Advertisement

Film and Dropwise Condensation

Reference work entry

Abstract

The chapter covers four main areas of condensation heat transfer. The process at the vapor-liquid interface during condensation is first discussed. In many cases it is adequate to assume equilibrium at the interface but in dropwise condensation and condensation of metals the interface temperature discontinuity plays and important role. The traditional problems of laminar film condensation on plates and tubes are covered in some detail including natural and forced convection problems, the effect of vapor superheat and of the presence of non-condensing gases in the vapor. The specific problems of condensation on finned surfaces and in microchannels are treated in some detail. An extensive section covers dropwise condensation and incudes both experimental investigations and theory.

Nomenclature

A

Cross-sectional area of channel

A(r)

Distribution function; see Eq. 65

b

Spacing between fin flanks at fin tip

D

Vapor-gas diffusion coefficient

d

Diameter of tube

d0

Tube diameter measured to fin tip

dr

Tube diameter measured to fin root

F

Defined in Eq. 23

Fx

Defined in Eq. 17

f

Fraction of surface area covered by drops with base radius greater than r

ff

Defined in Eq. 35

fs

Defined in Eq. 36

G

Dimensionless quantity defined in Eq. 12, mass flux of vapor in channel

g

Specific force of gravity

h

Radial height of fin

hv

Effective vertical height of fin; see Eqs. 40 and 41

hfg

Specific latent heat of evaporation

K

Defined in Eq. 19

K1

Constant in Eq. 47

K2

Constant defined in Eq. 60

K20

Ratio of base to curved surface area of drop; see Eq. 52

K21

Defined in Eq. 62

K3

Constant in Eq. 69

k

Thermal conductivity of condensate

L

Height of condensing surface

L0

Defined in Eq. 57

L3

Defined in Eq. 70

Mv

Molar mass of vapor

Mg

Molar mass of noncondensing gas

m

Interface mass flux, condensation mass flux

mx

Local condensation mass flux

\( \overline{Nu} \)

Mean Nusselt number

Nud

Nusselt number for condensation on horizontal tube

Nux

Local Nusselt number

N(r)

Distribution function; see Eq. 66

P

Pressure of vapor-gas mixture

Pv

Vapor pressure

p

Perimeter of channel

Psat(Tv)

Saturation temperature at Tv

Psat(T0)

Saturation temperature at T0

n

Constant in Eq. 64

Q

Heat flux

Q1

Defined in Eq. 58

Q2

Defined in Eq. 59

Q21

Value of Q2 for steam at Tsat = 373.15 K, i.e., Q21 = 2.556 GW/m2

\( q,\overline{q} \)

Heat flux, mean heat flux for surface

qb

Mean heat flux at base of drop

qi

Mean heat flux at curved surface of drop

qNu

Heat flux given by Nusselt theory

q*

Dimensionless heat flux defined in Eq. 72

R

Specific ideal-gas constant

Rex

Reynolds number, Uρvx/μv

Red

Reynolds number, Uρvd/μv

\( \overset{\sim }{R} \)ex

Two-phase Reynolds number, Uρx/μ

\( \overset{\sim }{R}e \)d

Two-phase Reynolds number, Uρd/μ

r

Base radius of drop

rc

Radius of curvature of condensate surface, radius of curved surface of drop

rmax

Effective mean base radius of largest drop

rmin

Base radius of smallest viable drop

Sc

Schmidt number, μvv D

Sp

Defined in Eq. 26

s

Spacing between fin flanks at fin root

Tv

Vapor temperature

Tw

Wall temperature

Tsat

Saturation temperature

T1sat

373.15 K

T0

Vapor-liquid interface temperature

T*

Reference temperature

Tt

Defined in Eq. 37

Tf

Defined in Eq. 38

Ts

Defined in Eq. 39, saturation temperature

t

Fin thickness at tip

tp

Promoter layer thickness

U

Vapor or vapor-gas mixture free stream velocity

u

Condensate streamwise velocity

vf

Specific volume of saturated liquid

vg

Specific volume of saturated vapor

vfg

v g − v f

W

Mass fraction of noncondensing gas in the bulk

W0

Mass fraction of noncondensing gas at the interface

X

Defined in Eq. 25

x

Coordinate along channel normal to streamwise direction

y

Coordinate normal to surface

z

Streamwise coordinate

Greek Symbols

α

Heat-transfer coefficient qT

αz

Local (averaged around perimeter) heat-transfer coefficient at distance z along channel

β

Constant in Eq. 6, half angle at fin tip in Eqs. 33, 34, 35, and 36, contact angle, channel inclination to vertical in Eq. 43.

