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Mixed convection from a sphere at small Reynolds and Grashof numbers

Published online by Cambridge University Press:  29 March 2006

C. A. Hieber  and
B. Gebhart
C. A. Hieber
Affiliation:
Department of Thermal Engineering, Cornell University
B. Gebhart
Affiliation:
Department of Thermal Engineering, Cornell University
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Abstract

Consideration is given to the effects of gravity which arise when a heated sphere, maintained at a steady uniform temperature, is located in a vertical uniform stream. Restricting analysis to a medium of unit Prandtl number (σ), the method of matched asymptotic expansions is employed in obtaining solutions for the velocity, temperature and pressure fields in the limit: G = o(R2), R ↓ 0 (G and R being, respectively, the Grashof and Reynolds numbers). Based on these results, conjectures are formed about the corresponding pure natural convection problem.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 1 , 14 August 1969 , pp. 137 - 159
Copyright
© 1969 Cambridge University Press

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References

Acrivos, A. & Taylor, T. D. 1962 Heat and mass transfer from single spheres in Stokes flow Phys. Fluids, 5, 387–394.Google Scholar
Fendell, F. E. 1968 Laminar natural convection about an isothermally heated sphere at small Grashof number J. Fluid Mech. 34, 163–176.Google Scholar
Hieber, C. A. & Gebhart, B. 1968 Low Reynolds number heat transfer from a circular cylinder J. Fluid Mech. 32, 21–28.Google Scholar
Kaplun, S. & Lagerstrom, P. A. 1957 Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers J. Math. Mech. 6, 585–593.Google Scholar
Kassoy, D. R. 1967 Heat transfer from circular cylinders at low Reynolds numbers. Theory for variable property flow Phys. Fluids, 10, 938–946.Google Scholar
Lagerstrom, P. A. 1964 Laminar flow theory. In Theory of Laminar Flows (ed. F. K. Moore). Princeton University Press.
Mahony, J. J. 1957 Heat transfer at small Grashof number. Proc. Roy. Soc A 238, 412–423.Google Scholar
Proudman, J. & Pearson, J. R. A. 1957 Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder J. Fluid Mech. 2, 237–262.Google Scholar
Rimmer, P. L. 1968 Heat transfer from a heated sphere in a uniform stream of small Reynolds number J. Fluid Mech. 32, 1–8.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic.
Yih, C. S. 1953 Free convection due to boundary sources. Fluid Models in Geophysics (Proceedings of First Symposium on Use of Models in Geophysical Fluid Dynamics). pp. 117–133. Govt. Printing Office, Washington.