The effects of the uniform heat flux and a linear velocity-slip on the heat transfer phenomena of spheres in Newtonian fluids are numerically investigated using semi-implicit marker and cell (SMAC) method implemented on a staggered grid arrangement in spherical coordinates. The solver is thoroughly benchmarked through domain independence, grid independence, and comparison with literature. Further extensive results are obtained in the range of conditions as: Reynolds number, Re = 0.1–200; Prandtl number, Pr = 1–100; and dimensionless slip number, λ = 0.01–100. The results are presented and discussed such that the isotherm contours and the local and average Nusselt numbers of isoflux spheres with velocity-slip at the interface are compared with their isothermal spheres counterparts under identical conditions. Briefly, the results indicate that the average Nusselt numbers of isoflux spheres are large compared to those of isothermal spheres under identical conditions. Finally, an empirical correlation is developed for the average Nusselt numbers of the spheres in Newtonian fluids with velocity-slip and the uniform heat flux conditions along the fluid–solid sphere interface.

References

References
1.
Denn
,
M. M.
,
2001
, “
Extrusion Instabilities and Wall Slip
,”
Annu. Rev. Fluid Mech.
,
33
(1), pp.
265
287
.
2.
Damianou
,
Y.
,
Georgiou
,
G. C.
, and
Moulitsas
,
I.
,
2013
, “
Combined Effects of Compressibility and Slip in Flows of a Herschel–Bulkley Fluid
,”
J. Non-Newtonian Fluid Mech.
,
193
, pp.
89
102
.
3.
Neto
,
C.
,
Evans
,
D. R.
,
Bonaccurso
,
E.
,
Butt
,
H. J.
, and
Craig
,
V. S. J.
,
2005
, “
Boundary Slip in Newtonian Liquid: A Review of Experimental Studies
,”
Rep. Prog. Phys.
,
68
(
12
), pp.
2859
2897
.
4.
Sochi
,
T.
,
2011
, “
Slip at Fluid-Solid Interface
,”
Polym. Rev.
,
51
(
4
), pp.
309
340
.
5.
Barnes
,
H. A.
,
1995
, “
A Review of the Slip (Wall Depletion) of Polymer Solutions, Emulsions and Particle Suspensions in Viscometers: Its Cause, Character, and Cure
,”
J. Non-Newtonian Fluid Mech.
,
56
(
3
), pp.
221
251
.
6.
Vinogradov
,
G. V.
,
Malkin
,
A. Y.
,
Yanovskil
,
Y. G.
,
Borisenkova
,
E. K.
,
Yarlykov
,
B. V.
, and
Berezhnaya
,
G. V.
,
1972
, “
Viscoelastic Properties and Flow of Narrow Distribution Polybutadienes and Polyisoprenes
,”
J. Polym. Sci. A
,
10
(
6
), pp.
1061
1084
.
7.
Kalika
,
D.
, and
Denn
,
M. M.
,
1987
, “
Wall Slip and Extrudate Distortion in Linear Low-Density Polyethylene
,”
J. Rheol.
,
31
(
8
), pp.
815
834
.
8.
Kalyon
,
D. M.
, and
Gevgilili
,
H.
,
2003
, “
Wall Slip and Extrudate Distortion of Three Polymer Melts
,”
J. Rheol.
,
47
(
3
), pp.
683
699
.
9.
Mennig
,
G.
,
1977
, “
Visual Observations of Slip in Flow of Polymer Melts
,”
J. Macromol. Sci.
,
14
(
2
), pp.
231
240
.
10.
den Otter
,
J. L.
,
1975
, “
Rheological Measurements on Two Uncrosslinked, Unfilled Synthetic Rubbers
,”
Rheol. Acta
,
14
(
4
), pp.
329
336
.
11.
Meijer
,
H. E. H.
, and
Verbraak
,
C. P. J. M.
,
1988
, “
Modeling of Extrusion With Slip Boundary Conditions
,”
Polym. Eng. Sci.
,
28
(
11
), pp.
758
772
.
12.
Navier
,
C. L. M. H.
,
1827
, “
Sur les Lois du Mouvement des Fluides
,”
Mem. Acad. R. Sci. Inst. Fr.
,
6
(2), pp.
389
440
.
13.
Kishore
,
N.
, and
Ramteke
,
R. R.
,
2015
, “
Slip in Flows of Power-Law Liquids Past Smooth Spherical Particles
,”
Acta Mech.
,
226
(
8
), pp.
2555
2571
.
14.
Kishore
,
N.
, and
Ramteke
,
R. R.
,
2016
, “
Slip in Flow Through Assemblages of Spherical Particles at Low to Moderate Reynolds Numbers
,”
Chem. Eng. Technol.
,
39
(
6
), pp.
1087
1098
.
15.
Ramteke
,
R. R.
, and
Kishore
,
N.
,
2017
, “
Heat Transfer Phenomena of Assemblages of Smooth Slip Spheres in Newtonian Fluids
,”
Heat Transfer Asian Res.
,
46
(
2
), pp.
160
175
.
16.
Ramteke
,
R. R.
, and
Kishore
,
N.
,
2017
, “
Computational Fluid Dynamics Study on Forced Convective Heat Transfer Phenomena of Spheres in Power-Law Liquids With Velocity Slip at the Interface
,”
Heat Transfer Eng.
,
38
, pp. 1–18.
17.
Ramteke
,
R. R.
, and
Kishore
,
N.
,
2015
, “
Heat Transfer From Slip Spheres to a Shear-Thickening Fluid: Effects of Slip Velocity and Particle Volume Fraction
,”
Procedia Eng.
,
127
, pp.
354
361
.
18.
Kishore
,
N.
, and
Ramteke
,
R. R.
,
2016
, “
Forced Convective Heat Transfer From Spheres to Newtonian Fluids in Steady Axisymmetric Flow Regime With Velocity Slip at Fluid-Solid Interface
,”
Int. J. Therm. Sci.
,
105
, pp.
206
217
.
19.
Harlow
,
F. H.
, and
Welch
,
J. E.
,
1965
, “
Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid With Free Surfaces
,”
Phys. Fluids
,
8
(
12
), pp.
2182
2188
.
20.
Leonard
,
B. P.
,
1979
, “
A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation
,”
Comput. Methods Appl. Mech. Eng.
,
19
(
1
), pp.
59
98
.
21.
Dhole
,
S. D.
,
Chhabra
,
R. P.
, and
Eswaran
,
V.
,
2006
, “
A Numerical Study on the Forced Convection Heat Transfer From an Isothermal and Isoflux Sphere in the Steady Axisymmetric Flow Regime
,”
Int. J. Heat Mass Transfer
,
49
(5–6), pp.
984
994
.
You do not currently have access to this content.