βx

Defined in Eq. 30

γ

Ratio of principal specific heat capacities of vapor

δ

Local condensate film thickness

ΔP

Difference between vapor pressure and saturation pressure at interface temperature

ΔT

Vapor-surface temperature difference

ΔTc

Temperature difference attributable to conduction in drop

ΔTi

Temperature difference attributable to interphase matter transfer

ΔTp

Temperature difference across promoter layer

ΔTσ

Temperature difference attributable to surface curvature

Δρ

ρfρg

ζ

Defined in Eq. 31, defined in Eq. 45

εΔ T

Enhancement ratio

θ

Celsius temperature, dimensionless temperature difference defined in Eq. 73

θ0

Defined in Eq. 74

λ

Thermal conductivity of liquid

λl

Thermal conductivity of liquid

λp

Thermal conductivity of promoter layer

μ

Viscosity of condensate

μv

Viscosity of vapor or vapor-gas mixture

v

μ/ρ

ξ

Constant in Eq. 1, function defined in Eq. 42

ρ

Density of liquid, condensate

ρv

Density of vapor or vapor-gas mixture

ρg

Density of saturated vapor

ρf

Density of saturated liquid

ρfg

ρfρg

\( \tilde{\rho} \)

ρρv

σ

Surface tension

τι

Streamwise vapor shear stress at condensate surface

ϕ

Retention angle measured from top of tube

χ

Vapor quality

ψ

Angle between normal to channel surface and Y coordinate (see Fig. 1 of Wang and Rose 2005)

