0
Research Papers: Micro/Nanoscale Heat Transfer

Multi-Objective Optimization of Laminar Heat Transfer and Friction Factor in Rectangular Microchannel With Rectangular Vortex Generators: An Application of NSGA-II With Gene Expression Programing Metamodel

[+] Author and Article Information
Aparesh Datta

Department of Mechanical Engineering,
National Institute of Technology Agartala,
Jirania, Tripura 799046, India
e-mail: adatta96@gmail.com

Ajoy Kumar Das

Department of Mechanical Engineering,
National Institute of Technology Agartala,
Jirania, Tripura 799046, India
e-mail: akdas_72@yahoo.com

Prasenjit Dey

Department of Mechanical Engineering,
National Institute of Technology Agartala,
Jirania, Tripura 799046, India
e-mail: prasenjitmit1@gmail.com

Dipankar Sanyal

Department of Mechanical Engineering,
Jadavpur University,
Kolkata, West Bengal 700032, India
e-mail: dipans26@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 31, 2016; final manuscript received January 24, 2017; published online March 21, 2017. Assoc. Editor: Guihua Tang.

J. Heat Transfer 139(7), 072401 (Mar 21, 2017) (12 pages) Paper No: HT-16-1545; doi: 10.1115/1.4035890 History: Received August 31, 2016; Revised January 24, 2017

