Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-08T07:28:10.406Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of buoyancy on the boundary layer about a heated horizontal circular cylinder in axial streaming

Published online by Cambridge University Press:  29 March 2006

Karen Plain Switzer
Karen Plain Switzer
Affiliation:
Department of Mathematics University of Manchester Institute of Science and Technology Present address: c/o Department of Mathematics, Cornell University, Ithaca, New York 14850.
Get access Rights & Permissions [Opens in a new window]

Abstract

The boundary-layer flow over a semi-infinite horizontal circular cylinder heated to a constant temperature and immersed in a uniform axial free stream is discussed in five situations corresponding to successively greater displacements from the leading edge. In the first three cases the drift velocity due to buoyancy is assumed small compared to the axial velocity component. Close to the leading edge of the cylinder the techniques of Seban & Bond are extended to include the drift velocity; far from the leading edge the asymptotic series methods of Stewartson, of Glauert & Lighthill, and of Eshghy & Hornbeck are employed to obtain a solution for the drift velocity. In the intermediate zone where the series solutions do not apply the appropriate partial differential equations are solved numerically. Still further downstream than the region where the ‘asymptotic’ solutions hold it is assumed that the boundary-layer flow is primarily convective and that the boundary layer is thin compared with the radius of the cylinder. A series solution is obtained which is valid near the lowest generator of the cylinder. Numerical methods are used to advance this solution upwards around the cylinder by solving the full boundary-layer equations step-by-step.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 44 , Issue 3 , 26 November 1970 , pp. 529 - 543
Copyright
© 1970 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

Eshghy, S. & Hornbeck, R. W. 1967 Flow and heat transfer in the axisymmetric boundary layer on a circular cylinder. Int. J. Heat Mass Transfer, 10, 1757–1766.Google Scholar
Glauert, M. B. & Lighthill, M. J. 1955 The axisymmetric boundary layer on a long thin cylinder. Proc. Roy. Soc. A 230, 188–203.Google Scholar
Mitchell, A. R. 1961 Solution of the von Mises boundary layer equation using a high-speed computer. Mathematics of Computation, XV, 238–242.Google Scholar
Ostrach, S. 1964 Laminar flows with body forces. In Theory of Laminar Flows. (Ed. F. K. Moore). Princeton University Press.
Poots, G. 1964 Laminar free convection near the lower stagnation point on an isotherma curved surface. Int. J. Heat Mass Transfer, 7, 863–874.Google Scholar
Saville, D. A. & Churchill, S. W. 1967 Laminar free convection in boundary layers near horizontal cylinders and vertical axisymmetric bodies. J. Fluid Mech. 29, 391–399.Google Scholar
Seban, R. A. & Bond, R. 1951 Skin friction and heat transfer characteristics of a laminar boundary layer on a cylinder in axial incompressible flow. J. Aeronaut. Sci. 18, 671–675.Google Scholar
Slater, L. J. 1960 Confluent Hypergeometric Functions. Cambridge University Press.
Stewartson, K. 1955 The asymptotic boundary layer on a circular cylinder in axial incompressible flow. Quart. Appl. Math. 13, 113–122.Google Scholar
Stewartson, K. 1957 On asymptotic expansions in the theory of boundary layers. J. Math. Phys. 36, 173–191.Google Scholar
Terrill, R. M. 1960 Laminar boundary layer flow near separation with and without suction. Phil. Trans. Roy. Soc. A 253, 55–100.Google Scholar
Supplementary material: PDF

Switzer supplementary material

Supplementary Material

Download Switzer supplementary material(PDF)
PDF 483.8 KB