ω

Defined in Eq. 29

References

  1. Adamek T, Webb RL (1990) Prediction of film condensation on horizontal integral fin tubes. Int J Heat Mass Transf 33:1721–1735CrossRefGoogle Scholar
  2. Ali H, Wang HS, Briggs A, Rose JW (2013) Effect of vapor velocity and pressure on Marangoni condensation of steam-ethanol mixtures on a horizontal tube. J Heat Transf 135:091602-1Google Scholar
  3. Bandhauer TM, Agarwal A, Garimella S (2006) Measurements and modelling of condensation heat transfer coefficients in circular microchannels. Trans ASME J Heat Transf 128:1050–1059CrossRefGoogle Scholar
  4. Beatty KO, Katz DL (1948) Condensation of vapors on outside of finned tubes. Chem Eng Prog 44:55–70Google Scholar
  5. Berman LD (1969) Determination of mass transfer coefficient in calculations on condensation of steam containing air. Teploenergetika 16:68–71Google Scholar
  6. Briggs A, Rose (1994) Effect of fin efficiency on a model for condensation heat transfer on a horizontal integral fin tube. Int J Heat Mass Transf 37(Suppl):457–463CrossRefGoogle Scholar
  7. Briggs A, Rose JW (1998) Effects of interphase matter transfer and non-uniform wall temperature on a model for condensation on low-finned tubes. I J Transp Phenom 1:41–49Google Scholar
  8. Cavallini A, Del Col D, Doretti L, Matkovic M, Rossetto L, Zilio C (2005) A model for condensation inside minichannels. In: Proceedings of the ASME National heat transfer conference, San Francisco, paper HT2005-72528Google Scholar
  9. Cess RD (1960) Laminar film condensation on a flat plate in the absence of a body force. Z Angew Math Phys 11:426–433MathSciNetMATHCrossRefGoogle Scholar
  10. Chen MM (1961a) Analytical solution of laminar film condensation: part 1 flat plates. Trans ASME J Heat Transf 83:48–54CrossRefGoogle Scholar
  11. Chen MM (1961b) Analytical solution of laminar film condensation: part 2 single and multiple horizontal tubes. Trans ASME J Heat Transf 83:55–60CrossRefGoogle Scholar
  12. Citakoglu E, Rose JW (1968) Dropwise condensation – some factors influencing the validity of heat-transfer measurements. Int J Heat Mass Transf 11:523–537CrossRefGoogle Scholar
  13. Citakoglu E, Rose JW (1969) Dropwise condensation – the effect of surface inclination. Int J Heat Mass Transf 12:645–651CrossRefGoogle Scholar
  14. Denny VE, Mills AF (1969) Laminar film condensation of a flowing vapor on a horizontal cylinder at normal gravity. Trans ASME 91C:495–501CrossRefGoogle Scholar
  15. Enright R, Miljkovic N, Alverado JL, Kim K, Rose JW (2014) Dropwise condensation on micro- and nanostructured surfaces. Nanoscale Microscale Thermophysical Eng 18(3):223–250CrossRefGoogle Scholar
  16. Fatica N, Katz DL (1949) Dropwise condensation. Chem Eng Prog 45:661–674Google Scholar
  17. Fujii T, Uehara H (1972) Laminar filmwise condensation on a vertical surface. Int J Heat Mass Transf 15:217–233CrossRefGoogle Scholar
  18. Fujii T, Uehara H, Kurata C (1972a) Laminar filmwise condensation of a flowing vapour on a horizontal cylinder. Int J Heat Mass Transf 15:235–246CrossRefGoogle Scholar
  19. Fujii T, Uehara H, Oda K (1972b) Film condensation on a surface with uniform heat flux and body force convection. Heat Transf Jpn Res 4:76–83Google Scholar
  20. Fujii T, Uehara H, Mihara K, Kato K (1977) Forced convection condensation in the presence of non-condensables – a theoretical treatment for two-phase laminar boundary layer. Univ Kyushu Res Inst Ind Sci Rep 66:53–80Google Scholar
  21. Graham C (1969) The limiting mechanisms of dropwise condensation. PhD thesis, M.I.TGoogle Scholar
  22. Honda H, Nozu S (1987) A prediction method for heat transfer during film condensation on horizontal low integral-fin tubes. Trans ASME J Heat Transf 109:218–225CrossRefGoogle Scholar
  23. Honda H, Nozu S, Mitsumori K (1983) Augmentation of heat transfer on horizontal finned tubes by attaching a porous drainage plate. Proc ASME-JSME Therm Eng Joint Conf 3:289–296Google Scholar
  24. Ishiyama T, Yano T, Fujikawa S (2004a) Molecular dynamics study of kinetic boundary condition at an interface between argon vapor and its condensed phase. Phys Fluids 16:2899–2906MATHCrossRefGoogle Scholar