Improvement of the effectiveness of heat exchanger is the demand of compact and efficient cooling devices. In that respect, a numerical study of fluid flow and heat transfer has been conducted with different arrangements of simple vortex generator (VG) in a rectangular microchannel Reynolds number (Re) in the range between 200 and 1100. The combined effect of spanwise and pitchwise distance of VG on heat transfer is investigated rigorously to observe the dependence of heat transfer on both. By processing the numerical predictions through gene expression programing and genetic algorithm optimization, the output variations in heat transfer, or Nusselt number, and friction factor with Re and locations of VGs in the channel are predicted in the form of explicit equations. The predicted monotonic increase of the outputs with Re shows heat transfer enhancement of 40–135% at the cost of increased pressure drop by 62–186.7% with respect to channels without VGs.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Tuckerman, D. B. , and Pease, R. , 1981, “ High-Performance Heat Sinking for VLSI,” IEEE Electron Device Lett., 2(5), pp. 126–129. [CrossRef]
Peng, X. , Wang, B. , Peterson, G. , and Ma, H. , 1995, “ Experimental Investigation of Heat Transfer in Flat Plates With Rectangular Microchannels,” Int. J. Heat Mass Transfer, 38(1), pp. 127–137. [CrossRef]
Peng, X. , and Peterson, G. , 1996, “ Convective Heat Transfer and Flow Friction for Water Flow in Microchannel Structures,” Int. J. Heat Mass Transfer, 39(12), pp. 2599–2608. [CrossRef]
Wang, B. , and Peng, X. , 1994, “ Experimental Investigation on Liquid Forced-Convection Heat Transfer Through Microchannels,” Int. J. Heat Mass Transfer, 37, pp. 73–82. [CrossRef]
Judy, J. , Maynes, D. , and Webb, B. , 2002, “ Characterization of Frictional Pressure Drop for Liquid Flows Through Microchannels,” Int. J. Heat Mass Transfer, 45(17), pp. 3477–3489. [CrossRef]
Qu, W. , and Mudawar, I. , 2002, “ Experimental and Numerical Study of Pressure Drop and Heat Transfer in a Single-Phase Micro-Channel Heat Sink,” Int. J. Heat Mass Transfer, 45(12), pp. 2549–2565. [CrossRef]
Kuppusamy, N. R. , Mohammed, H. , and Lim, C. , 2013, “ Numerical Investigation of Trapezoidal Grooved Microchannel Heat Sink Using Nanofluids,” Thermochim. Acta, 573, pp. 39–56. [CrossRef]
Kuppusamy, N. R. , Mohammed, H. , and Lim, C. , 2014, “ Thermal and Hydraulic Characteristics of Nanofluid in a Triangular Grooved Microchannel Heat Sink (TGMCHS),” Appl. Math. Comput., 246, pp. 168–183.
Xia, G. , Chai, L. , Zhou, M. , and Wang, H. , 2011, “ Effects of Structural Parameters on Fluid Flow and Heat Transfer in a Microchannel With Aligned Fan-Shaped Reentrant Cavities,” Int. J. Therm. Sci., 50(3), pp. 411–419. [CrossRef]
Xia, G. , Zhai, Y. , and Cui, Z. , 2013, “ Numerical Investigation of Thermal Enhancement in a Micro Heat Sink With Fan-Shaped Reentrant Cavities and Internal Ribs,” Appl. Therm. Eng., 58(1), pp. 52–60. [CrossRef]
Zhai, Y. , Xia, G. , Liu, X. , and Li, Y. , 2014, “ Heat Transfer in the Microchannels With Fan-Shaped Reentrant Cavities and Different Ribs Based on Field Synergy Principle and Entropy Generation Analysis,” Int. J. Heat Mass Transfer, 68, pp. 224–233. [CrossRef]
Schubauer, G. B. , and Spangenberg, W. , 1960, “ Forced Mixing in Boundary Layers,” J. Fluid Mech., 8(1), pp. 10–32. [CrossRef]
Johnson, T. , and Joubert, P. , 1969, “ The Influence of Vortex Generators on the Drag and Heat Transfer From a Circular Cylinder Normal to an Airstream,” ASME J. Heat Transfer, 91(1), pp. 91–99. [CrossRef]
Ahmed, H. , Mohammed, H. , and Yusoff, M. , 2012, “ An Overview on Heat Transfer Augmentation Using Vortex Generators and Nanofluids: Approaches and Applications,” Renewable Sustainable Energy Rev., 16(8), pp. 5951–5993. [CrossRef]
Bi, C. , Tang, G. , and Tao, W. , 2013, “ Heat Transfer Enhancement in Mini-Channel Heat Sinks With Dimples and Cylindrical Grooves,” Appl. Therm. Eng., 55(1), pp. 121–132. [CrossRef]
Zhao, X. , Tang, G. , Ma, X.-W. , Jin, Y. , and Tao, W. , 2014, “ Numerical Investigation of Heat Transfer and Erosion Characteristics for H-Type Finned Oval Tube With Longitudinal Vortex Generators and Dimples,” Appl. Energy, 127, pp. 93–104. [CrossRef]
Deb, P. , Biswas, G. , and Mitra, N. , 1995, “ Heat Transfer and Flow Structure in Laminar and Turbulent Flows in a Rectangular Channel With Longitudinal Vortices,” Int. J. Heat Mass Transfer, 38(13), pp. 2427–2444. [CrossRef]
Fiebig, M. , 1995, “ Vortex Generators for Compact Heat Exchangers,” J. Enhanced Heat Transfer, 2(1–2), pp. 43–61.
