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Applied Scientific Research, Section A

, Volume 7, Issue 5, pp 386–392 | Cite as

Steady laminar heat transfer in a circular tube with prescribed wall heat flux

  • R. Siegel
  • E. M. Sparrow
  • T. M. Hallman
Article

Summary

An analysis is performed to determine the heat transfer characteristics for a laminar forced convection flow in a circular tube with prescribed wall heat flux. Results are first obtained for the case of uniform heat flux, and these are then generalized to apply to the situation of arbitrary longitudinal variation of wall heat flux. The solution contains a series expansion whose form is similar to that obtained by Graetz for the uniform wall temperature problem.

Keywords

Heat Flux Nusselt Number Local Nusselt Number Circular Tube Wall Heat Flux 
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.

Symbols

Cn

coefficients in t he series expansion oft +, equation (6)

h

local coefficient of heat transfer

k

thermal conductivity

Nu

Nusselt number,h 2r 0/k

Pr

Prandtl number,c p μ/k =

q

local heat flux per unit area at tube wall

Rn

eigenfunctions of eq. (7)

Re

Reynolds number,ū 2r 0/v

r

radial coordinate measured from tube centerline;r 0, tube radius

t

temperature;t b , bulk fluid temperature;t fd , temperature where heat transfer is fully developed;t 0, fluid temperature at tube inlet (a constant);t w , local tube wall temperature

t+

difference temperature defined by (3)

u

fluid velocity inχ direction

ū

mean fluid velocity inχ direction

x

longitudinal coordinate along the tube length

x*

dummy integration variable

α

thermal diffusivity,k/ ρ c p

βn2

eigenvalues of (7)

μ

de]absolute viscosity

v

kinematic viscosity

ρ

fluid density

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References

  1. 1).
    Sellars, J. R., M. Tribus and J. S. Klein, Trans. Amer. Soc. Mech. Engrs78 (1956) 441.Google Scholar
  2. 2).
    Goldstein, S., Modern Developments in Fluid Dynamics. Clarendon Press, Oxford 1938, p. 622.MATHGoogle Scholar
  3. 3).
    Brinkman, H. C., Appl. Sci. Res.A2 (1951) 120.CrossRefGoogle Scholar
  4. 4).
    Yih, C. S. and J. E. Cermak, Laminar Heat Convection in Pipes and Ducts. Report No. 5, Sept. 1951, Civil Eng. Dept., Colorado Agricultural and Mechanical College.Google Scholar

Copyright information

© Martinus Nijhoff, The Hague/Kluwer Academic Publishers 1958

Authors and Affiliations

  • R. Siegel
    • 1
  • E. M. Sparrow
    • 1
  • T. M. Hallman
    • 1
  1. 1.Lewis Flight Propulsion LaboratoryNACAClevelandU.S.A.

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