Heat and Mass Transfer

, Volume 54, Issue 10, pp 3025–3033 | Cite as

Condensation heat transfer correlation for water-ethanol vapor mixture flowing through a plate heat exchanger

  • Weiqing Zhou
  • Shenhua Hu
  • Xiangrong Ma
  • Feng Zhou


Condensation heat transfer coefficient (HTC) as a function of outlet vapor quality was investigated using water-ethanol vapor mixture of different ethanol vapor concentrations (0%, 1%, 2%, 5%, 10%, 20%) under three different system pressures (31 kPa, 47 kPa, 83 kPa). A heat transfer coefficient was developed by applying multiple linear regression method to experimental data, taking into account the dimensionless numbers which represents the Marangoni condensation effects, such as Re, Pr, Ja, Ma and Sh. The developed correlation can predict the condensation performance within a deviation range from −22% to 32%. Taking PHE’s characteristic into consideration and bringing in Ma number and Sh number, a new correlation was developed, which showed a much more accurate prediction, within a deviation from −3.2% to 7.9%.





Ethanol concentration in main vapor flow stream, %, constant


Mass transfer coefficient, m2·s−1


Flux, kg.s−1


Heat transfer coefficient on condensation surface, kW·m−2·K−1

\( \overline{h} \)

Average surface heat transfer coefficient, kW·m−2·K−1


Latent heat, J·kg−1


Jackob number


Mass flow rate, kg·h−1


Marangoni number


Pressure, Pa


Prandtl number


Heat flux on condensation surface, kW·m−2


Sherwood number


Temperature, K


Liquid phase ethanol concentration at liquid-vapor interface, %


Vapor phase ethanol concentration at liquid-vapor interface, %


Vapor quality at exit

\( \overline{x} \)

Mean vapor quality in PHE

Greek symbols


Constant ratio of concentration over temperature in liquid vapor equilibrium


Conductivity, W·m−1·K−1


Ratio of constant pressure specific heat over constant volume specific heat


Mass transfer coefficient in vapor diffusion layer, m·s−1


Dynamic viscosity, Pa·s


Density, kg·m−3


Surface tension, N·m−1



















This project has been supported by National Natural Science Foundation of China through Grant No. 51166013, the Scientific Research Foundations of Nanjing Institute of Technology (YKJ201445, YKJ201533).


