A singular perturbation analysis and Green’s second theorem are used in order to obtain a general expression for the heat transfer from a particle at low Peclet numbers, when advection and conduction are heat transfer modes of comparable magnitude. The particle may have arbitrary shape, and its motion in the fluid is not constrained to be Stokesian. In the ensuring analysis, the governing equations for the temperature fields at short and long times are derived. The expressions are combined to yield a general equation for the temperature field and for the total rate of heat transfer. The final results for the rate of heat transfer demonstrate the existence of a history integral, whose kernel decays faster than the typical history integrals of the purely conduction regime. As applications of the general results, analytical expressions for the Nusselt number are derived in the case of a sphere undergoing a step temperature change.

Issue Section:
Porous Media, Particles and Droplets
Keywords:
Cumbustion, Evaporation, Multiphase Flows
Topics:
Particulate matter, Shapes, Transient heat transfer, Heat transfer, Temperature, Heat conduction, Evaporation, Fluids, Multiphase flow, Theorems (Mathematics)
1.
Abramzon
B.
, and
Elata
C.
,
1984
, “
Heat Transfer from a Single Sphere in Stokes Flow
,”
Int. J. Heat and Mass Transfer.
, Vol.
27
, pp.
687
–
695
.
2.
Acrivos
A.
,
1980
, “
A Note on the Rate of Heat or Mass Transfer from a Small Particle Freely Suspended in Linear Shear Field
,”
J. of Fluid Mechanics
, Vol.
98
, p.
229
229
.
3.
Bird, R. B., Stewart, W. E., and Lightfoot, E. N., 1960, Transport Phenomena, John Wiley and Sons, New York, p. 409.
4.
Childress
S.
,
1964
, “
The Slow Motion of a Sphere in a Rotating, Viscous Fluid
,”
J. of Fluid Mechanics
, Vol.
20
, p.
305
305
.
5.
Feng
Z.-G.
, and
Michaelides
E. E.
,
1996
, “
Unsteady Heat Transfer from a spherical Particle at finite Peclet Numbers
,”
J. of Fluids Engineering
, Vol.
118
, pp.
96
–
102
.
6.
Gopinath
A.
, and
Mills
A. F.
,
1993
, “
Conductive Heat Transfer From a Sphere due to Acoustic Streaming
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
115
, pp.
332
–
340
.
7.
Hinch
E. J.
,
1993
, “
The Approach to Steady State in Oseen Flows
,”
J. of Fluid Mechanics
, Vol.
256
, p.
601
601
.
8.
Jacobs
H. R.
, and
Golafshani
M.
,
1989
, “
A Heuristic Evaluation of the Governing Mode of Heat Transfer in a Liquid-Liquid Spray Column
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
111
, pp.
773
–
779
.
9.
Kaviani, M., 1994, Principles of Convective Heat Transfer, Springer-Verlag, New York.
10.
Kreysig, E., 1988, Advanced Engineering Mathematics, 6th Ed., John Wiley and Sons, New York, p. 560.
11.
Lovalenti
P. M.
, and
Brady
J. F.
,
1993
, “
The Hydrodynamic Force on a Rigid Particle Undergoing Arbitrary time-dependent Motion at Small Reynolds Number
,”
J. of Fluid Mechanics
, Vol.
256
, p.
561
561
.
12.
Maxey
M. R.
, and
Riley
J. J.
,
1983
, “
Equation of Motion of a Small rigid Sphere in a Non-uniform Flow
,”
Phys. of Fluids
, Vol.
26
, pp.
883
–
889
.
13.
Michaelides
E. E.
, and
Feng
Z. G.
,
1994
, “
The Heat Transfer from a sphere in Non-uniform and Unsteady Velocity and Temperature Fields
,”
Int. J. Heat and Mass Transfer
, Vol.
37
, p.
2069
2069
.
14.
Michaelides
E. E.
,
Liang
L.
, and
Lasek
A.
,
1992
, “
The Effects of Turbulence on the Phase Change of Droplets and Particles under Non-Equilibrium Conditions
,”
Int. J. Heat and Mass Transfer
, Vol.
35
, pp.
2069
–
2076
.
15.
Proudman
I. A.
, and
Pearson
J. R. A.
,
1957
, “
Expansions at Small Reynolds Numbers for the Flow Past a Sphere and a Circular Cylinder
,”
J. of Fluid Mechanics
, Vol.
2
, pp.
237
–
262
.
16.
Sano
T.
,
1981
, “
Unsteady Flow Past a Sphere at Low-Reynolds Number
,”
J. of Fluid Mechanics
, Vol.
112
, pp.
433
–
441
.
17.
Sirignano
W. A.
,
1993
, “
Fluid Dynamics of Sprays
,”
J. of Fluids Engineering
, Vol.
115
, pp.
345
–
378
.
This content is only available via PDF.
Copyright © 1998
 by The American Society of Mechanical Engineers
You do not currently have access to this content.