Optimization of Wave Inclination Angle in Parallel Wavy-Channel Heat Exchangers

  • Rahim HassanzadehEmail author
  • Mehran Abadtalab
  • Ali Bayat
Research Article - Mechanical Engineering


Effects of the wave inclination angle on the performance of a parallel wavy-channel heat exchanger are investigated three-dimensionally. Computations have been carried out in various Reynolds numbers in the laminar range from 100 to 600 by means of the finite volume approach. On the other hand, several wave inclination angles such as α = 0°, 20°, 40°, 60°, and 80° with respect to the spanwise direction have been examined to find the optimum value. The applied numerical method has been validated against the available data of the conventional parallel flat-channel heat exchanger. Several quantitative and qualitative results are presented in this investigation. It is demonstrated that deflection of waves of plates from zero to nonzero values onsets the three-dimensional flow in the heat exchanger. In addition, maximum heat transfer enhancement of 108% is achieved for Re = 600 at the wave inclination angle of 20°. Moreover, except at Re = 100, the wave inclination angle of 40° can be introduced as an optimum inclination angle for a wavy-channel heat exchanger from the perspective of thermal–hydraulic performance. At the end of this study, values of pressure drop penalty and thermal–hydraulic performance of all cases under consideration have been determined accordingly.


Heat transfer enhancement Wave inclination angle Heat exchanger Wavy channel 

List of Symbols


Wave amplitude (m)


Specific heat (J/kg °C)


Hydraulic diameter (m)


Channel height (m)


Thermal conductivity (W/m °C)


Channel length (m)


Mean Nusselt number


Local Nusselt number


Pressure (Pa)


Thermal–hydraulic performance index


Prandtl Number

\(\Delta p\)

Pressure drop (Pa)

\(\Delta p^{*}\)

Non-dimensional pressure drop


Reynolds number


Time (s)

\(\Delta t\)

Time interval (s)


Temperature (°C)


Inlet temperature (°C)


Bulk temperature (°C)


Surface temperature (°C)


Outlet temperature (°C)


Streamwise velocity (m/s)


Mean streamwise velocity (m/s)


Vertical velocity (m/s)


Velocity magnitude (m/s)


Root mean square of spanwise velocity (m/s)


Spanwise velocity (m/s)


Channel width (m)


Streamwise coordinate

\(x^{ + }\)

Dimensionless axial distance of hydrodynamic entrance region


Dimensionless axial distance of thermal entrance region


Vertical coordinate


Spanwise coordinate

Greek Symbols


Density (kg/m3)


Kinematic velocity (m2/s)


Wave inclination angle (°)


Non-dimensional temperature


Wave period (m)