Fiebig, M. , 1998, “ Vortices, Generators and Heat Transfer,” Chem. Eng. Res. Des., 76(2), pp. 108–123. [CrossRef]
Fiebig, M. , 1997, “ Vortices and Heat Transfer,” ZAMM: J. Appl. Math. Mech./Z. Angew. Math. Mech., 77(1), pp. 3–18. [CrossRef]
Wu, J. , and Tao, W. , 2008, “ Numerical Study on Laminar Convection Heat Transfer in a Rectangular Channel With Longitudinal Vortex Generator. Part A: Verification of Field Synergy Principle,” Int. J. Heat Mass Transfer, 51(5), pp. 1179–1191. [CrossRef]
Wu, J. , and Tao, W. , 2008, “ Numerical Study on Laminar Convection Heat Transfer in a Channel With Longitudinal Vortex Generator. Part B: Parametric Study of Major Influence Factors,” Int. J. Heat Mass Transfer, 51(13), pp. 3683–3692. [CrossRef]
Allison, C. , and Dally, B. , 2007, “ Effect of a Delta-Winglet Vortex Pair on the Performance of a Tube–Fin Heat Exchanger,” Int. J. Heat Mass Transfer, 50(25), pp. 5065–5072. [CrossRef]
Chen, Y. , Fiebig, M. , and Mitra, N. , 2000, “ Heat Transfer Enhancement of Finned Oval Tubes With Staggered Punched Longitudinal Vortex Generators,” Int. J. Heat Mass Transfer, 43(3), pp. 417–435. [CrossRef]
Chu, P. , He, Y. , Lei, Y. , Tian, L. , and Li, R. , 2009, “ Three-Dimensional Numerical Study on Fin-and-Oval-Tube Heat Exchanger With Longitudinal Vortex Generators,” Appl. Therm. Eng., 29(5), pp. 859–876. [CrossRef]
Kwak, K. , Torii, K. , and Nishino, K. , 2003, “ Heat Transfer and Pressure Loss Penalty for the Number of Tube Rows of Staggered Finned-Tube Bundles With a Single Transverse Row of Winglets,” Int. J. Heat Mass Transfer, 46(1), pp. 175–180. [CrossRef]
Li, J. , Wang, S. , Chen, J. , and Lei, Y.-G. , 2011, “ Numerical Study on a Slit Fin-and-Tube Heat Exchanger With Longitudinal Vortex Generators,” Int. J. Heat Mass Transfer, 54(9), pp. 1743–1751. [CrossRef]
Torii, K. , Kwak, K. , and Nishino, K. , 2002, “ Heat Transfer Enhancement Accompanying Pressure-Loss Reduction With Winglet-Type Vortex Generators for Fin-Tube Heat Exchangers,” Int. J. Heat Mass Transfer, 45(18), pp. 3795–3801. [CrossRef]
Wu, J. , and Tao, W. , 2007, “ Investigation on Laminar Convection Heat Transfer in Fin-and-Tube Heat Exchanger in Aligned Arrangement With Longitudinal Vortex Generator From the Viewpoint of Field Synergy Principle,” Appl. Therm. Eng., 27(14), pp. 2609–2617. [CrossRef]
Yang, K.-S. , Li, S.-L. , Chen, Y. , Chien, K.-H. , Hu, R. , and Wang, C.-C. , 2010, “ An Experimental Investigation of Air Cooling Thermal Module Using Various Enhancements at Low Reynolds Number Region,” Int. J. Heat Mass Transfer, 53(25), pp. 5675–5681. [CrossRef]
Zeng, M. , Tang, L. , Lin, M. , and Wang, Q. , 2010, “ Optimization of Heat Exchangers With Vortex-Generator Fin by Taguchi Method,” Appl. Therm. Eng., 30(13), pp. 1775–1783. [CrossRef]
Chomdee, S. , and Kiatsiriroat, T. , 2006, “ Enhancement of Air Cooling in Staggered Array of Electronic Modules by Integrating Delta Winglet Vortex Generators,” Int. Commun. Heat Mass Transfer, 33(5), pp. 618–626. [CrossRef]
Yang, K.-S. , Jhong, J.-H. , Lin, Y.-T. , Chien, K.-H. , and Wang, C.-C. , 2010, “ On the Heat Transfer Characteristics of Heat Sinks: With and Without Vortex Generators,” IEEE Trans. Compon. Packag. Technol., 33(2), pp. 391–397. [CrossRef]
Chomdee, S. , and Kiatsiriroat, T. , 2007, “ Air-Cooling Enhancement With Delta Winglet Vortex Generators in Entrance Region of In-Line Array Electronic Modules,” Heat Transfer Eng., 28(4), pp. 372–379. [CrossRef]
Ma, J. , Huang, Y. P. , Huang, J. , Wang, Y. L. , and Wang, Q. W. , 2010, “ Experimental Investigations on Single-Phase Heat Transfer Enhancement With Longitudinal Vortices in Narrow Rectangular Channel,” Nucl. Eng. Des., 240(1), pp. 92–102. [CrossRef]
Liu, C. , Teng, J.-T. , Chu, J.-C. , Chiu, Y.-L. , Huang, S. , Jin, S. , Dang, T. , Greif, R. , and Pan, H.-H. , 2011, “ Experimental Investigations on Liquid Flow and Heat Transfer in Rectangular Microchannel With Longitudinal Vortex Generators,” Int. J. Heat Mass Transfer, 54(13), pp. 3069–3080. [CrossRef]
Chen, C. , Teng, J.-T. , Cheng, C.-H. , Jin, S. , Huang, S. , Liu, C. , Lee, M.-T. , Pan, H.-H. , and Greif, R. , 2014, “ A Study on Fluid Flow and Heat Transfer in Rectangular Microchannels With Various Longitudinal Vortex Generators,” Int. J. Heat Mass Transfer, 69, pp. 203–214. [CrossRef]
Ebrahimi, A. , Roohi, E. , and Kheradmand, S. , 2015, “ Numerical Study of Liquid Flow and Heat Transfer in Rectangular Microchannel With Longitudinal Vortex Generators,” Appl. Therm. Eng., 78, pp. 576–583. [CrossRef]
