, S.S.: Valuable reconsideration in the constructal design of cavities. Energy Convers. Manag. 66, 33–40 (2013). http://dx.doi.org/10.1016/j.enconman.2012.09.031 CrossRefGoogle Scholar
  14. 14.
    Haupt, R.L.: Practical Genetic Algorithms, 2nd edn. Wiley, Hoboken (2004)zbMATHGoogle Scholar
  15. 15.
    Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. University of Michigan Press, Ann Arbor (1975)zbMATHGoogle Scholar
  16. 16.
    Jong, K.A.D., Spears, W.M.: An analysis of the interacting roles of population size and crossover in genetic algorithms. In: Schwefel, H.P., Männer, R. (eds.) Parallel Problem Solving from Nature, pp. 38–47. Springer, Berlin (1991)CrossRefGoogle Scholar
  17. 17.
    Kraus, A.D.: Developments in the analysis of finned arrays. Int. J. Transp. Phenom. 1, 141–164 (1999)Google Scholar
  18. 18.
    Kundu, B., Bhanja, D.: Performance and optimization analysis of a constructal T-shaped fin subject to variable thermal conductivity and convective heat transfer coefficient. Int. J. Heat Mass Transf. 53(1–3), 254–267 (2010). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2009.09.034 CrossRefGoogle Scholar
  19. 19.
    Lorenzini, G., Rocha, L.A.O.: Constructal design of Y-shaped assembly of fins. Int. J. Heat Mass Transf. 49(23–24), 4552–4557 (2006). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2006.05.019 CrossRefGoogle Scholar
  20. 20.
    Lorenzini, G., Rocha, L.A.O.: Constructal design of T-Y assembly of fins for an optimized heat removal. Int. J. Heat Mass Transf. 52(5–6), 1458–1463 (2009). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2008.09.007 CrossRefGoogle Scholar
  21. 21.
    Lorenzini, G., Rocha, L.A.O.: Geometric optimization of T-Y-shaped cavity according to constructal design. Int. J. Heat Mass Transf. 52(21–22), 4683–4688 (2009). http://dx.doi.org10.1016/j.ijheatmasstransfer.2009.06.020 CrossRefGoogle Scholar
  22. 22.
    Lorenzini, G., Biserni, C., Isoldi, L.A., Santos, E.D., Rocha, L.A.O.: Constructal design applied to the geometric optimization of Y-shaped cavities embedded in a conducting medium. J. Electron. Packag. 133(4), 41008–41015 (2011). http://dx.doi.org/10.1115/1.4005296 CrossRefGoogle Scholar
  23. 23.
    Lorenzini, G., Corrêa, R.L., Santos, E.D., Rocha, L.A.O.: Constructal design of complex assembly of fins. J. Heat Transf. 133(8), 81902–81908 (2011). http://dx.doi.org/10.1115/1.4003710 CrossRefGoogle Scholar
  24. 24.
    Lorenzini, G., Rocha, L.A.O., Biserni, C., Santos, E.D., Isoldi, L.: Constructal design of cavities inserted into a cylindrical solid body. J. Heat Transf. 134(7), 71301–71306 (2012). http://dx.doi.org/10.1115/1.4006103 CrossRefGoogle Scholar
  25. 25.
    Lorenzini, G., Biserni, C., Garcia, F., Rocha, L.: Geometric optimization of a convective t-shaped cavity on the basis of constructal theory. Int. J. Heat Mass Transf. 55(23–24), 6951–6958 (2012). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.07.009 CrossRefGoogle Scholar
  26. 26.
    Lorenzini, G., Garcia, F.L., Santos, E.D., Biserni, C., Rocha, L.A.O.: Constructal design applied to the optimization of complex geometries: T-Y-shaped cavities with two additional lateral intrusions cooled by convection. Int. J. Heat Mass Transf. 55(5–6), 1505–1512 (2012). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.10.057 CrossRefGoogle Scholar
  27. 27.
    Lorenzini, G., Biserni, C., Link, F., Santos, D., Isoldi, L., Rocha, L.A.O.: Constructal design of isothermal X-shaped cavities. Therm. Sci. 18(2), 349–356 (2014). http://dx.doi.org/10.2298/TSCI120804005L CrossRefGoogle Scholar
  28. 28.
    Lorenzini, G., Biserni, C., Rocha, L.: Geometric optimization of X-shaped cavities and pathways according to Bejan’s theory: comparative analysis. Int. J. Heat Mass Transf. 73, 1–8 (2014). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.01.055 CrossRefGoogle Scholar
  29. 29.
    Lorenzini, G., Biserni, C., Estrada, E.S.D., Santos, E.D., Isoldi, L.A., Rocha, L.A.O.: Genetic algorithm applied to geometric optimization of isothermal Y-shaped cavities. J. Electron. Packag. 136(3), 31011–31019 (2014). http://dx.doi.org/10.1115/1.4027421 CrossRefGoogle Scholar
  30. 30.
    Lorenzini, G., Biserni, C., Correa, R.L., Santos, E.D., Isoldi, L.A., Rocha, L.A.O.: Constructal design of T-shaped assemblies of fins cooling a cylindrical solid body. Int. J. Therm. Sci. 83, 96–103 (2014). http://dx.doi.org/10.1016/j.ijthermalsci.2014.04.011 CrossRefGoogle Scholar
  31. 31.
    Lorenzini, G., Biserni, C., Estrada, E.D., Isoldi, L.A., Santos, E. D., Rocha, L.A.O.: Constructal design of convective Y-shaped cavities by means of genetic algorithm. J. Heat Transf. 136(7), 71702–71702 (2014). http://dx.doi.org/10.1115/1.4027195 CrossRefGoogle Scholar
  32. 32.
    MATLAB: version 7.10.0 (R2010a). The MathWorks Inc., Natick (2010)Google Scholar
  33. 33.
    Renner, G., Ekárt, A.: Genetic algorithms in computer aided design. Comput. Aided Des. 35(8), 709–726 (2003). http://dx.doi.org/10.1016/S0010-4485(03)00003-4 CrossRefGoogle Scholar
  34. 34.
    Snider, A.D., Kraus, A.D.: The quest for the optimum longitudinal fin profile. Heat Transfer Eng. 8(2), 19–25 (1987). http://dx.doi.org/10.1080/01457638708962790 CrossRefGoogle Scholar
  35. 35.
    Xie, Z., Chen, L., Sun, F.: Geometry optimization of T-shaped cavities according to constructal theory. Math. Comput. Model. 52(9–10), 1538–1546 (2010). http://dx.doi.org/10.1016/j.mcm.2010.06.017 CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Emanuel da Silva Dias Estrada
    • 1
  • Elizaldo Domingues dos Santos
    • 2
  • Liércio André Isoldi
    • 2
  • Luiz Alberto Oliveira Rocha
    • 3
  1. 1.Centre for Computational SciencesFederal University of Rio GrandeRio GrandeBrazil
  2. 2.School of EngineeringFederal University of Rio GrandeRio GrandeBrazil
  3. 3.UNISINOSSão LeopoldoBrazil

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