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Wärme - und Stoffübertragung

, Volume 14, Issue 3, pp 157–164 | Cite as

Turbulent natural convection over a slender circular cylinder

  • T. Y. Na
  • J. P. Chiou
Article

Abstract

The transverse-curvature effect on the heat transfer in the turbulent natural convection flow from the outer surface of a slender vertical circular cylinder is studied by an improved integral method for various values of Prandtl numbers and for various values of a transverse curvature parameter.

Keywords

Heat Transfer Convection Outer Surface Apply Physic Natural Convection 
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

heat capacity, kcal/kg°C

g

gravitational acceleration

L,m,n

constants

q

heat flux, kcal/m2 h

r0

radius of cylinder

T

temperature, °C

u

velocity in x-direction, m/h

uβ

velocity head due to buoyancy, m/h\(u_\beta ^2 = \int {g\beta } (t - t_\infty )dx\)

v

velocity in y-direction, m/h

x

flow direction, m

y

normal direction to flow, m

r

r0-y

v*

friction velocity,\(\sqrt {\tau _w /\rho } \)

u+

dimensionless velocity, u=u/v*

T+

dimensionless temperature,

x+

dimensionless coordinate, x+=xv*

y+

dimensionless coordinate, y+=yv*

Rex

local Reynolds number, Rex=ux/ν

Nux

local Nusselt number, Nux=hx/k

Prx

Prandtl number, μCp/k

Grx

Grashof number, Grx=gβ x3(Tw-Tc2

Rax

Rayleigh number, Rax=Grx Pr

Greek Symbols

β

body expansion coefficient, l/°C

δ

boundary-layer thickness, m

ɛ

eddy diffusivity, m2 /h

θ

dimensionless temperature

ν

kinematic viscosity, m2 /h

ρ

density, kg/m3

τ

shear stress, N/m2

δ+

dimensionless boundary-layer thickness

Subscripts

w

wall condition

condition far from the wall

Turbulente natürliche Konvektion an einem schlanken Kreiszylinder

Zusammenfassung

Der Einfluß der Querkrümmung auf die Wärmeübertragung von der Außenoberfläche eines dünnen senkrechten Kreiszylinders in die turbulente, natürliche Konvektionsströmung wird mittels eines verbesserten Integral-Verfahrens für verschiedene Werte der Prandtl-Zahlen und der Querkrümmungsparameter untersucht.

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References

  1. 1.
    Sparrow, E. M.; Gregg, J. L.: Laminar Free Convection Heat Transfer From the Outer Surface of a Vertical Circular Cylinder. Trans. ASME, V 78 (1956) 1823Google Scholar
  2. 2.
    Cebeci, T.: Laminar-Free-Convective-Heat Transfer From the Outer Surface of a Vertical Slender Circular Cylinder. 5th International Heat Transfer Conference, Tokyo, Japan, 1974Google Scholar
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    Cebeci, T.; Qasim, J.; Na, T.Y.: Free Convection Heat Transfer From Slender Cylinders Subject to Uniform Wall Heat Flux. Heat and Mass Transfer, 1 (1974) 159–162Google Scholar
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    Fujii, T.; Takeuchi, M.; Fujii, M.; Suzaki, K.; Uehara, H.: Experiments on Natural-Convection Heat Transfer From the Outer Surface of a Vertical Cylinder to Liquids. International Journal of Heat and Mass Transfer. 13 (1970) 753–787Google Scholar
  7. 7.
    Jacob, M.: Heat Transfer. New York: John Wiley (1949)Google Scholar
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    Saunders, O.A.: The Effect of Pressure Upon Natural Convection in Air. Proc. Roy. Soc., Series A, A157 (1936) 278–291Google Scholar
  9. 9.
    Fujii, T.: Experimental Studies of Free Convection Heat Transfer. Bull. J.S.M.E., 2 (1959) 555–558Google Scholar
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    Touloukian, Y.S.; Hawkin, G.A.; Jacob, M.: Heat Transfer by Free Convection From Heated Vertical Surface to Liquids. Trans. ASME, (1948) 13–23Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • T. Y. Na
    • 1
  • J. P. Chiou
    • 2
  1. 1.University of Michigan-DearbornDearbornUSA
  2. 2.University of DetroitDetroitUSA

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