Wärme - und Stoffübertragung

, Volume 29, Issue 3, pp 145–151 | Cite as

Laminar natural convection between partially heated vertical parallel plates

  • K. T. Lee
  • W. M. Yan
Originalarbeiten
Received:

Abstract

A numerical analysis has been performed to examine the characteristics of laminar natural convection in vertical channel with unheated entry and unheated exit. The heated section is subjected to uniform wall temperature (UWT) or uniform heat flux (UHF). Theoretical results for average Nusselt number\(\overline {Nu} \) and induced volume flow rateQ were derived under fully developed condition. Particular attention is paid to investigating the effects of the partially heated section on the induced volume flow rate and Nusselt number for various conditions. Results show that for UWT the induced volume flow rateQ increases with decreasing unheated entry length or increasing total length of heated section and unheated exit. For a fixed unheated entry length, the channel with a longer heated section length causes a greaterQ. Additionally, for both UWT and UHF, the average Nusselt number\(\overline {Nu} \) under fully-developed condition increases with increasing value ofE1/E2.

Keywords

Convection Heat Flux Nusselt Number Apply Physic Parallel Plate 
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

b

half channel width

E1

ratio of unheated exit length to channel length,l1/l

E2

ratio of heated section length to channel length,l2/l

E3

ratio of unheated entry length to channel length,l3/l

GrL

Grashof number, Eq. (4)

g

gravitational acceleration

k

thermal conductivity

l

channel length

l1

unheated exit length

l2

heated section length

l3

unheated entry length

L

dimensionless channel length, Eq. (4)

L1

dimensionless unheated exit length

L2

dimensionless heated section length

L3

dimensionless unheated entry length

\(\overline {Nu} \)

average Nusselt number

Nux

local Nusselt number

p′

pressure defect

P

dimensionless pressure defect, Eq. (4)

Pr

Prandtl number,ν/α

qw

wall heat flux of heated section

Q

dimensionless induced volume flow rate, Eq. (8)

RaE

Rayleigh number based on the heated section length,RaL/E2

RaL

Rayleigh number based on the full channel length,GrLPr

T

temperature

T0

inlet temperature

Tw

wall temperature

u, v

velocity components in thex andy directions, respectively

U, V

dimensionless velocity components in thex andy directions, respectively, Eq. (4)

u0,U0

dimensional and dimensionless inlet velocity, respectively

x, y

coordinates in thex andy directions, respectively

X, Y

dimensionless coordinates in thex andy directions, respectively, Eq. (4)

X′

ratio of longitudinal distance from the entrance of heated section to the heated section length,X′=[X−(L−L1−L2)]/L2

Greek symbols

α

thermal diffusivity

β

thermal expansion coefficient

ν

kinematic viscosity

θ

dimensionless temperature, Eq. (4)

ϱ0

fluid density at ambient temperature

Laminare Naturkonvektion zwischen teilbeheizten senkrechten Parallelplatten

Zusammenfassung

Die numerische Untersuchung soll das Verhalten einer laminaren Strömung bei natürlicher Konvektion in einem senkrechten Kanal mit unbeheiztem Ein- und Austritt klären. Der beheizte Abschnitt wird entweder mit gleichförmiger Wandtemperatur (UWT) oder gleichförmigem Wärmefluß (UHF) beaufschlagt. Bezüglich voll ausgebildeter Strömung ließen sich theoretische Ergebnisse für die mittlere Nußelt-Zahl\(\overline {Nu} \) und den induzierten VolumenstromQ gewinnen. Besonderes Interesse galt der Untersuchung des Einflusses des teilbeaufschlagten Abschnittes auf Volumenstrom und Nußelt-Zahl unter verschiedenen Nebenbedingungen. Die Ergebnisse zeigen, daß im UWT-Fall der induzierte VolumenstromQ mit abnehmender unbeheizter Einlauflänge oder zunehmender Gesamtlänge des Heizabschnittes anwächst. Bei fester unbeheizter Einlauflänge erzeugt der Kanal mit längerem Heizabschnitt einen höheren StromQ.

