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Combined heat and mass transfer in natural convection between vertical parallel plates

Kombinierte Wärme- und Stoffübertragung bei freier Konvektion zwischen senkrechten parallelen Platten

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Abstract

This study purposes to examine the effects of latent heat transfer associated with the liquid films vaporization on the heat transfer in the natural convection flows driven by the simultaneous presence of combined buoyancy forces of thermal and mass diffusion. Results are especially presented for an air-water system under various conditions. The influence of channel length and system temperatures on the momentum, heat and mass transfer in the flow are investigated in great detail. The important role of transport of latent heat of vaporization under the situations of buoyancy-aiding and opposing flows is clearly demonstrated.

Zusammenfassung

Diese Studie beabsichtigt die Effekte der gemeinsamen Wärmeübertragung bei der Verdampfung eines Flüssigkeitsfilms und der Wärmeübertragung bei Strömung mit freier Konvektion, verursacht von kombinierten Auftriebskräften aus thermischer und Massendiffusion, zu untersuchen. Die Ergebnisse werden speziell für ein Luft-Wasser-System unter verschiedenen Bedingungen dargestellt. Der Einfluß der Kanallängen und der Systemtemperaturen auf den Impuls, die Wärme- und Stoffübertragung in der Strömung werden im Detail untersucht. Die wichtige Rolle des Wärmetransportes aus der Verdampfung unter Auftriebs- und Gegenstrombedingungen wird klar gezeigt.

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Abbreviations

A :

[(C p1-C p2)/C p ](W r -W o )

b :

half channel width

C p :

specific heat

D :

mass diffusivity

D h :

hydraulic diameter (=4b)

g :

gravitational acceleration

Gr M :

Grashof number (mass transfer)

Gr Mr :

reference Grashof number (mass transfer)

Gr T :

Grashof number (heat transfer)

Gr Tr :

reference Grashof number (heat transfer)

h fg :

latent heat of vaporization

h M :

local mass transfer coefficient

k :

thermal conductivity

l :

channel length

M :

molecular weight

Nu l :

local Nusselt number (latent heat)

Nu s :

local Nusselt number (sensible heat)

Nu x :

overall local Nusselt number

p :

pressure of the moist air in the channel

P:

dimensionless motion pressure (pressure defect)

p m :

motion pressure (pressure defect),p−p o

p o :

ambient pressure

Pr :

Prandtl number, ν/α

p w :

partial pressure of water vapor at interface

Q :

total heat transfer rate

Q o :

total heat transfer rate without liquid water film

q′' x :

interfacial energy flux flowing into air stream

Re :

Reynolds number at the inlet,u o D h /ν

S :

parameter, Eq. (16)

Sc :

Schmidt number, ν/D

Sh x :

local Sherwood number

T :

temperature

u :

axial velocity

u o ,U o :

average inlet velocity

U :

dimensionless axial velocity

ν :

transverse velocity

V :

dimensionless transverse velocity

w1 :

mass fraction of water vapor

W :

dimensionless mass fraction of water vapor

w r :

saturated mass fraction of water vapor atT w andp o

x :

axial coordinate

X :

dimensionless axial coordinate

y :

transverse coordinate

Y :

dimensionless transverse coordinate

α :

thermal diffusivity

θ :

dimensionless temperature, (T−T o )/(T w −T o )

θ′ :

dimensionless temperature, (T−Tw)/(To−Tw)

ν:

kinematic viscosity

ϱ :

density

φ :

relative humidity of air at ambient condition

1:

of water vapor

2:

of air

w :

condition at interface

0:

at inlet condition

r :

at reference condition

References

  1. Aihara, T.: Effects of inlet boundary-conditions on numerical solutions of free convection numerical solutions of free convection between vertical parallel plates. Report No. 258, Institute of High speed Mechanics. Tohoku University 1973

  2. Aung, W.; Fletcher, L. S.; Sernas, V.: Developing laminar free convection between vertical flat plates with asymmetric heating. Int. J. Heat Mass Transfer 15 (1973) 2293–2308

    Google Scholar 

  3. Bodoia, J. R.; Osterle, J. F.: The development of free convection between heated vertical plates. ASME, J. Heat Transfer 84 (1962) 40–44

    Google Scholar 

  4. Sparrow, E. M.; Azevedo, L. F.: Vertical-channel natural convection spanning between the fully-developed limit and the single-plate boundary-layer limit. Int. J. Heat Mass Transfer 28 (1985) 1847–1857

    Google Scholar 

  5. Chen, T. S.; Yuh, C. F.: Combined heat and mass transfer in natural convection on inclined surfaces. Num. Heat Transfer 2 (1979) 233–250

    Google Scholar 

  6. 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) 1135–1151

    Google Scholar 

  7. Chen, T. S.; Yuh, C. F.: Combined heat and mass transfer in natural convection along a vertical cylinder. Int. J. Heat Mass Transfer 23 (1979) 451–461

    Google Scholar 

  8. Hason, M.; Mujumdar, A. S.: Coupled heat and mass transfer in natural convection under flux condition along a vertical cone. Int. Comm. Heat Mass Transfer 11 (1984) 157–172

    Google Scholar 

  9. Lee, T. S.; Parikh, P. G.: Acrivos, A.; Bershader, P.: Natural convection in a vertical channel with opposing buoyancy forces. Int. J. Heat Mass Transfer 25 (1982) 499–511

    Google Scholar 

  10. 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) 1543–1552

    Google Scholar 

  11. Hubbard, G. L.; Denny, V. E.; Mills, A. F.: Droplet evaporation: effects of transients variable properties. Int. J. Heat Mass Transfer 18 (1975) 1003–1008

    Google Scholar 

  12. Fujii, 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 Dai Gaku, Kyu Shu, Japan 1977

    Google Scholar 

  13. Eckert, E. R. G.; Drake, R. M. Jr.: Analysis of Heat and Mass Transfer. New York: McGraw-Hill 1972

    Google Scholar 

  14. Manganaro, J. L.; Hanna, O. T.: Simultaneous energy and mass transfer in the laminar boundary layer with large mass transfer rates toward the surface. A. I. Ch. E. J. 16 (1970) 204–211

    Google Scholar 

  15. Patankar, S. V.: Numerical Heat Transfer and Fluid Flow. New York: McGraw-Hill 1980

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30049, R.O.C.

    W. M. Yan, T. F. Lin & C. J. Chang

Authors
  1. W. M. Yan
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  2. T. F. Lin
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  3. C. J. Chang
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Yan, W.M., Lin, T.F. & Chang, C.J. Combined heat and mass transfer in natural convection between vertical parallel plates. Wärme- und Stoffübertragung 23, 69–76 (1988). https://doi.org/10.1007/BF01637127

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  • DOI: https://doi.org/10.1007/BF01637127

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