Journal of Thermal Analysis and Calorimetry

, Volume 136, Issue 4, pp 1795–1806 | Cite as

Optimization of heat transfer and pressure drop in a tube with loose-fit perforated twisted tapes by Taguchi method and grey relational analysis

  • Sibel GunesEmail author
  • Ercan Senyigit
  • Ersin Karakaya
  • Veysel Ozceyhan


This work introduces the determination of the optimum values of the design parameters in a tube with loose-fit perforated twisted tapes. The effects of the design parameters such as twist ratio (y/D), width ratio (W/D), hole diameter ratio (d/D) and Reynolds number (Re) on heat transfer (i.e. Nusselt number) and pressure drop (i.e. friction factor) were analyzed by Taguchi method (TM) and grey relational analysis (GRA). The Nusselt number and friction factor were taken into account as performance parameters. Taguchi Method is based on analysis of variances and implements the orthogonal arrays for experimental design. L16 orthogonal array was selected as experimental plan. Firstly, each performance parameter was optimized, independently. Then, all the performance parameters were optimized together by TM and GRA. According to the experimental plan results, the most important factor for both Nusselt number and friction factor is Reynolds number, while the least significant factors are twist ratio (y/D) and width ratio (W/D).


Taguchi method Grey relational analysis Twisted tape Heat transfer Friction factor 

List of symbols


Specific heat capacity of air (J kg−1 K−1)


Grey relational coefficients


Hole diameter (m)


Inner diameter of the tube (m)


Outer diameter of the tube (m)


The rth response variable among p experiments


Friction factor


Grey relational grade


Heat transfer coefficient (W m−2 K−1)


Current (A)


Thermal conductivity (W m−1 K−1)


Length of the test tube (m)


Air mass flow rate (kg s−1)


The largest value of erp


The smallest value of erp


The count of iterations in confirmation of experiments


The normalized value rth response variable in the pth experiment


The ideal normalized value


Nusselt number


Pressure drop (Pa)


Reynolds number


Heat transfer (W)


Heat flux (W m−2)


Thickness of the test tube (m)


Steady state temperature (K)


Fluid velocity (m s−1)


Voltage (V)


Twisted tape width (m)


Twist length of twisted tape (m)


The achievement amount of ith observation


Achievement statistic

Greek letters


Fluid density (kg m−3)


Thickness of twisted tape (m)


Fluid kinematic viscosity (m2 s−1)