Reynolds number


Root mean square


Thermal–hydraulic performance index


  1. 1.
    Ganvir, R.B.; Walke, P.V.; Kriplani, V.M.: Heat transfer characteristics in nanofluid—a review. Renew. Sustain. Energy Rev. 75, 451–460 (2017)CrossRefGoogle Scholar
  2. 2.
    Pinto, R.V.; Augusto, F.; Fiorelli, S.: Review of the mechanisms responsible for heat transfer enhancement using nanofluids. Appl. Therm. Eng. 108, 720–739 (2016)CrossRefGoogle Scholar
  3. 3.
    Khanafer, K.; Vafai, K.: A review on the applications of nanofluids in solar energy field. Renew. Energy 123, 398–406 (2018)CrossRefGoogle Scholar
  4. 4.
    Ambreen, T.; Kim, M.: Heat transfer and pressure drop correlations of nanofluids: a state of art review. Renew. Sustain. Energy Rev. 91, 564–583 (2018)CrossRefGoogle Scholar
  5. 5.
    Mohammed, H.A.; Abed, A.M.; Wahid, M.A.: The effects of geometrical parameters of a corrugated channel with in out-of-phase arrangement. Int. Commun. Heat Mass Transf. 40, 47–57 (2013)CrossRefGoogle Scholar
  6. 6.
    Hassanzadeh, R.; Tokgoz, N.: Thermal–Hydraulic characteristics of nano fluid flow in corrugated ducts. J. Eng. Thermophys. 26(4), 498–513 (2017)CrossRefGoogle Scholar
  7. 7.
    Abou, T.M.; Kabeel, A.E.; Mahgoub, M.: Corrugated plate heat exchanger review. Renew. Sustain. Energy Rev. 70, 852–860 (2017)CrossRefGoogle Scholar
  8. 8.
    Yang, B.; Gao, T.; Gong, J.; Li, J.: Numerical investigation on flow and heat transfer of pulsating flow in various ribbed channels. Appl. Therm. Eng. 145, 576–589 (2018)CrossRefGoogle Scholar
  9. 9.
    Hyun, D.; Ju, B.; Shin, J.; Su, J.; Taek, J.: Effects of inlet velocity profile on flow and heat transfer in the entrance region of a ribbed channel. Int. J. Heat Mass Transf. 92, 838–849 (2016)CrossRefGoogle Scholar
  10. 10.
    Weihing, P.; Younis, B.A.; Weigand, B.: Heat transfer enhancement in a ribbed channel: development of turbulence closures. Int. J. Heat Mass Transf. 76, 509–522 (2014)CrossRefGoogle Scholar
  11. 11.
    Coletti, F.; Cresci, I.; Arts, T.: Spatio-temporal analysis of the turbulent flow in a ribbed channel. Int. J. Heat Fluid Flow 44, 181–196 (2013)CrossRefGoogle Scholar
  12. 12.
    Esmaeilzadeh, A.; Amanifard, N.; Deylami, H.M.: Comparison of simple and curved trapezoidal longitudinal vortex generators for optimum flow characteristics and heat transfer augmentation in a heat exchanger. Appl. Therm. Eng. 125, 1414–1425 (2017)CrossRefGoogle Scholar
  13. 13.
    Samadifar, M.; Toghraie, D.: Numerical simulation of heat transfer enhancement in a plate-fin heat exchanger using a new type of vortex generators. Appl. Therm. Eng. 133, 671–681 (2018)CrossRefGoogle Scholar
  14. 14.
    Wang, Y.; Liu, P.; Shan, F.; Liu, Z.; Liu, W.: Effect of longitudinal vortex generator on the heat transfer enhancement of a circular tube. Appl. Therm. Eng. 148, 1018–1028 (2019)CrossRefGoogle Scholar
  15. 15.
    Salviano, L.O.; Dezan, D.J.; Yanagihara, J.I.: Thermal-hydraulic performance optimization of inline and staggered fin-tube compact heat exchangers applying longitudinal vortex generators. Appl. Therm. Eng. 95, 311–329 (2016)CrossRefGoogle Scholar
  16. 16.
    Zeeshan, M.; Nath, S.; Bhanja, D.; Das, A.: Numerical investigation for the optimal placements of rectangular vortex generators for improved thermal performance of fin-and-tube heat exchangers. Appl. Therm. Eng. 136, 589–601 (2018)CrossRefGoogle Scholar
