Heat and Mass Transfer

, Volume 49, Issue 11, pp 1535–1548 | Cite as

Chaotic advection induced heat transfer enhancement in a chevron-type plate heat exchanger

  • A. Tohidi
  • S. M. HosseinalipourEmail author
  • P. Taheri
  • N. M. Nouri
  • A. S. Mujumdar


The present work examines the role of chaotic mixing as a means of heat transfer enhancement in plate heat exchangers. In order to demonstrate the chaotic behavior, sensitivity to initial conditions and horseshoe maps are visualized. The Nusselt number and the friction factor were computed in the range of reynolds number, 1 < Re < 10. The Nusselt number increases considerably in chaotic models whereas the friction factor increases only marginally.


Heat Transfer Heat Exchanger Nusselt Number Lyapunov Exponent Chevron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Projected length (m)


Cross section of PHE (m2)


Distance between chevron plates (m)


Sugar to water mass ratio in the mixture


Specific heat capacity (Jkg−1K−1)


Hydraulic diameter (m)


Distance of two article at time t = 0 (m)

\( \overline{{{\text{d}}_{\text{n}} }} \)

Mean distance of M tracers (m)


Fanning friction factor


Heat transfer coefficient (Jm−2K−1s−1)


Fluid Thermal conductivity (Jm−1K−1s−1)


Global iteration number


Effective of chevron plate length (m)


Total length of chevron plate (m)


Volumetric flow rate (kg/s)


Nusselt number


Wave length of chevron plate corrugation (m)


Constant heat flux (W/m2)


Reynolds number


Time (s)


Temperature (K)


Bulk fluid temperature (K)

\( {\text{T}}_{\text{w}} \)

Mean wall temperature in PHE channel cross section (K)


x component of fluid velocity (m/s)

\( \overline{\text{u}} \)

Mean velocity in PHE channel (m/s)


Velocity vector of fluid element (m/s)


y component of fluid velocity (m/s)


z component of fluid velocity (m/s)


Chevron plate width (m)


Total width of chevron plate (m)


x position (m)


Initial x position (m)


y position (m)


Initial y position (m)


z position (m)


Initial z position (m)

Greek symbols


Chevron plate angle (º)


Channel aspect ratio


Pressure loss (Pa)


Time step (s)


Lagrangian Lyapunov exponent


Localized Lyapunov exponent

\( \overline{{{{\uplambda}}_{\text{n}} }} \)

Finite time Lyapunov exponent


Viscosity of apple juice (Pa.s)

\( {{\upmu}}_{\text{w}} \)

Viscosity of water (Pa.s)

\( {{\uprho}} \)

Density of fluid (kg/m3)

\( \phi \)

Area enlargement factor

\( \psi \)

Degrees of freedom

\( M_{\psi } \)

