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Entry-length flow in a vertical cooled pipe

Published online by Cambridge University Press:  28 March 2006

H. S. Takhar
H. S. Takhar
Affiliation:
University of Manchester
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Abstract

A numerical solution is presented for predicting the flow and heat transfer due to free convection in the entry region of a cooled vertical pipe, open at both ends. Following Lighthill (1953) the Kármán-Pohlhausen method is used in this analysis. Velocity and temperature profiles are assumed satisfying the physical boundary conditions, and the integrated forms of the equations of motion and the equations themselves at the axis and the walls of the pipe are used to calculate the various parameters involved in the profiles assumed. Two cases of constant wall temperature and linearly decreasing temperature with height were considered. Cooling decelerates the fluid in the boundary layer that forms at the wall and the fluid in the core is accelerated by virtue of continuity. As cooling progresses, at Rayleigh number O(103) the fluid in the boundary layer starts reversing at first and then assumes progressively increasing velocities. Graphs are presented for the development of the predicted velocity and temperature profiles and the other parameters involved, for a situation when the boundary layer fills the whole pipe.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 34 , Issue 4 , 23 December 1968 , pp. 641 - 650
Copyright
© 1968 Cambridge University Press

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References

Bayley, F. J. & Lock, G. S. H. 1965 ASME J. Heat Transfer, 87, 30–39.
Elenbaas, W. 1942 Physica, 9, 1–28.
Hammitt, F. G. 1958 ASME Paper, no. 58-SA-30 (Semi-Annual Meeting, Detroit, Michigan).
Leslie, F. M. 1959 J. Fluid Mech. 7, 115–27.
Lighthill, M. J. 1953 Q. J. Mech. Appl. Math. 6, 398–439.
Martin, B. W. 1967 Proc. R. Soc A 301, 327–41.
Ostrach, S. 1954 NACA Tech. Note 3141.
Ostrach, S. 1964 High Speed Aerodynamics and Jet Propulsion. Vol. IV. Theory of Laminar Flows. Ed. by F. K. Moore. Oxford University Press.
Ostrach, S. & Thornton, P. R. 1958 Trans. ASME, 80, 363–6.
Ostroumov, G. A. 1958 Translation NACA Tech. Mem. 1407.
Schmidt, E. H. W. 1951 Proceedings of General Discussion on Heat Transfer, Section IV, 361–3. Institution of Mechanical Engineers.
Takhar, H. S. 1967 Proceedings of Japanese Society of Mechanical Engineers, Semi-International Symposium Paper no. 201, 1–8.