  25. Ishiyama T, Yano T, Fujikawa S (2004b) Molecular dynamics study of kinetic boundary condition at an interface between a polyatomic vapor and its condensed phase. Phys Fluids 16:4713–4726MATHCrossRefGoogle Scholar
  26. Ishiyama T, Yano T, Fujikawa S (2005) Kinetic boundary condition at a vapor-liquid interface. Phys Rev Lett 95:084504CrossRefGoogle Scholar
  27. Karkhu VA, Borovkov VP (1971) Film condensation of vapor at finely-finned horizontal tubes. Heat Transf Sov Res 3:183–191Google Scholar
  28. Kim S-M, Mudawar I (2012) Flow condensation in parallel microchannels – part 2: heat transfer results and correlation technique. Int J Heat Mass Transf 55:984–994MATHCrossRefGoogle Scholar
  29. Kim S-M, Kim J, Mudawar I (2012) Flow condensation in parallel microchannels – part 1: experimental results and pressure drop correlations. Int J Heat Mass Transf 55:971–983MATHCrossRefGoogle Scholar
  30. Knudsen M (1915) Die Maximale Verdampfungsgeschwindigkeit des Quecksilbers. Ann Phys Chem 47:697–708CrossRefGoogle Scholar
  31. Koh JC (1962) Laminar film condensation of condensable gases and mixtures on a flat plate. Proc 4th USA Nat Cong Appl Mech 2:1327–1336Google Scholar
  32. Koh JC, Sparrow EM, Hartnett JP (1961) The two-phase boundary layer in laminar film condensation. Int J Heat Mass Transf 2:69–82CrossRefGoogle Scholar
  33. Koyama S, Kuwahara K, Nakashita K (2003b) Condensation of refrigerant in a multi-port channel. In: 1st international conference on microchannels & minichannels, Rochester, pp 193–205Google Scholar
  34. Koyama S, Kuwahara K, Nakashita K, Yamamoto K (2003a) An experimental study on condensation of refrigerant R134a in a multi-port extruded tube. Int J Refrig 24:425–432CrossRefGoogle Scholar
  35. Labuntsov DA (1967) An analysis of evaporation and condensation processes. Teplofiz Vysok Temp 5:647–653Google Scholar
  36. Labuntsov DA, Kryukov AP (1979) Analysis of intensive evaporation and condensation. Int J Heat Mass Transf 22:989–1002MATHCrossRefGoogle Scholar
  37. Labuntsov DA, Muratova TM (1969) Influence of motion on evaporation and condensation. Teplofiz Vysok Temp 7:1146–1150Google Scholar
  38. Le Fevre EJ (1964) See appendix G of Rose (1964)Google Scholar
  39. Le Fevre EJ, Rose JW (1964) Heat-transfer during dropwise condensation of steam. Int J Heat Mass Transf 7:272–273CrossRefGoogle Scholar
  40. Le Fevre EJ, Rose JW (1965) An experimental study of heat transfer by dropwise condensation. Int J Heat Mass Transf 8:1117–1133CrossRefGoogle Scholar
  41. Le Fevre EJ, Rose JW (1966) A theory of heat transfer by dropwise condensation. Proc 3rd Int Heat Transf Conf 2:362–375Google Scholar
  42. Lee WC, Rose JW (1982) Film condensation on a horizontal tube – effect of vapour velocity. Proc 7th Int Heat Transf Conf 5:101–106Google Scholar
  43. Masuda H, Rose (1987) Static configuration of liquid film on horizontal tubes with low radial fins. Proc R Soc Lond A410:125–139CrossRefGoogle Scholar
  44. Meland R, Frezzotti A, Ytrehus T, Hafskjold B (2004) Nonequilibrium molecular-dynamics simulation of net evaporation and net condensation, and evaluation of the gas-kinetic boundary condition at the interface. Phys Fluids 16:223–243MATHCrossRefGoogle Scholar
  45. Memory SB, Rose JW (1986) Film condensation of ethylene glycol on a horizontal tube at high vapour velocity. Proc 8th Int Heat transfer Conf, San Francisco 4:1607–1612Google Scholar
  46. Memory SB, Rose JW (1991) Free convection laminar film condensation on a horizontal tube with variable wall temperature. Int J Heat Mass Transf 34:2775–2778MATHCrossRefGoogle Scholar
  47. Michael AG, Rose JW, Daniels LC (1989) Forced convection condensation on a horizontal tube. Trans ASME J Heat Transfer 111:792–797CrossRefGoogle Scholar
  48. Mijlkovic N, Preston DJ, Wang EN (2016) Recent developments in altered wettability for enhancing condensation. In: Thome JR, Kim J (eds) Encyclopaedia of two-phase heat transfer and flow II, special topics and applications 3 special topics in condensation. World Scientific, Singapore, pp 85–131Google Scholar
