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Natural convection heat transfer from round horizontal plate

Wärmeübertragung an einer kreisförmigen, horizontalen Platte bei freier Konvektion

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Abstract

A new approach to the model of natural convection from a horizontal, isothermal round plate and a simplified analytical solution of this model have been presented. In this model two separate regions with different fluid motions have been distinguished. In the first region, inside the boundary layer, the fluid flows concentrically towards the centre of the plate, while in the second one (stagnation region) the fluid is motionless. The presented theory has been verified experimentally.

Zusammenfassung

Ein neuer Lösungsweg für das Modell der freien Konvektion an einer isothermen, kreisförmigen, horizontalen Platte und eine vereinfachte analytische Lösung für dieses Modell werden hier vorgestellt. An diesem Modell wird zwischen zwei Bereichen mit verschiedenen Fluidbewegungen unterschieden. Im ersten Bereich, innerhalb der Grenzschicht, strömt das Fluid konzentrisch in Richtung Plattenmitte, während im zweiten Bereich (Stau-Bereich) die Flüssigkeit in Ruhe ist. Diese Theorie wurde experimentell überprüft.

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Abbreviations

a=λ/c p ·ϱ :

thermal diffusivity

A :

cross-section area (Fig. 2)

A1:

control surface of the plate

c p :

specific heat at constant pressure of the fluid

D :

diameter of the plate

F :

coefficient of boundary layer shape, def. (12)

g :

gravitational acceleration

h :

thickness of the tested fluid in experimental devices

H :

height of a fluid column (see Fig. 3)

i :

specific enthalpy

K,K1:

constants (Eqs. 16 and 26)

m :

mass flux

Nu D =αD/λ :

Nu R =αR/λ — Nusselt numbers

p :

pressure

\(\dot q\) :

heat flux density

Q :

heat flux

R :

radius of the plate

Ra D =g β ΔTD 3/(ν a):

Ra R =g β ΔTR 3/(ν α)Rayleigh numbers

s :

radius of the free buoyant stream (see Fig. 2)

s 1 :

radius of stagnation region

T :

temperature

W :

velocity

x :

length of the boundary layer

x :

horizontal coordinate to the surface

y :

vertical coordinate to the surface

α :

heat transfer coefficient

β :

coefficient of volumetric expansion

δ :

thickness of boundary layer

δ s :

thickness of boundary layer at region of its transformation

θ :

dimensionless temperature

Δ :

difference

λ :

thermal conductivity

ν :

kinematic viscosity

ϱ :

fluid density

Φ :

coefficient defined by Eq. (35)

cr:

critical

w :

related to the wall

x :

related to thex direction or to fluid properties inside boundary layer

y :

related to they direction

∞:

fluid ambient condition

References

  1. Lewandowski, W. M.; Kubski, P.: Methodical investigation of free convection from vertical and horizontal plates. Wärme-Stoffübertrag. 17 (1983) 147–157

    Google Scholar 

  2. Lewandowski, W. M.: Systematyczne badania przejmowania ciepła od płyty poziomej do ciezy w przestrzeni nieograniczonej w warunkach konwekcji natualnej (Systematic investigations of heat transfer from a horizontal plate to a fluid in an unlimited space in the conditions of natural convection) (1908), Doctor's Thesis, Techn. Univ. of Gdańsk

  3. Lewandowski, W. M.: Wymiana ciepła od płaskich powierzchni w warunkach laminarnej konwekcji swobodnej (Heat transfer from flat surfaces under conditions of laminar free convection), Zesz. Nauk, Polit. Gdańsk, t. Mechanika-53, 412, 1–90

  4. Lewandowski, W. M.; Kubski, P.: Effect of the use of the balance and gradient methods as a result of experimental investigation of natural convection action with regard to the conception and construction of measuring apparatus. Wärme-Stoffübertrag. 18 (1984) 247–256

    Google Scholar 

  5. Lewandowski, W. M.: The mechanism of natural convection heat transfer from isothermal vertical, horizontal and inclined plates. Arch. Thermod. 4 (1986) 235–255