  17. 17.
    Ahmed, M.A.; Yusoff, M.Z.; Ng, K.C.; Shuaib, N.H.: The effects of wavy-wall phase shift on thermal–hydraulic performance of Al2O3–water nanofluid flow in sinusoidal-wavy channel. Case Stud. Therm. Eng. 4, 153–165 (2014)CrossRefGoogle Scholar
  18. 18.
    Hassan Khan, H.; Aneesh, A.M.; Sharma, A.; Srivastava, A.; Chaudhuri, P.: Thermal-hydraulic characteristics and performance of 3D wavy channel based printed circuit heat exchanger. Appl. Therm. Eng. 87, 519–528 (2015)CrossRefGoogle Scholar
  19. 19.
    Akbarzadeh, M.; Rashidi, S.; Esfahani, J.A.: Influences of corrugation profiles on entropy generation, heat transfer, pressure drop, and performance in a wavy channel. Appl. Therm. Eng. 116, 278–291 (2017)CrossRefGoogle Scholar
  20. 20.
    Ničeno, B.; Nobile, E.: Numerical analysis of fluid flow and heat transfer in periodic wavy channels. Int. J. Heat Fluid Flow 22, 156–167 (2001)CrossRefGoogle Scholar
  21. 21.
    Ramgadia, A.G.; Saha, A.K.: Numerical study of fully developed unsteady flow and heat transfer in asymmetric wavy channels. Int. J. Heat Mass Transf. 102, 98–112 (2016)CrossRefGoogle Scholar
  22. 22.
    Yang, Y.; Wang, Y.; Tseng, P.: Numerical optimization of heat transfer enhancement in a wavy channel using nanofluids. Int. Commun. Heat Mass Transf. 51, 9–17 (2014)CrossRefGoogle Scholar
  23. 23.
    Pham, M.V.; Plourde, F.; Doan, S.K.: Turbulent heat and mass transfer in sinusoidal wavy channels. Int. J. Heat Fluid Flow 29, 1240–1257 (2008)CrossRefGoogle Scholar
  24. 24.
    Lin, L.; Zhao, J.; Lu, G.; Wang, X.; Yan, W.: Heat transfer enhancement in microchannel heat sink by wavy channel with changing wavelength/amplitude. Int. J. Therm. Sci. 118, 423–434 (2017)CrossRefGoogle Scholar
  25. 25.
    Pati, S.; Mehta, S.K.; Borah, A.: Numerical investigation of thermo-hydraulic transport characteristics in wavy channels: comparison between raccoon and serpentine channels. Int. Commun. Heat Mass Transf. 88, 171–176 (2017)CrossRefGoogle Scholar
  26. 26.
    Chang, S.W.; Liou, T.M.; Yu, K.C.; Huang, S.S.: Thermal-hydraulic performance of longitudinal wavy rib along wavy two-pass channel. Appl. Therm. Eng. 133, 224–236 (2018)CrossRefGoogle Scholar
  27. 27.
    Dormohammadi, R.; Farzaneh-gord, M.; Ebrahimi-moghadam, A.; Ahmadi, M.H.: Heat transfer and entropy generation of the nanofluid flow inside sinusoidal wavy channels. J. Mol. Liq. 269, 229–240 (2018)CrossRefGoogle Scholar
  28. 28.
    Sakanova, A.; Chun, C.; Zhao, J.: Performance improvements of microchannel heat sink using wavy channel and nanofluids. Int. J. Heat Mass Transf. 89, 59–74 (2015)CrossRefGoogle Scholar
  29. 29.
    Ahmed, M.A.; Shuaib, N.H.; Yusoff, M.Z.: Numerical investigations on the heat transfer enhancement in a wavy channel using nanofluid. Int. J. Heat Mass Transf. 55, 5891–5898 (2012)CrossRefGoogle Scholar
  30. 30.
    Esfahani, J.A.; Akbarzadeh, M.; Rashidi, S.; Rosen, M.A.; Ellahi, R.: Influences of wavy wall and nanoparticles on entropy generation over heat exchanger plat. Int. J. Heat Mass Transf. 109, 1162–1171 (2017)CrossRefGoogle Scholar
  31. 31.
    Vanaki, S.M.; Mohammed, H.A.; Abdollahi, A.; Wahid, M.A.: Effect of nanoparticle shapes on the heat transfer enhancement in a wavy channel with different phase shifts. J. Mol. Liq. 196, 32–42 (2014)CrossRefGoogle Scholar