  49. Mills AF, Tan C, Chung DK (1974) Experimental study of condensation from steam-air mixtures flowing over a horizontal tube: overall condensation rates. Proc 5th Int Heat Transf Conf Tokyo 5:20–23Google Scholar
  50. Minkowicz WJ, Sparrow EM (1966) Condensation heat transfer in the presence of noncondensables, interfacial resistance, superheating, variable properties and diffusion. Int J Heat Mass Transf 9:1125–1144CrossRefGoogle Scholar
  51. Nagayama G, Tsuruta T (2003) A general expression for the condensation coefficient based on transition state theory and molecular dynamics simulation. J Chem Phys 118:1392–1399CrossRefGoogle Scholar
  52. Niknejad J, Rose JW (1981) Interphase matter transfer – an experimental study of condensation of mercury. Proc R Soc London A 378:305–327CrossRefGoogle Scholar
  53. Niknejad J, Rose JW (1984) Comparisons between experiment and theory for dropwise condensation of mercury. Int J Heat Mass Transf 27:2253–2257CrossRefGoogle Scholar
  54. Nusselt W (1916) Die Oberflachencondensation des Wassserdampfes Z. Vereines Deutsch Ing 60:569–575Google Scholar
  55. Rahbar S, Rose JW (1984) New measurements for forced convection film condensation. 1st UK Natl Conf Heat Transf 1:609–632Google Scholar
  56. Rifert VG (1980) A new method for calculating rates of condensation on finned tubes. Heat Transfer Sov Res 12:142–147Google Scholar
  57. Rose JW (1964) Dropwise condensation of steam on vertical planes. PhD thesis, London UniversityGoogle Scholar
  58. Rose JW (1967) On the mechanism of dropwise condensation. Int J Heat Mass Transf 10:755–762CrossRefGoogle Scholar
  59. Rose JW (1969) Condensation of a vapour in the presence of a non-condensing gas. Int J Heat Mass Transf 12:233–237CrossRefGoogle Scholar
  60. Rose JW (1976) Further aspects of dropwise condensation theory. Int J Heat Mass Transf 19:1363–1370CrossRefGoogle Scholar
  61. Rose JW (1980) Approximate equations for forced convection condensation in the presence of a non-condensing gas on a flat plate and horizontal tube. Int J Heat Mass Transf 23:539–546CrossRefGoogle Scholar
  62. Rose JW (1984) Effect of pressure gradient in forced convection film condensation on a horizontal tube. Int J Heat Mass Transf 27:39–47CrossRefGoogle Scholar
  63. Rose JW (1988a) Fundamentals of condensation heat transfer: laminar film condensation. JSME Int J Ser 2(31):357–375Google Scholar
  64. Rose JW (1988b) Some aspects of condensation heat transfer theory. Int Com Heat Mass Transf 15:449–473CrossRefGoogle Scholar
  65. Rose (1989) A new interpolation formula for forced convection condensation on a horizontal surface. Trans ASME 111:818–819CrossRefGoogle Scholar
  66. Rose JW (1994) An approximate equation for the vapor-side heat-transfer coefficient for condensation on low-finned tubes. Int J Heat Mass Transf 37:865–875MATHCrossRefGoogle Scholar
  67. Rose JW (1998a) Interphase matter transfer the condensation coefficient and dropwise condensation. In: Proceedings of the 11th international heat transfer conference, vol 1, Kyongju, 23–28 Aug 1998, pp 89–104Google Scholar
  68. Rose JW (1998b) Condensation heat transfer fundamentals. Trans IChemE 76(part a):143–152CrossRefGoogle Scholar
  69. Rose JW (2000) Accurate approximate equations for intensive subsonic evaporation. Int J Heat Mass Transf 43:3869–3875MATHCrossRefGoogle Scholar
  70. Rose JW (2002) Dropwise condensation theory and experiment: a review. Proc Instn Mech Eng Part A J Power Energy 251:115–170CrossRefGoogle Scholar
  71. Rose JW, Glicksman LR (1973) Dropwise condensation – on the distribution of drop sizes. Int J Heat Mass Transf 16:411–425CrossRefGoogle Scholar
  72. Schmidt E, Schurig W, Sellschopp W (1936) Versuche uber die Kondensation in Film- und Tropfenform. Tech Mech Thermodynamik 1:53–63Google Scholar
  73. Schrage RW (1953) A theoretical study of interphase mass transfer. Columbia University Press, New YorkGoogle Scholar
  74. Shekriladze IG, Gomelauri VI (1966) The theoretical study of laminar film condensation of a flowing vapour. Int J Heat Mass Transf 9:581–591CrossRefGoogle Scholar