    Google Scholar 

  6. Schmidt, E.; Beckman, W.: Das Temperatur- und Geschwindigkeitsfeld von einer wärmeabgebenden senkrechten Platte bei natürlicher Konvektion. Techn. Mech. Thermodyn. (1930) 341–391

  7. Schmidt, E.: Forschung. 3 (1932) 181

    Google Scholar 

  8. Jaluria, Y.: Natural convection heat and mass transfer. Oxford: Pergamon 1980

    Google Scholar 

  9. Rotem, Z.; Claassen, L.: Natural convection above unconfined horizontal surfaces. J. Fluid Mech. 38 (1969) 173–192

    Google Scholar 

  10. Schmidt, E.: Proc. IV. Intern. Congr. for Applied Mech., Cambridge, (1934) 92–98

  11. Fujii, T.; Imura, H.: Natural convection heat transfer from a plate with arbitrary inclination. Int. J. Heat Mass Transfer 15 (1972) 755–765

    Google Scholar 

  12. Kierkus, W.: An analysis of laminar free convection flow and heat transfer about an inclined isothermal plate. Int. J. Heat Mass Transfer 11 (1968) 241–253

    Google Scholar 

  13. Chen, T. S.; Tien, H. C.; Armaly, B. F.: Natural convection on horizontal and vertical plates with variable surface temperature or heat flux. Int. J. Heat Mass Transfer 29 (1986) 1465–1478

    Google Scholar 

  14. Chang, Keun-Shik; Han, Jn-Cheol: Natural convective heat transfer over inclined short plates. Communications in Applied Numerical Methods (1988) 665–673

  15. Kubski, P.: Błonowa wymiana ciepła (Film heat transfer), Mat. Symp. Wym. Ciepła i Masy, Jabłonna (1979)

  16. Takeuchi, M.; Heya, N.; Kimura, T.: Numerical analysis of natural convection from an upward-facing horizontal surface. Heat Transf. Japanese Research, 15 (1986) 17–30

    Google Scholar 

  17. Yu, W.-S.; Lin, H.-T.: Free convection heat transfer from an isothermal plate with arbitrary inclination. Wärme-Stoffübertrag. 23 (1988) 203–211

    Google Scholar 

  18. Goldstein, R. J.; Kei-Shun, Lau: Laminar natural convection from a horizontal plate and the influence of plate edge extensions. J. Fluid Mech. 129 (1983) 55–75

    Google Scholar 

  19. Takeuchi, M.; Ota, Y.; Tanaka, Y.: Laminar natural convection heat transfer from a flat plate in a thermally stratified fluid. Trans. Jap. Soc. Mech. Engers. 40 (1974) 1046

    Google Scholar 

  20. Kamal-Eldin, H.; Salah, A. M.: Natural convection from isothermal flat surfaces. Int. J. Heat Mass. Transfer. 13 (1970) 1873.

    Google Scholar 

  21. Al-Arabi, M., El-Riedy, M.: Natural convection heat transfer from isothermal horizontal plates of different plates of different shapes. Int. J. Heat Mass. Transfer 19 (1976) 1399

    Google Scholar 

  22. Ling, F. F.: A simple laboratory apparatus for measurements of natural convection heat transfer over a flat plate in vertical, inclined and horizontal positions. Int. J. Mech. Eng. Educ. 11 (1982) 245

    Google Scholar 

  23. Churchill, S. W.: Free convection around immersed bodies. Singlephase Convective Heat Transfer. New York: Hemisphere 1983

    Google Scholar 

  24. Singh, P.: Narayan, K. A.: Free convection heat transfer over a horizontal plate at low Prandtl number. Canadian J. Chem. Eng. 67 (1989) 507–512

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Chemical Engineering, Technical University of Gdańsk, ul. Majakowskiego 11/12, 80-952, Gdańsk, Poland

    W. M. Lewandowski, P. Kubski & J. M. Khubeiz

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  1. W. M. Lewandowski
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  2. P. Kubski
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  3. J. M. Khubeiz
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Lewandowski, W.M., Kubski, P. & Khubeiz, J.M. Natural convection heat transfer from round horizontal plate. Wärme- und Stoffübertragung 27, 281–287 (1992). https://doi.org/10.1007/BF01589965

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