The present study is devoted to the problem of oscillatory convective flow in the presence of viscous dissipation around different positions of a sphere. The system of differential equations governing the flow phenomenon is transformed into dimensionless form by using suitable group of variables and then transformed into convenient form for integration by using primitive variable formulation. Numerical simulation based on finite difference method is carried out to analyze the mixed convection flow mechanism. Special focus is given on the transient shear stress and the rate of heat transfer characteristics and their dependency on various dimensionless parameters that is mixed convection parameter λ, Prandtl number Pr, dissipation parameter N, and angular frequency parameter ω. The angles X=30deg,90deg, and 360deg are the favorable positions around the sphere for different parameters, where the transient rate of shear stress and heat transfer is noted maximum. Later, the obtained results are presented graphically by using Tech Plot-360 and compared with the previous work given in the literature.

References

References
1.
Gebhart
,
B.
,
1962
, “
Effects of Viscous Dissipation in Natural Convection
,”
J. Fluid Mech.
,
14
(
2
), pp.
225
232
.
2.
Van Dorn
,
W. G.
,
1966
, “
Boundary Dissipation of Oscillatory Waves
,”
J. Fluid Mech.
,
24
(
4
), pp.
769
779
.
3.
Gebhart
,
B.
, and
Mollendorf
,
J.
,
1969
, “
Viscous Dissipation in External Natural Convection Flows
,”
J. Fluid Mech.
,
38
(
1
), pp.
97
107
.
4.
Hieber
,
C. A.
, and
Gebhart
,
B.
,
1969
, “
Mixed Convection From a Sphere at Small Reynolds and Grashof Numbers
,”
J. Fluid Mech.
,
38
(
1
), pp.
137
159
.
5.
Ishigaki
,
H.
,
1970
, “
Periodic Boundary Layer Near Two Dimensional Stagnation Points
,”
J. Fluid Mech.
,
43
(
3
), pp.
477
486
.
6.
Iqbal
,
M.
,
Aggarwala
,
B. D.
, and
Rokerya
,
M. S.
,
1970
, “
Viscous Dissipation Effects on Combined Free and Forced Convection Through Vertical Circular Tubes
,”
ASME J. Appl. Mech.
,
37
(4), pp.
931
935
.
7.
Ishigaki
,
H.
,
1971
, “
An Exact Periodic Solution of the Energy Equation
,”
J. Fluid Mech.
,
50
(
4
), pp.
657
668
.
8.
Ishigaki
,
H.
,
1972
, “
Heat Transfer in a Periodic Boundary Layer Near Two Dimension Stagnation Points
,”
J. Fluid Mech.
,
56
(
4
), pp.
619
627
.
9.
Graham
,
W.
,
1974
, “
A Separated Flow in Mixed Convection
,”
J. Fluid Mech.
,
62
(
2
), pp.
359
369
.
10.
Turcotte
,
D. L.
,
Hsui
,
A. T.
,
Torrance
,
K. E.
, and
Schubert
,
G.
,
1974
, “
Influence of Viscous Dissipation on Benard Convection
,”
J. Fluid Mech.
,
64
(
2
), pp.
369
374
.
11.
Van der Borght
,
R.
,
1975
, “
The Effect of Viscous Dissipation on Non-Linear Convection at High Rayleigh Number
,”
J. Aust. Math. Soc., Ser. B. Appl. Math.
,
19
(
2
), pp.
165
172
.
12.
Sparrow
,
E. M.
, and
Lee
,
L.
,
1976
, “
Analysis of Mixed Convection About Horizontal Cylinder
,”
Int. J. Heat Mass Transfer
,
19
(2), pp.
229
232
.
13.
Dowden
,
J.
,
1981
, “
The Stability of a Periodically Heated Layer of Fluid
,”
J. Fluid Mech.
,
110
, pp.
149
159
.
14.
Menendez
,
A. N.
, and
Ramaprian
,
B. R.
,
1984
, “
Prediction of Periodic Boundary Layers
,”
Int. J. Numer. Method Fluids
,
4
(
8
), pp.
781
80
.
15.
Philip
,
H.
,
1984
, “
On the Stability of the Unsteady Boundary Layer on a Cylinder Oscillating Transversely in a Viscous Fluid
,”
Int. J. Fluid Mech.
,
146
, pp.