This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Azevedo, L. F. A.: Natural convection in channel flows. Ph.D. Thesis, Department of Mechanical Engineering, University of Minnesota 1985Google Scholar
  2. 2.
    Burch, T.; Rhodes, T.; Acharya, S.: Laminar natural convection between finitely conducting vertical plates. Int. J. Heat Mass Transfer 28 (1985) 1173–1186Google Scholar
  3. 3.
    Aihara, T.: Effects of inlet boundary-conditions on numerical solutions of free convection between vertical parallel plates. Rep. Inst. High Speed Mech. 28 (1973) 1–27Google Scholar
  4. 4.
    Elenbass, W.: Heat dissipation of parallel plates by free convection. Physica 9 (1942) 1–28Google Scholar
  5. 5.
    Bodoia, J. R.; Osterle, J. F.: The development of free convection between heated vertical plates. ASME, Series C 84 (1962) 40–44Google Scholar
  6. 6.
    Aung, W.: Fully developed laminar free convection between vertical parallel plates heated asymmetrically. Int. J. Heat Mass Transfer 15 (1972) 1577–1580Google Scholar
  7. 7.
    Aung, W.; Fletcher, L. S.; Sernas, V.: Developing laminar free convection between vertical flat plates with asymmetric heating. Int. J. Heat Mass Transfer 15 (1972) 2293–2308Google Scholar
  8. 8.
    Wirtz, R. A.; Stutzman, R. J.: Experiments of free convection between vertical plates with symmetric heating. J. Heat Transfer 104 (1982) 501–507Google Scholar
  9. 9.
    Bar-Cohen, A.; Rohsenow, W. M.: Thermally optimum spacing of vertical, natural convection cooled, parallel plates. J. Heat Transfer 106 (1984) 116–123Google Scholar
  10. 10.
    Hung, Y. H.; Lu, C. T.; Perng, S. W.: A comparison Nu correlation for finite-length channels with asymmetric isoflux heating. 3rd ASME-JSME Thermal Engineering Joint Conf., Reno, Nevada (1991) 17–22 MarchGoogle Scholar
  11. 11.
    Yan, W. M.; Lin, T. F.: Natural convection heat transfer in vertical open channel flows with discrete heating. Int. Comm. Heat Mass Transfer 14 (1987) 187–120Google Scholar
  12. 12.
    Dyer, J. R.: Natural-convection flow through a vertical duct with a restricted entry. Int. J. Heat Mass Transfer 21 (1978) 1341–1354Google Scholar
  13. 13.
    Wirtz, R. A.; Haag, T.: Effects of an unheated entry on natural convection between vertical parallel plates. ASME (1985) 85-WA/HT-14Google Scholar
  14. 14.
    Oothuizen, P. H.: A numerical study of laminar free convection flow through a vertical open partially heated plate duct. Fundamentals of National Convection-Electronic Equipment Cooling, ASME, HTD-Vol. 32 (1984) 41–48Google Scholar
  15. 15.
    Tanda, G.: Natural convection in partially heated vertical channels. Wärme-und Stoffübertrag. 23 (1988) 307–312Google Scholar
  16. 16.
    Nelson, D. J.: Combined heat and mass transfer natural convection between parallel plates. Ph.D. Thesis, Department of Mechanical Engineering, Arizona State University 1986Google Scholar
  17. 17.
    Nelson, D. J.; Wood, B. D.: Fully developed combined heat and mass transfer natural convection between parallel plates with asymmetric boundary condition. Int. J. Heat Mass Transfer 32 (1989) 1789–1792Google Scholar
  18. 18.
    Patanker, S. V.: Numerical heat transfer and fluid flow. New York: Hemisphere/McGraw-Hill 1980, Chapters 4 and 5Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • K. T. Lee
    • 1
  • W. M. Yan
    • 2
  1. 1.Department of Mechanical EngineeringOriental Institute of TechnologyPan-Chiao, TaipeiTaiwan 22064, R.O.C.
  2. 2.Department of Mechanical EngineeringHua Fan Institute of TechnologyTaipeiTaiwan 22305, R.O.C.

Personalised recommendations