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The influence of suction on heat and mass transfer in condensation of mixed vapors

Einfluß der Absaugung auf den Wärme- und Stoffübergang bei der Kondensation von Gemischdämpfen

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Abstract

The film theory by Ackermann can be applied to simultaneous heat and mass transfer processes, if the mass flux normal to the wall is induced by diffusion. Since this condition mostly is not fulfilled when condensing vapor mixtures, an approximative procedure is developed taking into account the influence of suction in condensation heat transfer. The accuracy of the method turns out to be satisfactory compared with results obtained by numerical analysis.

Zusammenfassung

Vorgänge der gleichzeitigen Wärme- und Stoffübertragung lassen sich mit der Ackermannschen Filmtheorie berechnen, wenn der wandnormale Stoffstrom durch Diffusion verursacht wird. Da diese Voraussetzung bei der Kondensation von Gemischdämpfen selten erfüllt ist, wird ein Näherungsverfahren zur Berechnung des Wärmeübergangs unter Berücksichtigung der Absaugung an der Phasengrenze entwickelt. Die erhaltenen Ergebnisse stimmen mit bekannten numerischen Lösungen gut überein.

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Abbreviations

cp :

specific heat capacity

D12 :

binary diffusion coefficient

E:

energy parameter, seeEq.(9)

fi :

suction parameter at the interface

g:

gravitational acceleration

g* :

component of gravitational acceleration in flow direction

ΔhV :

latent heat of vaporzation

k:

correction factor

M:

mass per mol

q:

parameter, see Eq. (27)

q:

heat flux

q0 :

heat flux with vanishing mass transfer resistance

R:

properties parameter, see Eq.(9)

T:

temperature

ΔT=Td-Tw :

temperature difference

u:

velocity in x-direction

vi :

velocity in y-direction at the interface

x:

coordinate along the plate

x1 :

mass species concentration of low boiling component in the liquid

y1 :

mass species concentration of low boiling component in the vapor

Y:

reduced concentration difference

α:

heat transfer coefficient

β:

mass transfer coefficient

δ:

thickness of condensate film

δ′:

modified thickness of condensate film

ηδ :

reduced thickness of condensate film

λ:

thermal conductivity

μ:

dynamic viscosity

ν:

kinematic viscosity

ξ:

dimensionless coordinate, see Eq. (7)

ρ:

density

ϕ:

inclination angle

Gr:

Grashof number, see Eq. (24)

Nu=α·x/λ:

Nusselt number

Pr=ν·ρ·cp/λ:

Prandtl number

Rex =uD·x/ν:

Reynolds number of vapor bulk flow

Sc=ν/D12 :

Schmidt number

Sh=β·x/D12 :

Sherwood number

D:

vapor bulk

i:

interface

k:

corrected

L:

liquid

therm:

thermal suction

w:

wall

0:

vanishing suction

1:

component 1

2:

component 2

References

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Authors and Affiliations

  1. Institut für Techn. Thermodynamik und Verfahrenstechnik, Universität Stuttgart, D-7000, Stuttgart 80

    K. Stephan &  A. Laesecke

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  1. K. Stephan
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  2. A. Laesecke
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Stephan, K., Laesecke, A. The influence of suction on heat and mass transfer in condensation of mixed vapors. Wärme- und Stoffübertragung 13, 115–123 (1980). https://doi.org/10.1007/BF00997641

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  • DOI: https://doi.org/10.1007/BF00997641

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