347
367
.
16.
Golra
,
R. S. R.
,
Jankoswki
,
F.
, and
Textort
,
D.
,
1988
, “
Periodic Boundary Layer Near an Axisymmetric Stagnation Point on a Circular Cylinder
,”
Int. J. Heat Fluid Flow
,
9
(
4
), pp.
421
426
.
17.
Golra
,
R. S. R.
,
Jankoswki
,
F.
, and
Textort
,
D.
,
1988
, “
Thermal Response of Periodic Boundary Layer Near an Axisymmetric Stagnation Point on a Circular Cylinder
,”
Int. J. Heat Fluid Flow
,
9
(
4
), pp.
427
430
.
18.
Borisevich
,
V. D.
, and
Potanin
,
E. P.
,
1988
, “
Effects of Viscous Dissipation and Joule Heat on Heat Transfer Near a Rotating Disk in the Presence of Intensive Suction
,”
J. Eng. Phy.
,
55
(5), pp.
1220
1223
.
19.
Duck
,
P. W.
,
1989
, “
A Numerical Method for Treating Time Periodic Boundary Layers
,”
J. Fluid Mech.
,
204
, pp.
549
561
.
20.
Cheng
,
C.-H.
,
Kou
,
H.-S.
, and
Hiang
,
W.-H.
,
1990
, “
Flow Reversal and Heat Transfer of Fully Developed Mixed Convection in Vertical Channel
,”
J. Thermophys. Heat Transfer
,
4
(3), pp.
375
383
.
21.
Nguyen
,
H. D.
,
Paik
,
S.
, and
Chung
,
J. N.
,
1993
, “
Unsteady Mixed Convection Heat Transfer From a Solid Sphere: The Conjugate Problem
,”
Int. J. Heat Mass Transfer
,
36
(
18
), pp.
4443
4453
.
22.
Zanchini
,
E.
,
1998
, “
Effect of Viscous Dissipation on Mixed Convection in a Vertical Channel With Boundary Conditions of the Third Kind
,”
Int. J. Heat Mass Transfer
,
41
(
23
), pp.
3949
3959
.
23.
Barletta
,
A.
,
1998
, “
Laminar Mixed Convection With Viscous Dissipation in a Vertical Channel
,”
Int. J. Heat Mass Transfer
,
41
(22), pp.
3501
3513
.
24.
Barletta
,
A.
,
1999
, “
Combined Forced and Free Convection With Viscous Dissipation in a Vertical Circular Duct
,”
Int. J. Heat Mass Transfer
,
42
(12), pp.
2243
2253
.
25.
Hossain
,
M. A.
, and
Rees
,
D. A. S.
,
1999
, “
Combined Heat and Mass Transfer in Natural Convection Flow From a Vertical Wavy Surface
,”
Acta Mech.
,
136
(3–4), pp.
133
141
.
26.
Barletta
,
A.
, and
Zanchini
,
E.
,
2001
, “
Mixed Convection With Viscous Dissipation in an Inclined Channel With Prescribed Wall Temperatures
,”
Int. J. Heat Mass Transfer
,
44
(
22
), pp.
4267
4275
.
27.
Hossain
,
M. A.
,
Kabir
,
S.
, and
Rees
,
D. A. S.
,
2002
, “
Natural Convection of Fluid With Variable Viscosity From a Heated Vertical Wavy Surface
,”
J. Z. Angew. Math. Phys.
,
53
(1), pp.
48
57
.
28.
Antar
,
M. A.
, and
El-Shaarawi
,
M. A. I.
,
2002
, “
Mixed Convection Around a Liquid Sphere in an Air Stream
,”
Int. J. Heat Mass Transfer
,
38
(4–5), pp.
419
424
.
29.
Joseph
,
D. D.
, and
Wong
,
J.
,
2004
, “
The Dissipation Approximation and Viscous Potential Flow
,”
J. Fluid Mech.
,
505
, pp.
365
377
.
30.
Pantokratoras
,
A.
,
2005
, “
Effect of Viscous Dissipation in Natural Convection along a Heated Vertical Plate
,”
J. Appl. Math. Model.
,
29
(
6
), pp.
553
564
.
31.
Rieutord
,
M.
, and
Valdettaro
,
L.
