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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bejan, A.: Shape and Structure, from Engineering to Nature. Cambridge University Press, New York (2000)
Bejan, A.: The Physics of Life: The Evolution of Everything. St. Martins Press, New York City (2016)
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
Bejan, A., Lorente, S.: Design with Constructal Theory. Wiley, Hoboken (2008)
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)
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
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
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
COMSOL multiphysics: COMSOL multiphysics reference manual (2014). www.comsol.com
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning, 1st edn. Addison-Wesley Longman Publishing Co., Inc., Boston (1989)
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
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
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
Haupt, R.L.: Practical Genetic Algorithms, 2nd edn. Wiley, Hoboken (2004)
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)
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)
Kraus, A.D.: Developments in the analysis of finned arrays. Int. J. Transp. Phenom. 1, 141–164 (1999)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
MATLAB: version 7.10.0 (R2010a). The MathWorks Inc., Natick (2010)
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
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
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
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Estrada, E.d.S.D., dos Santos, E.D., Isoldi, L.A., Rocha, L.A.O. (2019). Constructal Design Associated with Genetic Algorithm to Maximize the Performance of H-Shaped Isothermal Cavities. In: Platt, G., Yang, XS., Silva Neto, A. (eds) Computational Intelligence, Optimization and Inverse Problems with Applications in Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-96433-1_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-96433-1_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-96432-4
Online ISBN: 978-3-319-96433-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)