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Wärme - und Stoffübertragung

, Volume 27, Issue 8, pp 457–463 | Cite as

Combined radiation and natural convection effects on graetz problem in horizontal isothermal circular tubes

  • J. M. Huang
  • J. D. Lin
Article
  • 98 Downloads

Abstract

A numerical analysis is performed on the combined thermal radiation and mixed convection for a gray fluid flow in a horizontal isothermally-heated circular tube. The governing equations of vorticity-velocity form are employed and solved by DuFort-Frankel method. The contribution of radiation is formulated by integral expression and solved by finite element nodal approximation. The effects of radiation and convection on local Nusselt number and the developing of bulk temperature are presented. The result shows that the heat transfer can be significantly enhanced by the effects of radiation and secondary flow induced by buoyancy. Besides, the fluctuation in local Nusselt number curve which is caused by the existence of secondary flow is reduced by the effect of thermal radiation.

Keywords

Convection Nusselt Number Natural Convection Thermal Radiation Secondary Flow 
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

a, d

tube radius and diameter

C

constant, (a2W f ) ∂Pf/∂Z

f

friction factor, 2τw/(ϱWf2)

g

gravitational acceleration

Gr

Grashof number

Ib

blackbody radiation intensity,σ T4/π

k

thermal conductivity

M, N

number of divisions inr andφ directions, respectively

m, n

number of nodal points inr andφ directions, respectively

ñ

refractive index

Nc

conduction to radiation parameter

Nu

local Nusselt number

P

pressure deviation

p

dimensionless quantity forP

Pe

Peclet number

Pr

Prandtl number

Qr

radiative heat flux

R, φ, Z

cylindrical coordinates

r, φ, z

dimensionless cylindrical coordinates

r, φ, z

optical cylindrical coordinates

Ra

Rayleigh number

Re

Reynolds number

T, T0

local temperature and uniform fluid temperature at entrance

Tr

temperature ratio of inlet fluid and wall

U, V, W

velocity components inR, φ, Z directions due to buoyancy

u, v, w

dimensionless quantities forU, V, W

W′

axial velocity in the thermal entrance region,Wf+W

w′

dimensionless axial velocity,wf+4Ra·w

Greek letters

α

thermal diffusivity

β

coefficient of thermal expansion

the absorption coefficient

μ

viscosity

ν

kinematic viscosity

θ

dimensionless temperature

θb

bulk temperature

ϱ

density

σ

Stefan-Boltzmann constant

τR

optical radius

τw

shear stress

ξ

dimensionless vorticity in axial direction

Subscript

c

characteristic quantity

f

fully developed quantity before thermal entrance

w

quantity at the tube wall

0

condition for purely forced convection

Superscript

-

average value

Der zusammenwirkende Einfluß von Wärmestrahlung und natürlicher Konvektion auf das Graetz-Problem in horizontalen isothermen Kreisrohren

Zusammenfassung

Das Zusammenwirken von Wärmestrahlung und Mischkonvektion auf den Strom eines „grauen“ Fluids in einem horizontalen, isotherm beheizten Kreisrohr wird numerisch untersucht. Der Ansatz der Grundgleichungen erfolgt in der Wirbel-Geschwindigkeitsform, die Lösung mit Hilfe der DuFort-Frankel-Methode. Der Beitrag der Strahlung wird in Integralform angesetzt und mittels einer Finitelement-Knotenpunkt-Approximation gelöst. Der Einfluß von Strahlung und Konvektion auf die lokale Nusselt-Zahl und die Mischtemperatur ist dargestellt. Die Ergebnisse zeigen, daß der Wärmeübergang unter dem Einfluß von Strahlung und auftriebsinduzierter Sekundärströmung wesentlich verstärkt werden kann. Daneben bewirkt die Wärmestrahlung eine Abschwächung der von den Sekundärströmungen ausgelösten Schwankungen im Verlauf der örtlichen Nusselt-Zahl.

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References

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • J. M. Huang
    • 1
  • J. D. Lin
    • 1
  1. 1.Department of Mechanical EngineeringNational Chiao Tung UniversityHsinchuTaiwan Republic of China

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