Skip to main content
SpringerLink
Log in

Laminar natural convection between partially heated vertical parallel plates

Laminare Naturkonvektion zwischen teilbeheizten senkrechten Parallelplatten

  • Originalarbeiten
  • Published:
Wärme - und Stoffübertragung Aims and scope Submit manuscript

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 ofE 1/E 2.

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 via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

b :

half channel width

E 1 :

ratio of unheated exit length to channel length,l 1/l

E 2 :

ratio of heated section length to channel length,l 2/l

E 3 :

ratio of unheated entry length to channel length,l 3/l

Gr L :

Grashof number, Eq. (4)

g :

gravitational acceleration

k :

thermal conductivity

l :

channel length

l 1 :

unheated exit length

l 2 :

heated section length

l 3 :

unheated entry length

L :

dimensionless channel length, Eq. (4)

L 1 :

dimensionless unheated exit length

L 2 :

dimensionless heated section length

L 3 :

dimensionless unheated entry length

\(\overline {Nu} \) :

average Nusselt number

Nu x :

local Nusselt number

p′ :

pressure defect

P :

dimensionless pressure defect, Eq. (4)

Pr :

Prandtl number,ν/α

q w :

wall heat flux of heated section

Q :

dimensionless induced volume flow rate, Eq. (8)

Ra E :

Rayleigh number based on the heated section length,Ra L/E2

Ra L :

Rayleigh number based on the full channel length,Gr LPr

T :

temperature

T 0 :

inlet temperature

T w :

wall temperature

u, v :

velocity components in thex andy directions, respectively

U, V :

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

u 0,U 0 :

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−L 1−L 2)]/L 2

α :

thermal diffusivity

β :

thermal expansion coefficient

ν :

kinematic viscosity

θ :

dimensionless temperature, Eq. (4)

ϱ 0 :

fluid density at ambient temperature

References

  1. Azevedo, L. F. A.: Natural convection in channel flows. Ph.D. Thesis, Department of Mechanical Engineering, University of Minnesota 1985

  2. Burch, T.; Rhodes, T.; Acharya, S.: Laminar natural convection between finitely conducting vertical plates. Int. J. Heat Mass Transfer 28 (1985) 1173–1186

    Google Scholar 

  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) 1–27

    Google Scholar 

  4. Elenbass, W.: Heat dissipation of parallel plates by free convection. Physica 9 (1942) 1–28

    Google Scholar 

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

    Google Scholar 

  6. Aung, W.: Fully developed laminar free convection between vertical parallel plates heated asymmetrically. Int. J. Heat Mass Transfer 15 (1972) 1577–1580

    Google Scholar 

  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) 2293–2308

    Google Scholar 

  8. Wirtz, R. A.; Stutzman, R. J.: Experiments of free convection between vertical plates with symmetric heating. J. Heat Transfer 104 (1982) 501–507

    Google Scholar 

  9. Bar-Cohen, A.; Rohsenow, W. M.: Thermally optimum spacing of vertical, natural convection cooled, parallel plates. J. Heat Transfer 106 (1984) 116–123

    Google Scholar 

  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 March

  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) 187–120

    Google Scholar 

  12. Dyer, J. R.: Natural-convection flow through a vertical duct with a restricted entry. Int. J. Heat Mass Transfer 21 (1978) 1341–1354

    Google Scholar 

  13. Wirtz, R. A.; Haag, T.: Effects of an unheated entry on natural convection between vertical parallel plates. ASME (1985) 85-WA/HT-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) 41–48

  15. Tanda, G.: Natural convection in partially heated vertical channels. Wärme-und Stoffübertrag. 23 (1988) 307–312

    Google Scholar 

  16. Nelson, D. J.: Combined heat and mass transfer natural convection between parallel plates. Ph.D. Thesis, Department of Mechanical Engineering, Arizona State University 1986

  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) 1789–1792

    Google Scholar 

  18. Patanker, S. V.: Numerical heat transfer and fluid flow. New York: Hemisphere/McGraw-Hill 1980, Chapters 4 and 5

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Oriental Institute of Technology, Pan-Chiao, Taipei, Taiwan 22064, R.O.C.

    K. T. Lee

  2. Department of Mechanical Engineering, Hua Fan Institute of Technology, Shih-Ting, Taipei, Taiwan 22305, R.O.C.

    W. M. Yan

Authors
  1. K. T. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. M. Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, K.T., Yan, W.M. Laminar natural convection between partially heated vertical parallel plates. Wärme- und Stoffübertragung 29, 145–151 (1994). https://doi.org/10.1007/BF01548598

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01548598

Keywords

Search

Navigation