Heat and Mass Transfer

, Volume 55, Issue 11, pp 3041–3051 | Cite as

Heat transfer during film condensation inside plain tubes. Review of theoretical research

  • Volodymyr Rifert
  • Volodymyr SeredaEmail author
  • Andrii Solomakha


This paper critically reviews the existing theoretical models of heat transfer prediction in condensing inside plain tubes. More than 20 theoretical methods and correlations for heat transfer prediction during different modes of condensate film flow and phase distribution are considered. Lack of prior substantiation of correct application of different turbulent viscosity models for heat transfer calculation in condensing with and without influence of interfacial shear stress has been noted. The existing discrepancy of ±10% between different theoretical methods for heat transfer prediction during fully developed turbulence flow of condensate film without predominant influence of vapour velocity is shown. The dependence of theoretical methods on accuracy of frictional pressure drop determination in condensing with predominant influence of vapour velocity is highlighted. The method by Bae and others (1969) is recommended as the most correct theoretical method for prediction of heat transfer coefficients in annular flow of the phases in various heat exchangers, particularly in the evaporative systems of thermal desalinating plants, air conditioning systems, safety systems of reactors, heaters of power plants and condensers of cooling equipment.



specific heat, [J/(kgK)]


friction coefficient


inner diameter of tube, [m]


frictional pressure drop, [Pa/m]


liquid Froude number (\( =\frac{\rho_v\left({\rho}_l-{\rho}_v\right){u}_v^2}{\rho_l^2{\left({v}_lg\right)}^{2/3}} \))


mass velocity, [kg/(m2s)]


gravitational acceleration, [m/s2]


Galileo number (\( ={\rho}_l\left({\rho}_l-{\rho}_v\right)g{d}^3/{\mu}_l^2 \))


height of the stream, [m]


Kutateladze number (=cplΔT/ΔvapH)


length of the tube, [m]


dimensionless Nusselt number (=αd/λl)


film Nusselt number, (\( =\frac{\alpha }{\lambda_l}{\left(\frac{v_l^2}{g}\right)}^{1/3} \))


Prandtl number


heat flux, [W/m2]


film Reynolds number (=qz/(Δvapl))


liquid Reynolds number (=G(1 − x)d/μl)


vapour Reynolds number (=Gxd/μv)


temperature, [°C]


axial velocity, [m/s]


mass vapour quality


Martinelli parameter (=(μl/μv)0.1(ρv/ρl)0.5[(1 − x)/x]0.9)


radial distance from the tube wall, [m]


axial coordinate, [m]

Greek symbols


heat transfer coefficient, [W/(m2K)]


parameter related to shear stress at the interphase, (=CfFrl/2)


thickness of the condensate film, [m]


heat of vapourization, [J/kg]


temperature difference (=ts-tw), [K]


turbulent viscosity, [m2/s]


eddy diffusivity of heat, [m2/s]


thermal conductivity, [W/(mK)]


dynamic viscosity, [Pa·s]


kinematic viscosity, [m2/s]


density, [kg/m3]


shear stress (\( ={C}_f{\rho}_v{u}_v^2/2 \)), [Pa]


gravity force (=ρl), [Pa]


angular coordinate, [°]


parameter that takes into account influence of two-phase flow


surface tension, [N/m]

Sub and superscripts








corresponding to the entire flow as a liquid














at the outer edge of the film


dimensionless symbol


Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”KyivUkraine
  2. 2.National University of Water and Environmental EngineeringRivneUkraine

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