Skip to main content
SpringerLink
Log in

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

  • Published:
Applied Scientific Research, Section A Aims and scope Submit manuscript

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.

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

C n :

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 =vα

q :

local heat flux per unit area at tube wall

R n :

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

βn 2 :

eigenvalues of (7)

μ:

de]absolute viscosity

v :

kinematic viscosity

ρ:

fluid density

References

  1. Sellars, J. R., M. Tribus and J. S. Klein, Trans. Amer. Soc. Mech. Engrs78 (1956) 441.

    Google Scholar 

  2. Goldstein, S., Modern Developments in Fluid Dynamics. Clarendon Press, Oxford 1938, p. 622.

    MATH  Google Scholar 

  3. Brinkman, H. C., Appl. Sci. Res.A2 (1951) 120.

    Article  Google Scholar 

  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.

Download references

Author information

Authors and Affiliations

  1. Lewis Flight Propulsion Laboratory, NACA, Cleveland, Ohio, U.S.A.

    R. Siegel, E. M. Sparrow & T. M. Hallman

Authors
  1. R. Siegel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. M. Sparrow
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. M. Hallman
    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

Siegel, R., Sparrow, E.M. & Hallman, T.M. Steady laminar heat transfer in a circular tube with prescribed wall heat flux. Appl. sci. Res. 7, 386–392 (1958). https://doi.org/10.1007/BF03184999

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03184999

Keywords

Search

Navigation