  75. Sone Y, Onishi Y (1973) Kinetic theory of evaporation and condensation. J Phys Soc Jpn 35:1773–1776CrossRefGoogle Scholar
  76. Sparrow EM, Gregg JL (1959) A boundary layer treatment of laminar film condensation. J Heat Transfer 81:13–23Google Scholar
  77. Sparrow EM, Lin SH (1964) Condensation in the presence of a non-condensing gas. J Heat Transfer 86:430–436CrossRefGoogle Scholar
  78. Sparrow EM, Minkowycz WM, Saddy M (1967) Forced convection condensation in the presence of non-condensables and interface resistance. Int J Heat Mass Transf 10:1829–1845CrossRefGoogle Scholar
  79. Stylianou S, Rose JW (1980) Dropwise condensation on surfaces having different thermal conductivity. J Heat Transfer 102:477–482CrossRefGoogle Scholar
  80. Stylianou S, Rose JW (1982) Dropwise condensation of ethane diol. PhysicoChem Hydrodyn 3:199–213Google Scholar
  81. Su Q, Yu GX, Wang HS, Rose JW (2009) Microchannel condensation: correlations and theory. Int J Refrig 32:1149–1152CrossRefGoogle Scholar
  82. Tanaka H (1975) A theoretical study on dropwise condensation. J Heat Transfer 97:72–98CrossRefGoogle Scholar
  83. Tanasawa H (1974). Critical size of departing drops. In: Proceedings of the 5th international heat transfer conference, vol 7, Tokyo, 3–7 Sept 1974, p 188Google Scholar
  84. Tanasawa I, Ochiai J (1973) Experimental study on heat transfer during dropwise condensation. Bull Jpn Soc Mech Eng 16:1184–1197CrossRefGoogle Scholar
  85. Tanasawa I, Ochiai J, Utaka Y, Enya S (1974) Proceedings of the 11th Japan heat transfer symposium, p 229 (in Japanese)Google Scholar
  86. Tasnasawa I, Utaka Y (1983) Measurement of condensation curves for dropwise condensation of steam at atmospheric pressure. J Heat Transf 105(3):633–638CrossRefGoogle Scholar
  87. Tsuruta T, Nagayama G (2005) A microscopic formulation of condensation coefficient and interface transport phenomena. Energy 30(6):795–805CrossRefGoogle Scholar
  88. Umur A, Griffith P (1965) Mechanism of dropwise condensation. J Heat Transf 87:275–282CrossRefGoogle Scholar
  89. Wang HS, Rose JW (2005) A theory of film condensation in horizontal noncircular section microchannels. Trans ASME J Heat Transf 127:1096–1105CrossRefGoogle Scholar
  90. Wang HS, Rose JW (2011) Theory of heat transfer during condensation in microchannels. Int J Heat Mass Transf 54:2525–2534MATHCrossRefGoogle Scholar
  91. Wang ZJ, Chen M, Guo ZY (2003) A molecular study of the liquid-vapor interphase transport. Microscale Thermophys Eng 7:275–289CrossRefGoogle Scholar
  92. Wanniarachchi AS, Marto PJ, Rose JW (1985) Film condensation of steam on horizontal finned tubes. Effect of fin spacing, thickness and height (1985). Multiphase flow and heat transfer. ASME HTD 47:93–99Google Scholar
  93. Webb RL, Rudy TM, Kedzierski MA (1985) Prediction of condensation coefficient on horizontal integral-fin tubes. Trans ASME J Heat Transfer 107:369–376CrossRefGoogle Scholar
  94. Wenzel H (1957) Versuche über Tropfenkondensation. Allg Wärmetech 8:53–59Google Scholar
  95. Wilmshurst R, Rose JW (1970) Dropwise condensation – further heat-transfer measurements. In: Proceedings of the 4th international heat-transfer conference, Versailles, Paper Cs 1.4Google Scholar
  96. Wilmshurst R, Rose JW (1974) Dropwise and filmwise condensation of aniline, ethane diol and nitrobenzene. In: Proceedings of the 5th international heat-transfer conference, Tokyo. Japan Soc Mech Eng, pp 269–273Google Scholar
  97. Ytrehus T, Alvestad J (1981) A Mott-Smith solution for non-linear condensation. In: Fisher SS (ed) Rarefied Gas Dynamics, Prog. Astro. and Aero.74, pp 330–345Google Scholar
  98. Zhou Y-Q, Rose (1996) Effect of two-dimensional conduction in the condensate film on laminar film condensation on a horizontal tube with variable wall temperature. Int J Heat Mass Transf 39:3187–3191CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Engineering and Materials ScienceQueen Mary University of LondonLondonUK

Section editors and affiliations

  • Vijay K. Dhir
    • 1
  1. 1.Mechanical and Aerospace EngineeringUniversity of California Los AngelesLos AngelesUSA

Personalised recommendations