Advertisement

Wärme - und Stoffübertragung

, Volume 25, Issue 4, pp 221–231 | Cite as

Combined heat and mass transfer in laminar gas stream flowing over an evaporating liquid film

  • Y. L. Tsay
  • T. F. Lin
Article

Abstract

A numerical analysis was carried out to study the detailed heat and mass transfer characteristics in laminar gas stream flowing over a falling liquid water film by solving the respective governing equations for the liquid film and gas stream together. It was observed that the cooling of the liquid film is mainly caused by the latent heat transfer connected with the vaporization of the liquid film. Significant liquid cooling results for the system with a high inlet liquid temperature, high gas stream velocity or a low liquid flowrate. Additionally, the predicted Nusselt and Sherwood numbers were correlated.

Keywords

Stream Flow Liquid Film Sherwood Number Liquid Cool Mass Transfer Characteristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

Cp

specific heat

D

mass diffusivity

g

gravitational acceleration

G

gas stream

Grx

Grashof number = [g β (T l,in T g,∞ )x3]/ν2

hfg

latent heat of evaporation

hm

mass transfer coefficient, Eq. (18)

hT

heat transfer coefficient, Eq. (14)

Ks,Kl

parameters, Eqs. (24), (25)

Ki,Km

parameters, Eqs. (26), (27)

L

liquid film

M

molecular weight

Mr

relative flux of film vaporization, Eq. (22)

\(\dot m_l \)

mass flowrate of liquid water per unit width

m″v,i

interfacial mass flux of water vapor, Eq. (12)

Nul

Nusselt number for latent heat transport, Eq. (17)

Nui

overall Nusselt number =Nu l +Nu s

Nus

Nusselt number for sensible heat transport, Eq. (16)

Rex

Reynolds number=(u g,∞ )/ν g

ng,nl

number of grid points in gas stream and liquid film iny direction

nx

number of grid points inx direction

P

pressure

q″l,i

interfacial latent heat flux =m″ v, i h fg

q″i

overall interfacial heat flux =q″ l,i +q″ s,i

q″s,i

interfacial sensible heat flux in gas side = −(λ g ∂T g /∂y) i

Sh

Sherwood number, Eq. (19)

T

temperature

u, υ

longitudinal and lateral velocities

wv

mass fraction of water vapor

x, y

longitudinal and lateral coordinates

Δx,Δy

longitudinal and lateral grid sizes

Greek symbols

β

expansion coefficient

δl

film thickness

λ

conductivity

μ

dynamic viscosity

ν

kinematic viscosity

ϱ

density

Subscripts

a

of air

ave

average

g

of gas stream

i

at interface

in

at inlet

j, k

thejth longitudinal andkth lateral grid points

l

of liquid

v

of water vapor

sat

at saturated state

w

at wall

free stream value

Kombinierte Wärme- und Stoffübertragung in einem laminaren Gasstrom über einen verdunstenden Flüssigkeitsfilm