Convergence monitor


  1. 1.
    Brennan JG (2006) Food processing handbook. Wiley, KGaAGoogle Scholar
  2. 2.
    Fernandes CS, Dias RP, Nobrega JM, Maia JM (2007) Laminar flow in chevron-type plate heat exchangers: CFD analysis of tortuosity, shape factor and friction factor. Chem Eng Process 46:825–833CrossRefGoogle Scholar
  3. 3.
    Kakaç S, Liu H (2002) Heat exchangers: selection, rating and thermal design. CRC Press, UKCrossRefGoogle Scholar
  4. 4.
    Durmus A, Benli H, Kurtbas I, Gül H (2009) Investigation of heat transfer and pressure drop in plate heat exchangers having different surface profiles. Int J Heat Mass Transf 52:1451–1457CrossRefGoogle Scholar
  5. 5.
    Gut JAW, Pinto JM (2007) Optimal configuration design for plate heat exchangers. Int J Heat Mass Transf 47:4833–4848CrossRefGoogle Scholar
  6. 6.
    Wang L, Sunden B (2003) Optimal design of plate heat exchangers with and without pressure drop specifications. Appl Therm Eng 23:295–311CrossRefGoogle Scholar
  7. 7.
    Kanaris AG, Mouza AA, Paras SV (2009) Optimal design of a plate heat exchanger with undulated surfaces. Int J Therm Sci 48:1184–1195CrossRefGoogle Scholar
  8. 8.
    Chagny C, Castelain C, Peerhossaini H (2000) Chaotic heat transfer for heat exchanger design and comparison with a regular regime for a large range of Reynolds numbers. Appl Therm Eng 20:1615–1648CrossRefGoogle Scholar
  9. 9.
    Metcalfe G, Lester D (2009) Mixing and heat transfer of highly viscous food products with a continuous chaotic duct flow. J Food Eng 95:21–29CrossRefGoogle Scholar
  10. 10.
    Acharya N, SEN M (1991) Heat transfer enhancement in coiled tubes by chaotic mixing. Int J Heat Mass Transf 35(10):2475–2489CrossRefGoogle Scholar
  11. 11.
    Jones SW, Thomas OM, Aref H (1989) Chaotic advection by laminar flow in twisted pipe. J Fluid Mech 209:335–357MathSciNetCrossRefGoogle Scholar
  12. 12.
    Acharya N, Sen M, Cheng HC (1992) Heat transfer enhancement in coiled tubes by chaotic mixing. Int J Heat Mass Transf 35:2475–2489CrossRefGoogle Scholar
  13. 13.
    Peerhossaini H, Le Guer Y (1991) Chaotic motion in the Dean instability flow-a heat exchanger design. Bull Am Phys Soc 35:2229Google Scholar
  14. 14.
    Mokrani A, Castelain C, Le Guer Y, Peerhossaini H (1998) Mesure du compartment chaotique des trajectories produites dans un ecoulementde Dean alterneen regimelaminaire. Rev Gen Therm 37:459–474CrossRefGoogle Scholar
  15. 15.
    Mokrani A, Castelain C, Peerhossaini H (1997) The effects of chaotic advection on heat transfer. Int J Heat Mass Transf 40:3089–3104CrossRefGoogle Scholar
  16. 16.
    Acharya N, Sen M, Chang HC (1992) Applications of chaotic heat and mass transfer enhancement. AIChE Symp Ser 286:44–49Google Scholar
  17. 17.
    Yamagishi A, Inaba T, Yamaguchi Y (2007) Chaotic analysis of mixing enhancement in steady laminar flows through multiple pipe bends. Int J Heat Mass Transf 50:1238–1247CrossRefGoogle Scholar
  18. 18.
    Kumar V, Nigam KDP (2005) Numerical simulation of steady flow fields in coiled flow inverter. Int J Heat Mass Transf 48:4811–4828CrossRefGoogle Scholar
  19. 19.
    Kumar V, Mridha M, Gupta AK, Nigam KDP (2007) Coiled flow inverter as a heat exchanger. Chem Eng Sci 62:2386–2396CrossRefGoogle Scholar
  20. 20.
    Mridha M, Nigam KDP (2008) Coiled flow inverter as an inline mixer. Chem Eng Sci 63:1724–1732CrossRefGoogle Scholar
  21. 21.
    Kumar V, Nigam KDP (2007) Laminar convective heat transfer in chaotic configuration. Int J Heat Mass Transf 50:2469–2479CrossRefGoogle Scholar
  22. 22.
    Castelain C, Peerhossaini H (2006) A chaotic heat exchanger for PEMFC cooling applications. J Power Sour 156(1):114–118CrossRefGoogle Scholar
  23. 23.
    Fernandes CS, Dias RP, N′obrega IM, Afonso JM, Melo LF, Maia JM (2005) Simulation of stirred yoghurt processing in plate heat exchangers. J Food Eng 69:281–290CrossRefGoogle Scholar
  24. 24.
    Costenla DT, Lozano JE, Crapiste GH (1989) Thermophysical properties of clarified apple juice as a function of concentration and temperature. J Food Sci 54(3):663–668CrossRefGoogle Scholar
  25. 25.
    Martin H (1996) A theoretical approach to predict the performance of chevron type plate heat exchangers. Chem Eng Process 35:301–310CrossRefGoogle Scholar
  26. 26.
    Afonso IM, Cruz P, Maia JM, Melo LF (2008) Simplified numerical simulation to obtain heat transfer correlations for stirred yoghurt in a plate heat exchanger. Food Bioprod Process 86:296–303CrossRefGoogle Scholar
  27. 27.
    Ding J, Manglik RM (1996) Analytical solutions for laminar fully developed flows in double-sine shaped ducts. Heat Mass Transf 31:269–277CrossRefGoogle Scholar
  28. 28.
    Wanniarachchi AS, Ratnam U, Tilton BE, Dutta-Roy K (1995) Approximate correlations for chevron-type plate heat exchangers. In: Proceedings ASME HTD, 314, National heat transfer conference, 12:145–151Google Scholar
  29. 29.
    Kumar H. (1984) The plate heat exchanger: construction and design. Proceedings first UK national conference on heat transfer, University of Leeds, Inst Chem Symp 86:1275–1288Google Scholar
  30. 30.
    Ottino JM (1989) The kinematics of mixing: stretching, chaos and transport. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • A. Tohidi
    • 1
  • S. M. Hosseinalipour
    • 1
    Email author
  • P. Taheri
    • 1
  • N. M. Nouri
    • 2
  • A. S. Mujumdar
    • 3
  1. 1.CFD and CAE Laboratory, Department of Mechanical EngineeringIran University of Science and TechnologyNarmakIran
  2. 2.Hydrodynamic Laboratory, Department of Mechanical EngineeringIran University of Science and TechnologyNarmakIran
  3. 3.Mineral, Metal and Materials Technology Centre (M3TC), Department of Mechanical EngineeringNational University of SingaporeSingaporeSingapore

Personalised recommendations