Constructal Design Applied to a Channel with Triangular Fins Submitted to Forced Convection

Abstract:

The purpose of this work is to present a numerical study of a two-dimensional channel with two triangular fins submitted to a laminar flow with forced convection heat transfer, evaluating the geometry of the first fin through the Constructal Design method. The main objectives are to maximize the heat transfer rate and minimize the pressure difference between the inlet and outlet flow of the channel for different dimensions of the first channel fin, considering the same Reynolds (Re_H = 100) and Prandtl numbers (Pr = 0.71). The problem is subjected to three constraints given by the channel area, fin area and maximum occupancy area of ​​each fin. The system has three degrees of freedom. The first is given by the ratio between height and length of the channel, which is kept fixed, H/L = 0.0625. The other two are the ratio between height and width of the upstream fin base (H₃/L₃) positioned on the lower surface of the channel, and the ratio between height and width of the downstream fin (H₄/L₄) positioned on the upper surface of the channel, which is also kept fixed, H₄/L₄ = 1.11. The problem is simulated for three different values ​​of the fraction area of upstream fin (φ₁ = 0.1, 0.2 and 0.3). For the numerical approach of the problem, the conservation equations of mass, momentum and energy are solved using the finite volume method (MVF). The results showed that a ratio of φ₁ = 0.2 is the one that best meets the proposed multi-objective. It was also observed that φ₁ = 0.1 led to a better fluid dynamics performance with a ratio between the best and the worst performance for fluid dynamics case of 25.2 times. For φ₁ = 0.3, the best thermal performance is achieved, where the optimal case has a performance 65.75% higher than that reached for the worst case.

• Periodical: Defect and Diffusion Forum (Volume 372)
• Pages: 152-162
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.372.152
• Online since: March 2017
• Authors: Bruno Costa Feijó, Martim dos Santos Pereira, Filipe Branco Teixeira, Liércio André Isoldi, Luiz Alberto Oliveira Rocha, Jhon Nero Vaz Goulart, Elizaldo Domingues dos Santos*
• Keywords: Channel Flows, Constructal Design, Forced Convection, Triangular Fin

References

[1] D. Jua, Y. Man-Ni, Y. Shi-Fang, Correlations and optimization of a heat exchanger with offset fins by genetic algorithm combining orthogonal design, Appl. Therm. Eng. 107 (2016) 1091-1103.

DOI: 10.1016/j.applthermaleng.2016.04.074

[2] A. A. Bhuiyan, A. K. M. Sadrul Islam, Thermal and hydraulic performance of finned-tube heat exchangers under different flow ranges: a review on modeling and experiment, Int. J. Heat Mass Transfer 101 (2016) 38-59.

DOI: 10.1016/j.ijheatmasstransfer.2016.05.022

[3] H. Peng, X. Ling, J. Li, Performance investigation of an innovative offset strip fin arrays in compact heat exchangers, Energy Convers. Manage. 80 (2014) 287-297.

DOI: 10.1016/j.enconman.2014.01.050

[4] N. Zhao, J. Yang, S. Li, Q. Wang, Numerical investigation of laminar thermal-hydraulic performance of Al2O3–water nanofluids in offset strip fins channel, Int. Commun. Heat Mass Transfer 75 (2016) 42-51.

DOI: 10.1016/j.icheatmasstransfer.2016.03.024

[5] J. Fernández-Seara, R. Diz, F. J. Uhía, Pressure drop and heat transfer characteristics of a titanium brazed plate-fin heat exchanger with offset strip fins, Appl. Therm. Eng. 51 (2013) 502-511.

DOI: 10.1016/j.applthermaleng.2012.08.066

[6] A. Bejan, Shape and Structure, from Engineering to Nature, Cambridge University Press, Cambridge, UK, (2000).

[7] A. Bejan, S. Lorente, Design with Constructal Theory, Wiley, Hoboken, (2008).

[8] A. Bejan, J. P. Zane, Design in Nature, Doubleday, New York, (2012).

[9] L. A. O. Rocha, S. Lorente, A. Bejan, Constructal Law and the unifying principle of design, Springer-Verlag, (2013).

[10] A. Bejan, G. W. Merkx, Constructal theory of social dynamics, Springer, New York, (2007).

[11] A. F. Miguel, The emergence of design in pedestrian dynamics: Locomotion, self-organization, walking paths and constructal law, Phys. Life Rev. 10 (2013) 168-190.

DOI: 10.1016/j.plrev.2013.03.007

[12] A. Bejan, S. Lorente, The constructal law and the evolution of design in nature, Phys. Life Rev. 8 (2011) 209–240.

[13] A. Bejan, S. Lorente, The constructal law makes biology and economics be like physics Reply to comments on The constructal law and the evolution of design in nature, Phys. Life Rev. 8 (2011) 261-263.

DOI: 10.1016/j.plrev.2011.08.001

[14] A. Bejan, J. H. Marden, The constructal unification of biological and geophysical design, Phys. Life Rev. 6 (2009) 85-102.

DOI: 10.1016/j.plrev.2008.12.002

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

DOI: 10.1016/j.ijheatmasstransfer.2003.12.018

[16] G. Lorenzini, L. A. O. Rocha, Constructal design of Y-shaped assembly of fins, Int. J. Heat Mass Transfer 49 (2006) 4552-4557.

DOI: 10.1016/j.ijheatmasstransfer.2006.05.019

[17] A. K. Prasad, J. R. Koseff, Reynolds Number and End-wall Effects on a Lid-driven Cavity Flow, Phys. Fluids A 1 (1989) 208-218.

DOI: 10.1063/1.857491

[18] L. -S. Lin, Y. -C. Chen, C. -A. Lin, Multi relaxation time lattice Boltzmann simulations of deep lid driven cavity flows at different aspect ratios, Comput. Fluids 45 (2011) 233–240.

DOI: 10.1016/j.compfluid.2010.12.012

[19] R. Iwatsu, J. M. Hyun, Threedimensional driven-cavity flows with a vertical temperature gradient. Int. J. Heat Mass Transfer 38 (1995) 3319 – 3328.

DOI: 10.1016/0017-9310(95)00080-s

[20] Y. Song, M. Asadi, G. Xie, L. A. O. Rocha, Constructal wavy-fin channels of a compact heat exchanger with heat transfer rate maximization and pressure losses minimization, Appl. Therm. Eng. 75 (2015) 24-32.

DOI: 10.1016/j.applthermaleng.2014.05.027

[21] S. V. Patankar, Numerical heat transfer and fluid flow, McGraw Hill, New York, (1980).

[22] H. K. Versteeg, W. Malalasekera, An introduction to computational fluid dynamics – the finite volume method, Pearson, England, (2007).

[23] Fluent (version 6. 3. 16), ANSYS, Inc., (2007).

[24] A. Bejan, Convection Heat Transfer, John Wiley, Durham, USA, (2014).