Insulated test tube


Inner wall of test tube






  1. 1.
    Chang SW, Huang BJ. Thermal performances of tubular flows enhanced by ribbed spiky twist tapes with and without edge notches. Int J Heat Mass Transf. 2014;73:645–63.CrossRefGoogle Scholar
  2. 2.
    Eiamsa-ard S. Study on thermal and fluid flow characteristics in turbulent channel flows with multiple twisted tape vortex generators. Int Commun Heat Mass Transf. 2010;31:644–51.CrossRefGoogle Scholar
  3. 3.
    Mokkapati V, Lin CS. Numerical study of an exhaust heat recovery system using corrugated tube heat exchanger with twisted tape inserts. Int Commun Heat Mass Transf. 2014;57:53–64.CrossRefGoogle Scholar
  4. 4.
    Hong Y, Du J, Wang S. Experimental heat transfer and flow characteristics in a spiral grooved tube with overlapped large/small twin twisted tapes. Int J Heat Mass Transf. 2017;106:1178–90.CrossRefGoogle Scholar
  5. 5.
    Bas H, Ozceyhan V. Heat transfer enhancement in a tube with twisted tape inserts placed separately from the tube wall. Exp Therm Fluid Sci. 2012;41:51–8.CrossRefGoogle Scholar
  6. 6.
    Nanan K, Yongsiri K, Wongcharee K, Thianpong C, Eiamsa-ard S. Heat transfer enhancement by helically twisted tapes inducing co- and counter-swirl flows. Int Commun Heat Mass Transf. 2013;46:67–73.CrossRefGoogle Scholar
  7. 7.
    Eiamsa-ard S, Yongsiri K, Nanan K, Thianpong C. Heat transfer augmentation by helically twisted tapes as swirl and turbulence promoters. Chem Eng Process. 2012;60:42–8.CrossRefGoogle Scholar
  8. 8.
    Man C, Lv X, Hu J, Sun P, Tang Y. Experimental study on effect of heat transfer enhancement for single-phase forced convective flow with twisted tape inserts. Int J Heat Mass Transf. 2017;106:877–83.CrossRefGoogle Scholar
  9. 9.
    Jaramillo OA, Borunda M, Velazquez-Lucho KM, Robles M. Parabolic trough solar collector for low enthalpy processes: an analysis of the efficiency enhancement by using twisted tape inserts. Renew Energy. 2016;93:125–41.CrossRefGoogle Scholar
  10. 10.
    Vashistha C, Patil AK, Kumar M. Experimental investigation of heat transfer and pressure drop in a circular tube with multiple inserts. Appl Therm Eng. 2016;96:117–29.CrossRefGoogle Scholar
  11. 11.
    Abdolbaqi MK, Azmi WH, Mamat R, Mohamed NMZN, Najafi G. Experimental investigation of turbulent heat transfer by counter and co-swirling flow in a flat tube fitted with twin twisted tapes. Int Commun Heat Mass Transf. 2016;75:295–302.CrossRefGoogle Scholar
  12. 12.
    Gunes S, Karakaya E. Thermal characteristics in a tube with loose-fit perforated twisted tapes. Heat Transf Eng. 2015;36:1504–17.CrossRefGoogle Scholar
  13. 13.
    Saysroy A, Eiamsa-ard S. Periodically fully-developed heat and fluid flow behaviors in a turbulent tube flow with square-cut twisted tape inserts. Appl Therm Eng. 2017;112:895–910.CrossRefGoogle Scholar
  14. 14.
    Lin ZM, Wang LB, Lin M, Dang W, Zhang YH. Numerical study of the laminar flow and heat transfer characteristics in a tube inserting a twisted tape having parallelogram winglet vortex generators. Appl Therm Eng. 2017;115:644–58.CrossRefGoogle Scholar
  15. 15.
    Bhuiya MMK, Chowdhury MSU, Saha M, Islam MT. Heat transfer and friction factor characteristics in turbulent flow through a tube fitted with perforated twisted tape inserts. Int Commun Heat Mass Transf. 2013;46:49–57.CrossRefGoogle Scholar
  16. 16.
    Bhuiya MMK, Chowdhury MSU, Shahabuddin M, Saha M, Memon LA. Thermal characteristics in a heat exchanger tube fitted with triple twisted tape inserts. Int Commun Heat Mass Transf. 2013;48:124–32.CrossRefGoogle Scholar
  17. 17.
    Bhuiya MMK, Azad AK, Chowdhury MSU, Saha M. Heat transfer augmentation in a circular tube with perforated double counter twisted tape inserts. Int Commun Heat Mass Transf. 2016;74:18–26.CrossRefGoogle Scholar
  18. 18.
    Piriyarungroda N, Eiamsa-ard S, Thianpong C, Pimsarn M, Nanan K. Heat transfer enhancement by tapered twisted tape inserts. Chem Eng Process. 2015;96:62–71.CrossRefGoogle Scholar
  19. 19.
    Hasanpour A, Farhad M, Sedighi K. Experimental heat transfer and pressure drop study on typical, perforated, V-cut and U-cut twisted tapes in a helically corrugated heat exchanger. Int Commun Heat Mass Transf. 2016;71:126–36.CrossRefGoogle Scholar
  20. 20.
    Nanan K, Thianpong C, Promvonge P, Eiamsa-ard S. Investigation of heat transfer enhancement by perforated helical twisted-tapes. Int Commun Heat Mass Transf. 2014;52:106–12.CrossRefGoogle Scholar