,
2010
, “
Viscous Dissipation by Tidally Forced Inertial Modes in a Rotating Spherical Shell
,”
Int. J. Fluid Mech.
,
643
, pp.
363
394
.
32.
Elgazery
,
N. S.
, and
Abd Elazem
,
Y.
,
2011
, “
Effect of Viscous Dissipation and Joule Heating on Natural Convection Flow of a Viscous Fluid From Heated Vertical Wavy Surface
,”
Z. Naturforch
,
66a
, pp.
427
440
.
33.
Jha
,
B. K.
, and
Ajibade
,
A. O.
,
2012
, “
Effect of Viscous Dissipation on Natural Convection Flow Between Vertical Parallel Plates With Time-Periodic Boundary Conditions
,”
J. Commun. Nonlinear Sci. Numer. Simul.
,
17
(
4
), pp.
1576
1587
.
34.
Praveen
,
N.
,
Nath
,
S.
, and
Abdul Alim
,
M.
,
2014
, “
Viscous Dissipation Effects on a Natural Convection Flow Along a Vertical Wavy Surface
,”
Proceedia Eng.
,
90
, pp.
294
300
.
35.
Juncu
,
G.
,
2015
, “
The Influence of Viscous Dissipation on the Unsteady Conjugate Forced Convection Heat Transfer From a Fluid Sphere
,”
Int. J. Heat Mass Transfer
,
90
, pp.
542
555
.
36.
Hossain
,
M. Z.
, and
Floryan
,
J. M.
,
2015
, “
Mixed Convection in a Periodically Heated Channel
,”
J. Fluid Mech.
,
768
, pp.
51
90
.
37.
Miklavic
,
M.
,
2015
, “
Stability Analysis of Some Fully Developed Mixed Convection Flow in a Vertical Channel
,”
Z. Angew. Math. Mech.
,
95
(
9
), pp.
982
986
.
38.
Reger
,
K.
, and
Gorder
,
R. A. V.
,
2013
, “
Lane-Emden Equations of Second Kind Modeling Thermal Expansion in Infinite Cylinder and Sphere
,”
Appl. Math. Mech.
,
34
(
12
), pp.
1439
1452
.
39.
Ravindran
,
R.
, and
Ganapathirao
,
M.
,
2013
, “
Non-Uniform Slot Suction/Injection Into Mixed Convection Boundary Layer Flow Over Vertical Cone
,”
Appl. Math. Mech.
,
34
(
11
), pp.
1327
1338
.
40.
Aman
,
F.
,
Ishaq
,
A.
, and
Pop
,
I.
,
2011
, “
Mixed Convection Boundary Layer Flow Near Stagnation Point on Vertical Surface With Slip
,”
Appl. Math. Mech.
,
32
(
12
), pp.
1599
1606
.
41.
Ali
,
F. M.
,
Nazar
,
R.
,
Arifin
,
N. M.
, and
Pop
,
I.
,
2014
, “
Mixed Convection Stagnation Point Flow on Vertical Stretching Sheet With External Magnetic Field
,”
Appl. Math. Mech.
,
35
(
2
), pp.
155
166
.
42.
Wei
,
L.
,
Lu
,
Y.
, and
Wei
,
J.
,
2014
, “
Numerical Study on Laminar Free Convection Heat Transfer Between Sphere Particle and High Pressure Water in Pseudo-Critical Zone
,”
Therm. Sci.
,
18
(
4
), pp.
1293
1303
.
43.
Ashraf
,
M.
,
Ahmad
,
M.
, and
Anwar Hossain
,
M.
,
2015
, “
Numerical Simulation of Radiative Natural Convection Flow Around a Magnetized Sphere
,”
J. Thermophys. Heat Transfer
,
29
(
3
), pp.
602
609
.
44.
Ashraf
,
M.
,
Fatima
,
A.
, and
Gorla
,
R. S. R.
,
2017
, “
Periodic Momentum and Thermal Boundary Layer Mixed Convection Flow Around Surface of the Sphere in the Presence of Viscous Dissipation
,”
Can. J. Phys.
,
95
(
10
), pp.
976
986
.
45.
Sphaier
,
L. A.
,
Barletta
,
A.
, and
Celli
,
M.
,
2015
, “
Unstable Mixed Convection in Heated Inclined Porous Channel
,”
J. Fluid Mech.
,
778
, pp.
428
450
.
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