Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-18T22:25:25.052Z Has data issue: false hasContentIssue false
  • English
  • Français

Heat transfer at high Péclet number from a small sphere freely rotating in a simple shear field

Published online by Cambridge University Press:  29 March 2006

Andreas Acrivos
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of heat transfer at high Péclet number Pe from a sphere freely rotating in a simple shear field is considered theoretically for the case of small shear Reynolds numbers. It is shown that the present problem is in many respects similar to that of heat transfer past a freely rotating cylinder which was recently solved by Frankel & Acrivos (1968). By taking advantage of the close analogy between these two problems, an approximate method of solution is developed according to which the asymptotic Nusselt number for Pe → ∞ is 9, i.e. 4½ times its value for pure conduction. As in the corresponding case of the cylinder, the fact that the asymptotic Nusselt number is independent of Pe results from the presence of a region of closed streamlines which completely surrounds the rotating sphere.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 46 , Issue 2 , 29 March 1971 , pp. 233 - 240
Copyright
© 1971 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

Cox, R. G., Zia, I. Y. Z. & Mason, S. G. 1968 Particle motions in sheared suspensions. XXV. Streamlines around cylinders and spheres J. Colloid Interface Sci. 27, 7.Google Scholar
Frankel, N. A. & Acrivos, A. 1968 Heat and mass transfer from small spheres and cylinders freely suspended in shear flow Phys. Fluids, 11, 1913.Google Scholar
Grimshaw, R. 1969 On steady recirculating flows J. Fluid Mech. 39, 695.Google Scholar
Pan, Y. & Acrivos, A. 1968 Heat transfer at high Péclet number in regions of closed streamlines Int. J. Heat and Mass Transfer, 11, 439.Google Scholar
Robertson, C. R. & Acrivos, A. 1970 Low Reynolds number shear flow past a rotating circular cylinder. Part 1. Momentum transfer. Part 2. Heat transfer. J. Fluid Mech. 40, 685, 705.Google Scholar