  21. 21.
    Murugesan P, Mayilsamy K, Suresh S. Turbulent heat transfer and pressure drop in tube fitted with square-cut twisted tape. Chinese J Chem Eng. 2010;18:609–17.CrossRefGoogle Scholar
  22. 22.
    Chang SW, Jan YJ, Liou JS. Turbulent heat transfer and pressure drop in tube fitted with serrated twisted tape. Int J Therm Sci. 2007;46:506–18.CrossRefGoogle Scholar
  23. 23.
    Chang SW, Jan YJ, Liou JS. Heat transfer and pressure drop in tube with broken twisted tape insert. Exp Therm Fluid Sci. 2007;32:489–501.CrossRefGoogle Scholar
  24. 24.
    Eiamsa-ard S, Wongcharee K, Eiamsa-ard P, Thianpong C. Heat transfer enhancement in a tube using delta-winglet twisted tape inserts. Appl Therm Eng. 2010;30:310–8.CrossRefGoogle Scholar
  25. 25.
    Eiamsa-ard S, Seemawute P, Wongcharee K. Influences of peripherally-cut twisted tape insert on heat transfer and thermal performance characteristics in a laminar and turbulent tube flows. Exp Therm Fluid Sci. 2010;34:711–9.CrossRefGoogle Scholar
  26. 26.
    Rahimi M, Shabanian SR, Alsairafi AA. Experimental and CFD studies on heat transfer and friction factor characteristics of a tube equipped with modified twisted tape inserts. Chem Eng Process. 2009;48:762–70.CrossRefGoogle Scholar
  27. 27.
    Kackar RN. Off-line quality control, parameter design and Taguchi method. J Qual Technol. 1985;17:176–209.CrossRefGoogle Scholar
  28. 28.
    Phadke MS, Kackar RN, Speeney DV, Grieco MJ. Off-line quality control in integrated fabrication using experimental design. AT&T Tech J. 1983;62:1273–309.Google Scholar
  29. 29.
    Taguchi G. Taguchi techniques for quality engineering. New York: Quality Resources; 1987.Google Scholar
  30. 30.
    Ross PJ. Taguchi techniques for quality engineering. New York: McGraw-Hill; 1988.Google Scholar
  31. 31.
    Phadke MS. Quality engineering using robust design. Upper Saddle River: Prentice Hall; 1989.Google Scholar
  32. 32.
    Roy RK. Design of experiments using the Taguchi approach. New York: Wiley; 2001.Google Scholar
  33. 33.
    Topuz A, Engin T, Ozalp AA, Erdogan B, Mert S, Yeter A. Experimental investigation of optimum thermal performance and pressure drop of water-based Al2O3, TiO2 and ZnO nanofluids flowing inside a circular microchannel. J Therm Anal Calorim. 2018;131:2843–63.CrossRefGoogle Scholar
  34. 34.
    Abadeh A, Passandideh-Dard M, Maghrebi MJ, Mohammadi M. Stability and magnetization of Fe3O4/water nanofluid preparation characteristics using Taguchi method. J Therm Anal Calorim. 2018. Scholar
  35. 35.
    Qi Z, Chen J, Chen Z. Parametric study on the performance of a heat exchanger with corrugated louvered fins. ApplTherm Eng. 2007;27:539–44.Google Scholar
  36. 36.
    Turgut E, Cakmak G, Yildiz C. Optimization of the concentric heat exchanger with injector turbulators by Taguchi method. Energy Convers Manag. 2012;53:268–75.CrossRefGoogle Scholar
  37. 37.
    Yakut K, Sahin B, Celik C, Alemdaroglu N, Kurnuc A. Effects of tapes with double-sided delta-winglets on heat and vortex characteristics. Appl Energy. 2005;80:77–95.CrossRefGoogle Scholar
  38. 38.
    Gunes S, Manay E, Senyigit E, Ozceyhan V. A Taguchi approach for optimization of design parameters in a tube with coiled wire inserts. Appl Therm Eng. 2011;31:2568–77.CrossRefGoogle Scholar
  39. 39.
    Hsieh C, Jang J. Parametric study and optimization of louver finned-tube heat exchangers by Taguchi method. Appl Therm Eng. 2012;42:101–10.CrossRefGoogle Scholar
  40. 40.
    Chamoli S. A Taguchi approach for optimization of flow and geometrical parameters in a rectangular channel roughened with V down perforated baffles. Case Stud Therm Eng. 2015;5:59–69.CrossRefGoogle Scholar
  41. 41.
    Sahin B, Demir A. Thermal performance analysis and optimum design parameters of heat exchanger having perforated pin fins. Energy Convers Manag. 2008;49:1684–95.CrossRefGoogle Scholar
  42. 42.
    Bilen K, Yapici S, Celik CA. Taguchi approach for investigation of heat transfer from a surface equipped with rectangular blocks. Energ Convers Manag. 2001;42:951–61.CrossRefGoogle Scholar
  43. 43.
    Zeng M, Tang LH, Lin M, Wang QW. Optimization of heat exchangers with vortex-generator fin by Taguchi method. Appl Therm Eng. 2010;30:1775–83.CrossRefGoogle Scholar
  44. 44.
    Aghaie AZ, Rahimi AB, Akbarzadeh A. A general optimized geometry of angled ribs for enhancing the thermo-hydraulic behavior of a solar air heater channel—a Taguchi approach. Renew Energy. 2015;83:47–54.CrossRefGoogle Scholar