Datta, A. , Sanyal, D. , and Das, A. K. , 2016, “ Numerical Investigation of Heat Transfer in Microchannel Using Inclined Longitudinal Vortex Generator,” Appl. Therm. Eng., 108, pp. 1008–1019. [CrossRef]
Ebrahimi, A. , Rikhtegar, F. , Sabaghan, A. , and Roohi, E. , 2016, “ Heat Transfer and Entropy Generation in a Microchannel With Longitudinal Vortex Generators Using Nanofluids,” Energy, 101, pp. 190–201. [CrossRef]
Al-Asadi, M. T. , Alkasmoul, F. , and Wilson, M. , 2016, “ Heat Transfer Enhancement in a Micro-Channel Cooling System Using Cylindrical Vortex Generators,” Int. Commun. Heat Mass Transfer, 74, pp. 40–47. [CrossRef]
Yadav, V. , Baghel, K. , Kumar, R. , and Kadam, S. , 2016, “ Numerical Investigation of Heat Transfer in Extended Surface Microchannels,” Int. J. Heat Mass Transfer, 93, pp. 612–622. [CrossRef]
Ferreira, C. , 2002, “ Gene Expression Programming in Problem Solving,” Soft Computing and Industry, Springer-Verlag, London, pp. 635–653.
Dey, P. , and Das, A. K. , 2016, “ A Utilization of GEP (Gene Expression Programming) Metamodel and PSO (Particle Swarm Optimization) Tool to Predict and Optimize the Forced Convection Around a Cylinder,” Energy, 95, pp. 447–458. [CrossRef]
Nazari, A. , and Riahi, S. , 2013, “ Predicting the Effects of Nanoparticles on Compressive Strength of Ash-Based Geopolymers by Gene Expression Programming,” Neural Comput. Appl., 23(6), pp. 1677–1685. [CrossRef]
Azarkish, H. , Sarvari, S. , and Behzadmehr, A. , 2010, “ Optimum Design of a Longitudinal Fin Array With Convection and Radiation Heat Transfer Using a Genetic Algorithm,” Int. J. Therm. Sci., 49(11), pp. 2222–2229. [CrossRef]
Dey, P. , and Das, A. K. , “ Prediction and Optimization of Unsteady Forced Convection Around a Rounded Cornered Square Cylinder in the Range of Re,” Neural Comput. Appl. (published online).
Copiello, D. , and Fabbri, G. , 2009, “ Multi-Objective Genetic Optimization of the Heat Transfer From Longitudinal Wavy Fins,” Int. J. Heat Mass Transfer, 52(5), pp. 1167–1176. [CrossRef]
Fabbri, G. , 1997, “ A Genetic Algorithm for Fin Profile Optimization,” Int. J. Heat Mass Transfer, 40(9), pp. 2165–2172. [CrossRef]
Hajabdollahi, F. , Rafsanjani, H. H. , Hajabdollahi, Z. , and Hamidi, Y. , 2012, “ Multi-Objective Optimization of Pin Fin to Determine the Optimal Fin Geometry Using Genetic Algorithm,” Appl. Math. Modell., 36(1), pp. 244–254. [CrossRef]
Ge, Y. , Liu, Z. , and Liu, W. , 2016, “ Multi-Objective Genetic Optimization of the Heat Transfer for Tube Inserted With Porous Media,” Int. J. Heat Mass Transfer, 101, pp. 981–987. [CrossRef]
Ge, Y. , Liu, Z. , Liu, W. , and Chen, G. , 2015, “ Active Optimization Design Theory and Method for Heat Transfer Unit and Its Application on Shape Design of Cylinder in Convective Heat Transfer,” Int. J. Heat Mass Transfer, 90, pp. 702–709. [CrossRef]
Zeng, X. , Ge, Y. , Shen, J. , Zeng, L. , Liu, Z. , and Liu, W. , 2017, “ The Optimization of Channels for a Proton Exchange Membrane Fuel Cell Applying Genetic Algorithm,” Int. J. Heat Mass Transfer, 105, pp. 81–89. [CrossRef]
Zheng, Z.-J. , Li, M.-J. , and He, Y.-L. , 2015, “ Optimization of Porous Insert Configurations for Heat Transfer Enhancement in Tubes Based on Genetic Algorithm and CFD,” Int. J. Heat Mass Transfer, 87, pp. 376–379. [CrossRef]
Okhotin, A. , Pushkarskij, A. , and Gorbachev, V. , 1972, “ Thermophysical Properties of Semiconductors,” Atomizdat, Moscow, Russia.
Lan, J. , Xie, Y. , and Zhang, D. , 2012, “ Flow and Heat Transfer in Microchannels With Dimples and Protrusions,” ASME J. Heat Transfer, 134(2), p. 021901. [CrossRef]
Gee, D. L. , and Webb, R. , 1980, “ Forced Convection Heat Transfer in Helically Rib-Roughened Tubes,” Int. J. Heat Mass Transfer, 23(8), pp. 1127–1136. [CrossRef]
Guo, J. , Xu, M. , and Cheng, L. , 2011, “ Second Law Analysis of Curved Rectangular Channels,” Int. J. Therm. Sci., 50(5), pp. 760–768. [CrossRef]
Davis, L. , 1991, Handbook of Genetic Algorithms, Van Nostrand Reinhold, New York.
Deb, K. , 2001, Multi-Objective Optimization Using Evolutionary Algorithms, Wiley, Chichester, UK.
Deb, K. , Pratap, A. , Agarwal, S. , and Meyarivan, T. , 2002, “ A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Trans. Evol. Comput., 6(2), pp. 182–197. [CrossRef]
Song, K. , Liu, S. , and Wang, L. , 2016, “ Interaction of Counter Rotating Longitudinal Vortices and the Effect on Fluid Flow and Heat Transfer,” Int. J. Heat Mass Transfer, 93, pp. 349–360. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic diagram of channel