  32. 32.
    Akbarzadeh, M.; Rashidi, S.; Bovand, M.; Ellahi, R.: A sensitivity analysis on thermal and pumping power for the flow of nanofluid inside a wavy channel. J. Mol. Liq. 220, 1–13 (2016)CrossRefGoogle Scholar
  33. 33.
    Shi, X.; Wang, Y.; Huai, X.; Cheng, K.: Influence of geometrical parameters on thermal–hydraulic performance and entropy generation in cross-wavy channels with variable air properties. Appl. Therm. Eng. 157, 113714 (2019)CrossRefGoogle Scholar
  34. 34.
    Harikrishnan, S.; Tiwari, S.: Heat transfer characteristics of sinusoidal wavy channel with secondary corrugations. Int. J. Therm. Sci. 145, 105973 (2019)CrossRefGoogle Scholar
  35. 35.
    Ahmadpour, A.; Noori Rahim Abadi, S.M.A.: Thermal-hydraulic performance evaluation of gas-liquid multiphase flows in a vertical sinusoidal wavy channel in the presence/absence of phase change. Int. J. Heat Mass Transf. 138, 677–689 (2019)CrossRefGoogle Scholar
  36. 36.
    Singh, N.; Sivan, R.; Sotoa, M.; Faizal, M.; Ahmed, M.R.: Experimental studies on parallel wavy channel heat exchangers with varying channel inclination angles. Exp. Therm. Fluid Sci. 75, 173–182 (2016)CrossRefGoogle Scholar
  37. 37.
    Harikrishnan, S.; Tiwari, S.: Effect of skewness on flow and heat transfer characteristics of a wavy channel. Int. J. Heat Mass Transf. 120, 956–969 (2018)CrossRefGoogle Scholar
  38. 38.
    Patankar, S.V.: Numerical Heat transfer and Fluid Flow. Taylor & Francis, New York (1980)zbMATHGoogle Scholar
  39. 39.
    Bodoia, J.R.: The finite difference analysis of confined viscous flows. Ph.D. thesis, Carnegie Institute of Technology, Pittsburgh, Pennsylvania (1959)Google Scholar
  40. 40.
    Liu, J.: Flow of a bingham fluid in the entrance region of an annular tube. M.S. thesis, University of Wisconsin-Milwaukee (1974)Google Scholar
  41. 41.
    Hwang, C.L.: Personal Communication. Kansas State University, Manhattan (1973)Google Scholar
  42. 42.
    Stephan, K.: Warmeubergang und druckabfall bei nicht ausgebildeter Laminarstromung in Rohren und in ebenen Spalten. Chem. Ing. Tech. 31, 773–778 (1959)CrossRefGoogle Scholar
  43. 43.
    Bhowmik, H.; Lee, K.-S.: Analysis of heat transfer and pressure drop characteristics in an offset strip fin heat exchanger. Int. J. Commun. Heat Mass 36, 259–263 (2009)CrossRefGoogle Scholar
  44. 44.
    Kim, J.H.; Yun, J.H.; Lee, C.S.: Heat-transfer and friction characteristics for the louver-fin heat exchanger. J. Thermophys. Heat Transf. 18, 58–64 (2004)CrossRefGoogle Scholar
  45. 45.
    Li, J.; Dang, C.; Hihara, E.: Heat transfer enhancement in a parallel, finless heat exchanger using a longitudinal vortex generator, Part A: numerical investigation. Int. J. Heat Mass Transf. 128, 87–97 (2019)CrossRefGoogle Scholar
  46. 46.
    Arman, S.; Hassanzadeh, R.: Effects of the geometric parameters on the thermal-hydraulic performance of the wavy tubes. Int. J. Commun. Heat Mass 96, 27–36 (2018)CrossRefGoogle Scholar
  47. 47.
    Hassanzadeh, R.; Pirdavari, P.; Akbari Rendi, M.: Effects of hot gas passages on the performance of multi-pass cast-iron sectional boilers. Appl. Therm. Eng. 122, 171–180 (2017)CrossRefGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUrmia University of TechnologyUrmiaIran

Personalised recommendations