  45. 45.
    Kotcioglu I, Cansiz A, Khalaji MN. Experimental investigation for optimization of design parameters in a rectangular duct with plate-fins heat exchanger by Taguchi method. Appl Therm Eng. 2013;50:604–13.CrossRefGoogle Scholar
  46. 46.
    Kotcioglu I, Khalaji MN, Cansiz A. Heat transfer analysis of a rectangular channel having tubular router in different winglet configurations with Taguchi method. Appl Therm Eng. 2018;132:637–50.CrossRefGoogle Scholar
  47. 47.
    Senthilkumar N, Tamizharasan T, Anandakrishnan V. Experimental investigation and performance analysis of cemented carbide inserts of different geometries using Taguchi based grey relational analysis. Measurement. 2014;58:520–36.CrossRefGoogle Scholar
  48. 48.
    Yeh J, Tsai T. Optimizing the fine-pitch copper wire bonding process with multiple quality characteristics using a grey-fuzzy Taguchi method. Microelectron Reliab. 2014;54:287–96.CrossRefGoogle Scholar
  49. 49.
    Lau C, Abdullah MZ, Ani FC. Optimization modeling of the cooling stage of reflow soldering process for ball grid array package using the gray-based Taguchi method. Microelectron Reliab. 2012;52:1143–52.CrossRefGoogle Scholar
  50. 50.
    Chiang Y-M, Hsieh HH. The use of the Taguchi method with grey relational analysis to optimize the thin-film sputtering process with multiple quality characteristic in color filter manufacturing. Comput Ind Eng. 2009;56:648–61.CrossRefGoogle Scholar
  51. 51.
    Pan LK, Wang CC, Wei SL, Sher HF. Optimizing multiple quality characteristics via Taguchi method-based grey analysis. J Mater Process Technol. 2007;182:107–16.CrossRefGoogle Scholar
  52. 52.
    Sarıkaya M, Gullu A. Multi-response optimization of minimum quantity lubrication parameters using Taguchi-based grey relational analysis in turning of difficult-to-cut alloy Haynes 25. J Clean Prod. 2015;91:347–57.CrossRefGoogle Scholar
  53. 53.
    Equbal I, Kumar R, Shamim M, Ohdard RK. A grey-based Taguchi method to optimize hot forging process. Proc Mater Sci. 2014;6:1495–504.CrossRefGoogle Scholar
  54. 54.
    Chamoli S, Yu P, Kumar A. Multi-response optimization of geometric and flow parameters in a heat exchanger tube with perforated disk inserts by Taguchi grey relational analysis. Appl Therm Eng. 2016;103:1339–50.CrossRefGoogle Scholar
  55. 55.
    Celik N, Pusat G, Turgut E. Application of Taguchi method and grey relational analysis on a turbulated heat exchanger. Int J Therm Sci. 2018;124:85–97.CrossRefGoogle Scholar
  56. 56.
    Celik N, Turgut E, Yildiz S, Eren H. Applying Taguchi and grey relational methods to a heat exchanger with coil springs. In: 10th International conference on heat transfer, fluid mechanics and thermodynamics, HEFAT’14, Orlando, FL, USA, 14–16 July 2014.Google Scholar
  57. 57.
    Kumbhar DG, Sane NK. numerical analysis and optimization of heat transfer and friction factor in dimpled tube assisted with regularly spaced twisted tapes using Taguchi and grey relational analysis. Proc Eng. 2015;127:652–9.CrossRefGoogle Scholar
  58. 58.
    Kline SJ, McClintock FA. Describing uncertainties in single sample experiments. Mech Eng. 1953;75:385–7.Google Scholar
  59. 59.
    Senyigit E, Dugenci M, Aydin ME. Heuristic-based neural networks for stochastic dynamic lot sizing problem. Appl Soft Comput. 2013;13:1332–9.CrossRefGoogle Scholar
  60. 60.
    Babayigit B, Şenyigit E. Design optimization of circular antenna arrays using Taguchi method. Neural Comput Appl. 2017;28:1443–52.CrossRefGoogle Scholar
  61. 61.
    Yildiz Y, Senyigit E, Irdemez S. Optimization of specific energy consumption for Bomaplex red Cr-ldye removal from aqueous solution by electrocoagulation using Taguchi-neural method. Neural Comput Appl. 2013;23:1061–9.CrossRefGoogle Scholar
  62. 62.
    Babayigit B, Şenyigit E, Mumcu G. Optimum broadband E-patch antenna design with Taguchi method. J Electromagn Wave. 2016;30:915–27.CrossRefGoogle Scholar
  63. 63.
    Deng JL. Introduction to grey system. J Grey Syst. 1989;1:1–24.Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Sibel Gunes
    • 1
    Email author
  • Ercan Senyigit
    • 2
  • Ersin Karakaya
    • 1
  • Veysel Ozceyhan
    • 1
  1. 1.Department of Mechanical Engineering, Faculty of EngineeringErciyes UniversityKayseriTurkey
  2. 2.Department of Industrial Engineering, Faculty of EngineeringErciyes UniversityKayseriTurkey

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