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Film and Dropwise Condensation

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Handbook of Thermal Science and Engineering

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.

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Abbreviations

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

d 0 :

Tube diameter measured to fin tip

d r :

Tube diameter measured to fin root

F :

Defined in Eq. 23

F x :

Defined in Eq. 17

f :

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

f f :

Defined in Eq. 35

f s :

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

h v :

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

h fg :

Specific latent heat of evaporation

K :

Defined in Eq. 19

K 1 :

Constant in Eq. 47

K 2 :

Constant defined in Eq. 60

K 20 :

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

K 21 :

Defined in Eq. 62

K 3 :

Constant in Eq. 69

k :

Thermal conductivity of condensate

L :

Height of condensing surface

L 0 :

Defined in Eq. 57

L 3 :

Defined in Eq. 70

M v :

Molar mass of vapor

M g :

Molar mass of noncondensing gas

m :

Interface mass flux, condensation mass flux

m x :

Local condensation mass flux

\( \overline{Nu} \) :

Mean Nusselt number

Nu d :

Nusselt number for condensation on horizontal tube

Nu x :

Local Nusselt number

N(r):

Distribution function; see Eq. 66

P :

Pressure of vapor-gas mixture

P v :

Vapor pressure

p :

Perimeter of channel

P sat(T v ):

Saturation temperature at T v

P sat(T 0 ):

Saturation temperature at T 0

n :

Constant in Eq. 64

Q :

Heat flux

Q 1 :

Defined in Eq. 58

Q 2 :

Defined in Eq. 59

Q 21 :

Value of Q 2 for steam at T sat = 373.15 K, i.e., Q 21 = 2.556 GW/m2

\( q,\overline{q} \) :

Heat flux, mean heat flux for surface

q b :

Mean heat flux at base of drop

q i :

Mean heat flux at curved surface of drop

q Nu :

Heat flux given by Nusselt theory

q* :

Dimensionless heat flux defined in Eq. 72

R :

Specific ideal-gas constant

Re x :

Reynolds number, U ∞ ρ v x/μ v

Re d :

Reynolds number, U ∞ ρ v d/μ v

\( \overset{\sim }{R} \)e x :

Two-phase Reynolds number, U ∞ ρx/μ

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

Two-phase Reynolds number, U ∞ ρd/μ

r :

Base radius of drop

r c :

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

r max :

Effective mean base radius of largest drop

r min :

Base radius of smallest viable drop

Sc :

Schmidt number, μ v /ρ v D

Sp :

Defined in Eq. 26

s :

Spacing between fin flanks at fin root

T v :

Vapor temperature

T w :

Wall temperature

T sat :

Saturation temperature

T 1sat :

373.15 K

T 0 :

Vapor-liquid interface temperature

T*:

Reference temperature

T t :

Defined in Eq. 37

T f :

Defined in Eq. 38

T s :

Defined in Eq. 39, saturation temperature

t :

Fin thickness at tip

t p :

Promoter layer thickness

U ∞ :

Vapor or vapor-gas mixture free stream velocity

u :

Condensate streamwise velocity

v f :

Specific volume of saturated liquid

v g :

Specific volume of saturated vapor

v fg :

v g − v f

W ∞ :

Mass fraction of noncondensing gas in the bulk

W 0 :

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

α :

Heat-transfer coefficient q/ΔT

α z :

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.

β x :

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

ΔT c :

Temperature difference attributable to conduction in drop

ΔT i :

Temperature difference attributable to interphase matter transfer

ΔT p :

Temperature difference across promoter layer

ΔT σ :

Temperature difference attributable to surface curvature

Δρ :

ρ f − ρ g

ζ :

Defined in Eq. 31, defined in Eq. 45

ε ΔT :

Enhancement ratio

θ :

Celsius temperature, dimensionless temperature difference defined in Eq. 73

θ 0 :

Defined in Eq. 74

λ :

Thermal conductivity of liquid

λ l :

Thermal conductivity of liquid

λ p :

Thermal conductivity of promoter layer

μ :

Viscosity of condensate

μ v :

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

ρ v :

Density of vapor or vapor-gas mixture

ρ g :

Density of saturated vapor

ρ f :

Density of saturated liquid

ρ fg :

ρ f − ρ g

\( \tilde{\rho} \) :

ρ – ρ v

σ :

Surface tension

τ ι :

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

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Authors and Affiliations

  1. School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, E1 4NS, London, UK

    John W. Rose

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  1. Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota, USA

    Francis A. Kulacki

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  1. Politecnica/COPPE, Universidade Federal do Rio de Janeiro,, Rio de Janeiro, Brasília, Brazil

    Renato Cotta

  2. Department of Mechanical Engineering, University of California, Riverside, California, USA

    Kambiz Vafai

  3. Herff College of Engineering, The University of Memphis, Memphis, Tennessee, USA

    Sumanta Acharya

  4. Gas Technology Institute, Illinois, Illinois, USA

    Yaroslav Chudnovsky

  5. Rm 8260, University of Toronto, Toronto, Ontario, Canada

    Javad Mostaghimi

  6. Cekmeköy Campus, Özyegin University, Çekmeköy - Istanbul, Turkey

    Pinar Mengüc

  7. Mechanical and Aerospace Engineering, University of California Los Angeles, Los Angeles, California, USA

    Vijay K. Dhir

  8. Mechanical and Aerospace Engineering, University of California Los Angeles, 48-121 E4, Box 951597, 900095-1597, Los Angeles, California, USA

    Vijay K. Dhir

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Rose, J.W. (2017). Film and Dropwise Condensation. In: Kulacki, F. (eds) Handbook of Thermal Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-32003-8_50-1

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