Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-26T13:23:36.213Z Has data issue: false hasContentIssue false
  • English
  • Français

Entry flow in a heated straight tube

Published online by Cambridge University Press:  19 April 2006

Lun-Shin Yao
Lun-Shin Yao
Affiliation:
The Rand Corporation, Santa Monica, California
Get access Rights & Permissions [Opens in a new window]

Abstract

The developing flow in the entry region of a heated horizontal pipe is analysed. The asymptotic solution of the developing flow near the entrance of the heated straight pipe, distance O(a), is obtained by perturbing the solution of the developing flow in an unheated straight pipe. Two vortices result from the combination of the radial-directional and the downward motions of the fluid particles which are induced by the displacement of the boundary layer and develop along the pipe. The axial velocity has a concave profile in the inviscid core with its maximum off the centre-line near the entrance and it grows toward a uniformly distributed profile downstream. The downward stream caused by the displacement of the secondary boundary layer forces the axial velocity profile to turn anticlockwise continuously along the pipe if the flow is from left to right. The core flow induced by the axial boundary-layer displacement generates a favourable pressure gradient. Simultaneously, the secondary boundary-layer displacement affects the core flow to induce a favourable pressure gradient on the bottom of the pipe and an unfavourable pressure gradient on the top wall. The effect of the axial boundary-layer displacement is stronger than that of the secondary boundary layer near to the entrance. Downstream the growth of the boundary-layer thickness is suppressed by the inviscid secondary flow. It is expected that the displacement effect of the secondary boundary layer becomes dominant downstream from the region of O(d) when Gr is large.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 88 , Issue 3 , 13 October 1978 , pp. 465 - 483
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agrawal, Y., Talbot, L. & Gong, K. 1978 Laser anemometer study of flow development in curved circular pipes. J. Fluid Mech. 85, 497–518.Google Scholar
Barker, S. J. & Jennings, C. G. 1977 The effect of wall heating on transition in water boundary layers. AGARD Symposium on Laminar Turbulent Transition, Copenhagen, Denmark, 2–4 May 1977.Google Scholar
Barua, S. N. 1963 Secondary flow in stationary curved pipes. Quart. J. Mech. Appl. Math. 16, 61–77.Google Scholar
Dean, W. R. 1927 Note on the motion of fluid in a curved pipe. Phil. Mag. 4, 208–223.Google Scholar
Dean, W. R. 1928 The stream-line motion of fluid in a curved pipe. Phil. Mag. 5, 673–695.Google Scholar
Ito, H. 1961 Pressure losses in smooth pipe bends. Rep. Inst. High Sp. Mech., Japan 12 (112), 41–62.Google Scholar
Lighthill, M. J. 1958 Introduction to Fourier Analysis and Generalised Functions. Cambridge University Press.CrossRefGoogle Scholar
Mori, Y. & Futagami, K. 1967 Forced convective heat transfer in uniformly heated horizontal tubes. Int. J. Heat Mass Transfer 10, 1801–1813.Google Scholar
Morton, B. R. 1959 Laminar convection in uniformly heated horizontal pipes at low Rayleigh numbers. Quart. J. Mech. Appl. Math. 12, 410–420.Google Scholar
Singh, M. P. 1974 Entry flow in a curved pipe. J. Fluid Mech. 65, 517–539.Google Scholar
Smith, F. T. 1976 Proc. Roy. Soc. A 351, 71–87.Google Scholar
Van Dyke, M. D. 1970 Entry flow in a channel. J. Fluid Mech. 44, 813–823.Google Scholar
Wilson, S. D. R. 1971 Entry flow in a channel. Part 2. J. Fluid Mech. 46, 787–799.Google Scholar
Yao, L.-S. 1977 Entry Flow in a Heated Tube. The Rand Corporation, R-2111-ARPA.Google Scholar
Yao, L.-S. & Berger, S. A. 1975 Entry flow in a curved pipe. J. Fluid Mech. 67, 177–196.Google Scholar
Yao, L.-S. & Catton, I. 1976 The Buoyancy and Variable Viscosity Effects on a Water Laminar Boundary Layer Along a Heated Longitudinal Horizontal Cylinder. The Rand Corporation, R-1966-ARPA.Google Scholar
Yao, L.-S. & Catton, I. 1977 Buoyancy cross-flow effects on longitudinal boundary layer flow of a heated horizontal hollow cylinder. J. Heat Transfer, Trans. A.S.M.E. C 99, 122–124. (See also The Rand Corporation, R-1907-ARPA, 1976.)CrossRefGoogle Scholar
Yao, L.-S., Catton, I. & Mcdonough, J. M. 1978 Free-forced convection from a heated longitudinal horizontal cylinder. Numerical Heat Transfer (in the Press).CrossRefGoogle Scholar