The problem of heat and mass transfer from small spheres and cylinders freely suspended in a shear flow is considered in the limit of Reynolds number Re → 0. Asymptotic formulas are derived which relate the Nusselt number Nu to the Péclet number Pe in the limit Pe → 0, and for the case of the cylinder, Pe → ∞. At high Pe, the Nusselt number is found to approach a constant value, whereas, at low Pe it is shown to increase with Pe12 for the sphere and with —(log Pe)−1 for the cylinder. These results indicate the existence of a fundamental difference at high Pe between the shear flow problem studied here and the corresponding classical problem of uniform flow at infinity.

1.
A.
Acrivos
and
T. D.
Taylor
,
Phys. Fluids
5
,
387
(
1962
).
2.
F. Y.
Pan
and
A.
Acrivos
,
Intern. J. Heat Mass Transfer
11
,
439
(
1968
).
3.
I.
Proudman
and
J. R. A.
Pearson
,
J. Fluid Mech.
2
,
237
(
1957
).
4.
F. P.
Bretherton
,
J. Fluid Mech.
12
,
591
(
1962
).
5.
J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice‐Hall, Inc., Englewood Cliffs, New Jersey, 1965), p. 65.
6.
R. G.
Cox
,
I. Y. Z.
Zia
, and
S. G.
Mason
,
J. Colloid and Interface Sci.
27
,
7
(
1968
).
7.
D. E.
Elrick
,
Australian J. Phys.
15
,
283
(
1962
).
8.
H. A.
Wilson
,
Proc. Cambridge Phil. Soc.
12
,
406
(
1904
).
9.
N. A. Frankel, Ph.D. thesis, Stanford University (1968).
10.
C. Truesdell, The Kinematics of Vorticity (Indiana University Press, Bloomington, Indiana, 1954), p. 23.
This content is only available via PDF.
You do not currently have access to this content.