  1. 1.
    Wang JS, Yan JJ, Hu SH et al (2009) Marangoni condensation heat transfer of water-ethanol mixtures on a vertical surface with temperature gradients. Int J Heat Mass Transf 52(9–10):2324–2334CrossRefGoogle Scholar
  2. 2.
    Utaka Y, Wang S (2004) Characteristic curves and the promotion effect of ethanol addition on steam condensation heat transfer. Int J Heat Mass Transf 47(21):4507–4516CrossRefGoogle Scholar
  3. 3.
    Murase T, Wang HS, Rose JW (2007) Marangoni condensation of steam–ethanol mixtures on a horizontal tube. Int J Heat Mass Transf 50(19–20):3774–3779CrossRefGoogle Scholar
  4. 4.
    Hu SH, Yan JJ, Wang JS (2007) Effect of temperature gradient on Marangoni condensation heat transfer for ethanol–water mixtures. Int J Multiphase Flow 33(9):935–947CrossRefGoogle Scholar
  5. 5.
    Nusselt W (1916) Die Oberflachencondensation des Wasserdamphes. Zeitschrift VDI 60:541–569Google Scholar
  6. 6.
    Troupe RA, Morgan JC, Prifiti J (1960) The plate heater versatile chemical engineering tool. Chem Eng Prog 56:124–128Google Scholar
  7. 7.
    Buonopane RA, Troupe RA, M JC(1963)Heat transfer design methods for plate heat exchangers. Chem Eng Prog 59: 57–61Google Scholar
  8. 8.
    Clark DF (1974) Plate heat exchanger design and recent developments. Chem Eng 285:275–279Google Scholar
  9. 9.
    Thonon B, Bontemps A (2002) Condensation of Pure and Mixture of Hydrocarbons in a Compact Heat Exchanger: Experiments and Modelling. Heat Transf Eng 23(6):3–17CrossRefGoogle Scholar
  10. 10.
    YanYY LHC, Lin TF (1999) Condensation heat transfer and pressure drop of refrigerant R-134a in a plate heat exchanger. Int J Heat Mass Transf 42(6):993–1006CrossRefGoogle Scholar
  11. 11.
    Würfel R, Ostrowski N (2004) Experimental investigations of heat transfer and pressure drop during the condensation process within plate heat exchangers of the herringbone-type. Int J Therm Sci 43(1):59–68CrossRefGoogle Scholar
  12. 12.
    Longo GA (2008) Refrigerant R134a condensation heat transfer and pressure drop inside a small brazed plate heat exchanger. Int J Refrig 31(5):780–789CrossRefGoogle Scholar
  13. 13.
    Mancin S, Col DD, Rossetto L (2012) Partial condensation of R407C and R410A refrigerants inside a plate heat exchanger. Exp Thermal Fluid Sci 36:149–157CrossRefGoogle Scholar
  14. 14.
    Mancin S, Col DD, Rossetto L (2012) Condensation of superheated vapour of R410A and R407C inside plate heat exchangers: experimental results and simulation procedure. Int J Refrig 35(7):2003–2013CrossRefGoogle Scholar
  15. 15.
    Alberto C, Davide DC, Luca D et al (2006) Condensation in horizontal smooth tubes: a new heat transfer model for heat exchanger design. Heat Transf Eng 27(8):31–38CrossRefGoogle Scholar
  16. 16.
    Mancin S, Col DD, Rossetto L (2013) R32 partial condensation inside a brazed plate heat exchanger. Int J Ref 36(2):601–611CrossRefGoogle Scholar
  17. 17.
    Hayes N, Jokar A, Ayub ZH (2011) Study of carbon dioxide condensation in chevron plate exchangers; heat transfer analysis. Int J Heat Mass Transf 54(5):1121–1131CrossRefGoogle Scholar
  18. 18.
    Kuo WS, Lie YM, Hsieh YY et al (2005) Condensation heat transfer and pressure drop of refrigerant R-410A flow in a vertical plate heat exchanger. Int J Heat Mass Transf 48(25):5205–5220CrossRefGoogle Scholar
  19. 19.
    Kandlikar SG (1990) A general correlation for saturated two-phase flow boiling heat transfer inside horizontal and vertical tubes. J Heat Transf 112(1):219–228CrossRefGoogle Scholar
  20. 20.
    Hu SH, Ma XR, Zhou WQ (2017) Condensation heat transfer of ethanol-water vapor in a plate heat exchanger. Appl Therm Eng 113:1047–1055Google Scholar
  21. 21.
    Fredenlund A, Jones RL, Prausnitz JM (1975) Group Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AICHE J 27(5):1086–1099CrossRefGoogle Scholar
  22. 22.
    Moffat RJ (1982) Contributions to the theory of single-sample uncertainty analysis. J Fluids Eng Trans ASME 104:250–260CrossRefGoogle Scholar
  23. 23.
    Fujii T (1991) Theory of laminar film condensation. Springer, New YorkCrossRefzbMATHGoogle Scholar
  24. 24.
    Hu SH, Yan JJ, Li Y (2011) Interface temperature of condensate for binary mixtures. Proc Chin Soc Elect Eng 31(11):68–73Google Scholar
  25. 25.
    Hwang CC, Weng CI (1987) Finite-amplitude stability analysis of liquid films down a vertical wall with and without interfacial phase change. Int J Multiphase Flow 13(6):803–814CrossRefzbMATHGoogle Scholar
  26. 26.
    Stephan K (2006) Interface temperature and heat transfer in forced convection laminar film condensation of binary mixtures. Int J Heat Mass Transf 49(3):805–809MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Lucas K (1976) Combined body force and forced convection in laminar film condensation of mixed vapours—integral and finite difference treatment. Int J Heat Mass Transf 19(11):1273–1280CrossRefGoogle Scholar
  28. 28.
    Wilke CR (1950) A viscosity equation for gas mixtures. J Chem Phys 18(4):517–519CrossRefGoogle Scholar
  29. 29.
    Li R (1987) Mass Transfer (in Chinese). Beijing Aviation College Press, BeijingGoogle Scholar
  30. 30.
    Wang JS, Yan JJ, Li Y, Hu SH et al (2016) Correlation for marangoni condensation heat transfer of water–ethanol mixture vapors. Heat Transf Eng 37(9):774–782CrossRefGoogle Scholar
  31. 31.
    Wang ZZ, Zhao ZN (1993) Analysis of performance of steam condensation heat transfer and pressure drop in plate condensers. Heat Transf Eng 14(4):32–41CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Weiqing Zhou
    • 1
  • Shenhua Hu
    • 1
  • Xiangrong Ma
    • 2
  • Feng Zhou
    • 3
  1. 1.Electric Power Simulation and Control Engineering CenterNanjing Institute of TechnologyNanjingChina
  2. 2.School of Communication EngineeringNanjing Institute of TechnologyNanjingChina
  3. 3.Toyota Research Institute of North AmericaAnn ArborUSA

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