Zusammenfassung

Eine numerische Analyse wurde ausgearbeitet, um einzelne Wärme- und Stoffübertragungsmerkmale in einem laminaren Gasstrom zu untersuchen, der über einen frei fallenden Wasserfilm strömt. Die in Betracht kommenden bestehenden Gleichungen für den Flüssigkeitsfilm und den Gasstrom wurden zusammen gelöst. Es wurde beobachtet, daß die Kühlwirkung des Flüssigkeitsfilms hauptsächlich von der latenten Wärmeübertragung verursacht wird, die mit der Verdampfung des Flüssigkeitsfilms verbunden ist. Bedeutende Ergebnisse der Flüssigkeitskühlung wurden für Systeme mit hoher Eintrittstemperatur der Flüssigkeit, hoher Gasstromgeschwindigkeit oder niedriger Fließgeschwindigkeit der Flüssigkeit erzielt. Die Nusselt- und Sherwood-Zahlen sind dargestellt worden.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gill, W. N.; Casal, E. D., Zeh, D. W.: Binary diffusion and heat transfer in laminar free convection boundary layers on a vertical plate. Int. J. Heat Mass Transfer 8 (1965) 1135–1151Google Scholar
  2. 2.
    Saville, D. A.; Churchill, S. W.: Simultaneous heat and mass transfer in free convection boundary layers. A.I.Ch.E. Jl 16 (1970) 268–273Google Scholar
  3. 3.
    Bottemanne, F. A.: Theoretical solution of simultaneous heat and mass transfer by free convection about a vertical flat plate. Appl. Sci. Res. 25 (1971) 137–149Google Scholar
  4. 4.
    Gebhart, B.; Pera, L.: The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion. Int. J. Heat Mass Transfer 14 (1971) 2025–2050Google Scholar
  5. 5.
    Chen, T. S.; Yuh, C. F.: Combined heat and mass transfer in natural convection on inclined surfaces. Numer. Heat Transfer 2 (1979) 233–250Google Scholar
  6. 6.
    Chang, C. J.; Lin, T. F.; Yan, W. M.: Natural convection flows in a vertical, open tube resulting from combined buoyancy effects of thermal and mass diffusion. Int. J. Heat Mass Transfer 29 (1986) 1543–1552Google Scholar
  7. 7.
    Chandra, V.; Savery, C. W.: Forced convective heat and mass transfer from a falling film to a laminar external boundary layer. Int. J. Heat Mass Transfer 17 (1974) 1549–1557Google Scholar
  8. 8.
    Chandra, V.: Mass, momentum and heat transfer from a falling film to a countercurrent air stream. Ph.D. thesis, Diexel University (1975)Google Scholar
  9. 9.
    Schröppel, J.; Thiele, F.: On the calculation of momentum, heat and mass transfer in laminar and turbulent boundary layer flows along a vaporizing liquid film. Numer. Heat Transfer 6 (1983) 475–496Google Scholar
  10. 10.
    Chow, L. C.; Chung, J. N.: Evaporation of water into a laminar stream of air and superheated steam. Int. J. Heat Mass Transfer 26 (1983) 373–380Google Scholar
  11. 11.
    Chow, L. C.; Chung, J. N.: Water evaporation into a turbulent stream of air, humid air or superheated steam. 21st ASME/AICHE National Heat Transfer Conference, Seattle, WA, ASME paper No. 83-HT-2 (1983)Google Scholar
  12. 12.
    Haji, M.; Chow, L. C.: Experimental measurement of water evaporation rates into air and superheated steam. J. Heat Transfer 110 (1988) 237–242Google Scholar
  13. 13.
    Shembharkar, T. R.; Pai, B. R.: Prediction of film cooling with a liquid coolant. Int. J. Heat Mass Transfer 29 (1986) 899–908Google Scholar
  14. 14.
    Baumann, W. W.; Thiele, F.: Heat and mass transfer in two-component film evaporation in a vertical tube. Proc. 8th Int. Heat Transfer Conf. 4 (1986) 1843–1848Google Scholar
  15. 15.
    Anderson, D. A.; Tannehill, J. C.; Pletcher, R. H.: Computational fluid mechanics and heat transfer. New York: Hemisphere/McGraw-Hill 1984Google Scholar
  16. 16.
    Szewezyk, A. A.: Combined forced and free-convection laminar flow. J. Heat Transfer 86 (1964) 501–507Google Scholar
  17. 17.
    Fuji, T.; Kato, Y.; Mihara, K.: Expressions of transport and thermodynamic properties of air, steam and water. Sei San Ka Gaku Ken Kyu, Jo, Report No. 66, Kyu Shu University, Kyu Shu, Japan 1977Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Y. L. Tsay
    • 1
  • T. F. Lin
    • 1
  1. 1.Department of Mechanical EngineeringNational Chiao Tung UniversityHsinchuTaiwan ROC

Personalised recommendations