0
Research Papers: Forced Convection

Forced Heat and Mass Transfer From a Slightly Deformed Sphere at Small but Finite Peclet Numbers in Stokes Flow

[+] Author and Article Information
Zhi-Gang Feng

Department of Mechanical Engineering,
University of Texas at San Antonio,
San Antonio, TX 78259
e-mail: zhigang.feng@utsa.edu

1Corresponding author, also an adjunct professor of Changzhou University, China.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received October 11, 2012; final manuscript received February 25, 2013; published online July 11, 2013. Assoc. Editor: Wilson K. S. Chiu.

J. Heat Transfer 135(8), 081702 (Jul 11, 2013) (8 pages) Paper No: HT-12-1554; doi: 10.1115/1.4023937 History: Received October 11, 2012; Revised February 25, 2013

The fundamental problem of heat and mass transfer from a slightly deformed sphere at low but finite Peclet numbers in Stokes flow is solved by a combined regular and singular perturbation method. The deformed sphere is assumed to be axisymmetric and its shape is described by a power series in a small parameter; the correction to the Nusselt number due to the deformation of the sphere is obtained through a regular perturbation with respect to this parameter. On the contrary, the correction to the Nusselt number due to the small Peclet number is derived by applying a singular perturbation method. The analytical solution is derived for the averaged Nusselt number in terms of the Peclet number and the deformation parameter.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Fourier, J., 1822, Theorie Analytique de la Chaleur, F. Didot, Paris.
Carslaw, H. S. and Jaeger, J. C., 1947, Conduction of Heat in Solids, Oxford University Press, Oxford, UK.
Feng, Z.-G., and Michaelides, E. E., 1997, “Unsteady Heat And Mass Transfer From a Spheroid,” AIChE J., 43, pp. 609–614. [CrossRef]
Acrivos, A., and Taylor, T. E., 1962, “Heat and Mass Transfer From Single Spheres in Stokes Flow,” Phys. Fluids, 5, pp. 387–394. [CrossRef]
Proudman, I., and Pearson, J. R. A., 1956, “Expansions at Small Reynolds Numbers for the Flow Past a Sphere and a Circular Cylinder,” J. Fluid Mech., 2, pp. 237–262.
Brunn, P. O., 1982, “Heat or Mass Transfer From Single Spheres in a Low Reynolds Number Flow,” Int. J. Eng. Sci., 20, pp. 817–822. [CrossRef]
Feng, Z.-G., and Michaelide, E. E., 2012, “Heat Transfer From a Nano-Sphere With Temperature and Velocity Discontinuities at the Interface,” Int. J. Heat Mass Transfer, 55, pp. 6491–6498. [CrossRef]
Feng, Z.-G., and Michaelides, E. E., 1996, “Unsteady Heat Transfer From a Spherical Particle at Finite Peclet Numbers,” ASME J. Fluids Eng., 118, pp. 96–102. [CrossRef]
Brenner, H., 1963, “Forced Convection Heat and Mass Transfer at Small Peclet Numbers From a Particle of Arbitrary Shape,” Chem. Eng. Sci., 18, pp. 109–122. [CrossRef]
Sampson, R. A., 1891, “On Stokes Current Function,” Philos. Trans. R. Soc. London, Ser. A., 182, pp. 449–518. [CrossRef]
Palaniappan, H., 1994, “Creeping Flow About a Slightly Deformed Sphere,” Z. Angew. Math Phys., 45, pp. 833–838. [CrossRef]
Payne, L. E., and Pell, W. H., 1960, “The Stokes Flow Problem for a Class of Axially Symmetric Bodies,” J. Fluid Mech., 7, pp. 529–549. [CrossRef]
Brenner, H., 1964, “The Stokes Resistance of a Slightly Deformed Sphere,” Chem. Eng. Sci., 19, pp. 519–539. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Nusselt number versus Peclet number for ɛ = -0.2 (prolate), ɛ = 0 (sphere), and ɛ = 0.2 (oblate)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In