Evaluation of a Differential Evolution/Constructal Design Algorithm for Geometrical Optimization of Double T-Shaped Cavity Intruded into a Heat Generating Wall

Abstract:

In the present work it is investigated the performance of an algorithm that associates Differential Evolution and Constructal Design for geometrical optimization of a heat transfer problem. It is considered the intrusion of a cooled Double T-shaped cavity into a rectangular conducting solid wall with internal heat generation. The main purpose here is to evaluate the algorithm capability to reproduce the effect of geometric ratios over the dimensionless maximum excess of temperature (performance indicator of the heat transfer problem), as well as, the influence of Differential Evolution (DE) parameters over the optimization analysis. The definition of search space for each degree of freedom and problem constraints is performed with Constructal Design, while the Differential Evolution algorithm is used in the optimization process. Here parameters as mutation operator (M), crossover constant (CR), differential amplification factor (F), Population Size (PS) and Generations number (G) are evaluated. A theoretical recommendation about the suitable parameters set for the optimization algorithm for this kind of heat transfer problem is proposed. Results indicated that the crossover constant (CR) and amplification factor (F) are important parameters for suitable prediction of the effect of degrees of freedom over thermal performance. Moreover, when CR = 0.7 and F = 1.5 results obtained with the algorithm are more robust for the achievement of the best shapes and requires lower number of iterations (IT = PS × G) for reproduction of effect of geometric variables over performance.

• Periodical: Defect and Diffusion Forum (Volume 396)
• Pages: 145-154
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.396.145
• Online since: August 2019
• Authors: Gill Velleda Gonzales*, Liércio André Isoldi, Luiz Alberto Oliveira Rocha, Antônio José da Silva Neto, Elizaldo Domingues dos Santos
• Keywords: Constructal Design, Differential Evolution, Geometric Optimization, Heat Transfer

References

[1] C. Biserni, L.A.O. Rocha, A. Bejan, Inverted fins: Geometric optimization of the intrusion into a conducting wall, Int. J. Heat Mass Transf. 47 (2004) 2577–2586.

DOI: 10.1016/j.ijheatmasstransfer.2003.12.018

[2] A. Bejan, Constructal Theory Network of Conducting Paths for Cooling a Heat Generating Volume, Int. J. Heat Mass Transf. 40 (1997) 799–816.

DOI: 10.1016/0017-9310(96)00175-5

[3] A. Bejan, Shape and Structure, from Engineering to Nature, Cambridge University Press, New York, (2000).

[4] A. Bejan, S. Lorente, Design with Constructal Theory, John Wiley & Sons, Hoboken, N.J, (2008).

[5] A. Bejan, P. Zane, Design in Nature: How the Constructal Law Governs Evolution in Biology, Physics, Technology, and Social Organization, 1st Ed, Doubleday, New York, (2012).

[6] A. Bejan, The Physics of Life: the Evolution of Everything, St. Martins Press, New York City, (2016).

[7] G. Lorenzini, C. Biserni, E.D. Estrada, L.A. Isoldi, E.D. dos Santos, L.A.O. Rocha, Constructal Design of Convective Y-shaped Cavities by means of Genetic Algorithm, J. Heat Transf. 136 (2014) 71702.

DOI: 10.1115/1.4027195

[8] G. V Gonzales, E.D. dos Santos, L.A. Isoldi, E. da S.D. Estrada, L.A.O. Rocha, Constructal Design of Isothermal Double T-shaped Cavity by means of Simulated Annealing, in: Proc. XXXVI Iber. Lat.-Am. Congr. Comput. Methods Eng. - CILAMCE 2015, Rio de Janeiro, Brazil, 2015.

DOI: 10.20906/CPS/CILAMCE2015-0582

[9] C. Biserni, L.A.O. Rocha, G. Stanescu, E. Lorenzini, Constructal H-shaped Cavities According to Bejan's Theory, Int. J. Heat Mass Transf. 50 (2007) 2132–2138.

DOI: 10.1016/j.ijheatmasstransfer.2006.11.006

[10] G. Lorenzini, C. Biserni, L.A. Isoldi, E.D. dos Santos, L.A.O. Rocha, Constructal Design Applied to the Geometric Optimization of Y-shaped Cavities Embedded in a Conducting Medium, J. Electron. Packag. 133 (2011) 041008.

DOI: 10.1115/1.4005296

[11] C. Biserni, F.L. Dalpiaz, T.M. Fagundes, L.A.O. Rocha, Constructal Design of T-shaped Morphing Fins Coupled with a Trapezoidal Basement: A Numerical Investigation by means of Exhaustive Search and Genetic Algorithm, Int. J. Heat Mass Transf. 109 (2017) 73–81.

DOI: 10.1016/j.ijheatmasstransfer.2017.01.033

[12] G.V. Gonzales, E. da S.D. Estrada, L.R. Emmendorfer, L.A. Isoldi, G. Xie, L.A.O. Rocha, E.D. dos Santos, A Comparison of Simulated Annealing Schedules for Constructal Design of Complex Cavities intruded into Conductive Walls with Internal Heat Generation, Energy. 93 (2015) 372–382.

DOI: 10.1016/J.ENERGY.2015.09.058

[13] G.V. Gonzales, E.D. Dos Santos, L.A. Isoldi, L.A.O. Rocha, A.J. Da Silva Neto, W.R. Telles, Constructal Design of Double T-shaped Cavity with Stochastic Methods Luus-Jaakola and Simulated Annealing, Defect Diffus. Forum. 370 (2017).

DOI: 10.4028/www.scientific.net/DDF.370.152

[14] G.V. Gonzales, E.D. dos Santos, A.J.S. Neto, A Comparison between Differential Evolution and Simulated Annealing Associated with Constructal Design for a Geometrical Evaluation of a Double T-shaped Cavity (in portuguese), Mundi Eng. Tecnol. e Gest. 3 (2018) 85–104. doi:http://dx.doi.org/10.21575/25254782rmetg2018vol3n2573.

[15] J.N. Reddy, D.K. Gartling, The Finite Element Method in Heat Transfer and Fluid Dynamics, McGrawHill, New York, (1994).

[16] T.M. Inc., Partial Differential Equation ToolboxTM User's Guide R2018b, Natick, (1995).

[17] R. Storn, K. Price, Differential Evolution - A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces, J. Glob. Optim. 11 (1997) 341–359.

DOI: 10.1023/A:1008202821328