Combined Forced and Free Turbulent Convection in a Vertical Circular Tube With Volume Heat Sources and Constant Wall Heat Addition

[+] Author and Article Information
M. S. Ojalvo

Special Engineering Programs, Engineering Division, National Science Foundation, Washington, D. C.

D. K. Anand

Space Research and Analysis, Applied Physics Laboratory, The Johns Hopkins University, Silver Spring, Md.; Mechanical Engineering, University of Maryland, College Park, Md.

R. P. Dunbar

USN, USS Harry E. Yarnell

J. Heat Transfer 89(4), 328-334 (Nov 01, 1967) (7 pages) doi:10.1115/1.3614393 History: Received March 10, 1967; Online August 25, 2011


A study is made of turbulent heat transfer in a vertical circular tube under conditions of combined forced and free convection with uniform heat flux at the wall and volume heat sources. The basic conservation laws are reduced to three coupled, linear integrodifferential equations which are numerically solved by means of a digital computer. An improved expression for eddy viscosity variation with radial distance and degree of turbulence is used in the solution, as is an expression for the ratio of eddy diffusivity of heat to momentum. The parameters in the integrodifferential equations are: Prandtl number, Pr; Rayleigh number, Ra; friction Reynolds number, Re*; and a volume heat source parameter, F. For fixed values of these parameters, the solution results in: the velocity and temperature profiles; the pressure drop parameter, C; mixed-mean-to-wall temperature difference, φm ; Nusselt number, Nu; and Reynolds number, Re. The solutions to this fairly general problem compare very closely to solutions of the following special cases (with no volume heat source): pure forced convection, laminar flow; pure forced convection, turbulent flow; and combined forced and free-convection, laminar flow.

Copyright © 1967 by ASME
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In