Grahic Jump Location
Fig. 2

Flowchart of numerical simulation by computational fluid dynamics (CFD)

Grahic Jump Location
Fig. 3

Comparison of present numerical results with experiment by Liu et al. [36]

Grahic Jump Location
Fig. 4

Flowchart of algorithm of NSGA-II technique

Grahic Jump Location
Fig. 5

Computational time of NSGA-II technique

Grahic Jump Location
Fig. 6

Flowchart of GEP model

Grahic Jump Location
Fig. 7

Linear-fit model of CFD and optimizer predicted (a) Nusselt number and (b) friction factor

Grahic Jump Location
Fig. 8

Pareto-optimal solutions using the NSGA-II

Grahic Jump Location
Fig. 9

Variation in relative Nusselt number Nu/Nu0 for different channels

Grahic Jump Location
Fig. 10

Thermal performance of different channels

Grahic Jump Location
Fig. 11

Variation in relative friction factor f/f0 for different channels

Grahic Jump Location
Fig. 12

Velocity contour at Re 400 for C1, C2, C3, and C4 channels at Z = 0.5H

Grahic Jump Location
Fig. 13

Velocity contour at Re 1000 for C1, C2, C3, and C4 channels at Z = 0.5H

Grahic Jump Location
Fig. 14

Temperature contour on cross sections along the flow direction

Grahic Jump Location
Fig. 15

Temperature contour and limiting streamline at the top surface of C1 and C4 channels at Re 600: C1—S = 100 μm, P = 0.005 m, and Re = 600; C4—S = 350 μm, P = 0.005 m, and Re = 600

Grahic Jump Location
Fig. 16

Temperature contour and limiting streamline at the top surface of C2 and C4 channels at Re 1000: C2—S = 200 μm, P = 0.005 m, and Re = 1000; C4—S = 350 μm, P = 0.005 m, and Re = 1000

Grahic Jump Location
Fig. 17

Temperature contour and limiting streamline at the top surface of C2 and C6 channels at Re 600: C2—S = 200 μm, P = 0.005 m, and Re = 600; C6—S = 200 μm, P = 0.00285 m, and Re = 600

Grahic Jump Location
Fig. 18

Temperature contour and limiting streamline at the top surface of C4 and C12 channels at Re 1000: C4—S = 350 μm, P = 0.005 m, and Re = 1000; C12—S = 350 μm, P = 0.002 m, and Re = 1000

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In