This work studies numerically the combined heat and mass transfer of uniform blowing/suction, non-Newtonian power-law fluid, and thermal radiation effects on free convection adjacent to a vertical cone within a porous medium in the presence of Soret/Dufour effects. The surface of the vertical cone has a uniform wall temperature and uniform wall concentration (UWT/UWC). The Rosseland diffusion approximation is employed to describe the radiative heat flux. A nonsimilarity analysis is performed, and the transformed governing equations are solved by Keller box method (KBM). The effects of these major parameters of the Dufour parameter, Soret parameter, Lewis number, buoyancy ratio, power-law index of the non-Newtonian fluids, blowing/suction parameter, and thermal radiation parameter on the heat and mass transfer characteristics have been carried out. In general, for the case of blowing, both the local Nusselt number and the local Sherwood number decrease. This trend reversed for suction of fluid. The physical aspects of the problem are discussed in detail.

References

References
1.
Nield
,
D. A.
, and
Bejan
,
A.
,
2013
,
Convection in Porous Media
,
Springer-Verlag
,
New York
.
2.
Shenoy
,
A. V.
,
1994
, “
Non-Newtonian fluid Heat Transfer in Porous Media
,”
Adv. Heat Transfer
,
24
, pp.
101
190
.
3.
Chen
,
H. T.
, and
Chen
,
C. K.
,
1988
, “
Free Convection Flow of Non-Newtonian Fluids Along a Vertical Plate Embedded in a Porous Medium
,”
ASME J. Heat Transfer
,
110
(
1
), pp.
257
260
.
4.
Yang
,
Y. T.
, and
Wang
,
S. J.
,
1996
, “
Free Convection Heat Transfer of Non-Newtonian Fluids Over Axisymmetric and Two-Dimensional Bodies of Arbitrary Shape Embedded in a Fluid-Saturated Porous Medium
,”
Int. J. Heat Mass Transfer
,
39
(
1
), pp.
203
210
.
5.
Kumari
,
M.
, and
Jayanthi
,
S.
,
2004
, “
Non-Darcy Non-Newtonian Free Convection Flow Over a Horizontal Cylinder in a Saturated porous medium
,”
Int. Commun. Heat Mass Transfer
,
31
(
8
), pp.
1219
1226
.
6.
Cheng
,
C. Y.
,
2009
, “
Natural Convection Heat Transfer of Non-Newtonian Fluids in Porous Media From a Vertical Cone Under Mixed Thermal Boundary Conditions
,”
Int. Commun. Heat Mass Transfer
,
36
(
7
), pp.
693
697
.
7.
Rastogi
,
S. K.
, and
Poulikakos
,
D.
,
1995
, “
Double-Diffusion From a Vertical Surface in a Porous Region Saturated With a Non-Newtonian Fluid
,”
Int. J. Heat Mass Transfer
,
38
(
5
), pp.
935
946
.
8.
EL-Kabeir
,
S. M. M.
,
EL-Hakiem
,
M. A.
, and
Rashad
,
A. M.
,
2008
, “
Group Method Analysis of Combined Heat and Mass Transfer by MHD Non-Darcy Non-Newtonian Natural Convection Adjacent to Horizontal Cylinder in a Saturated Porous Medium
,”
Appl. Math. Model.
,
32
(
11
), pp.
2378
2395
.
9.
Cheng
,
C. Y.
,
2009
, “
Natural Convection Heat and Mass Transfer From a Vertical Truncated Cone in a Porous Medium Saturated With a Non-Newtonian Fluid With Variable Wall Temperature and Concentration
,”
Int. Commun. Heat Mass Transfer
,
36
(
6
), pp.
585
589
.
10.
Kairi
,
R. R.
, and
Murthy
,
P. V. S. N.
,
2011
, “
Effect of Viscous Dissipation on Natural Convection Heat and Mass Transfer From Vertical Cone in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium
,”
Appl. Math. Comput.
,
217
(
20
), pp.
8100
8114
.
11.
Kairi
,
R. R.
, and
RamReddy
,
Ch.
,
2014
, “
Solutal Dispersion and Viscous Dissipation Effects on Non-Darcy Free Convection Over a Cone in Power-Law Fluids
,”
Heat Transfer–Asian Research
,
43
(
5
), pp.
476
488
.
12.
Yih
,
K. A.
, and
Huang
,
C. J.
,
2015
, “
Effect of Internal Heat Generation on Free Convection Heat and Mass Transfer of Non-Newtonian Fluids Flow Over a Vertical Plate in Porous Media: VWT/VWC
,”
J. Aeronaut. Astronaut. Aviat., Ser. A
,
47
(
2
), pp.
115
122
.
13.
Postelnicu
,
A.
,
2004
, “
Influence of a Magnetic Field on Heat and Mass Transfer by Natural Convection From Vertical Surfaces in Porous Media Considering Soret and Dufour Effects
,”
Int. J. Heat Mass Transfer
,
47
(
6–7
), pp.
1467
1472
.
14.
Mansour
,
A.
,
Amahmid
,
A.
,
Hasnaoui
,
M.
, and
Bourich
,
M.
,
2006
, “
Multiplicity of Solutions Induced by Thermosolutal Convection in a Square Porous Cavity Heated From Below and Submitted to Horizontal Concentration Gradient in the Presence of Soret Effect
,”
Numer. Heat Transfer A Appl.
,
49
(
1
), pp.
69
94
.
15.
Partha
,
M. K.
,
Murthy
,
P. V. S. N.
, and
Raja Sekhar
,
G. P.
,
2006
, “
Soret and Dufour Effects in a Non-Darcy Porous Medium
,”
ASME J. Heat Transfer
,
128
(
6
), pp.
605
610
.
16.
Lakshmi Narayana
,
P. A.
,
2007
, “
Soret and Dufour Effects on Free Convection Heat and Mass Transfer in a Doubly Stratified Darcy Porous Medium
,”
J. Porous Media
,
10
(
6
), pp.
613
624
.
17.
Cheng
,
C. Y.
,
2009
, “
Soret and Dufour Effects on Natural Convection Heat and Mass Transfer From a Vertical Cone in a Porous Medium
,”
Int. Commun. Heat Mass Transfer
,
36
(
10
), pp.
1020
1024
.
18.
Raptis
,
A.
,
1998
, “
Radiation and Free Convection Flow Through a Porous Medium
,”
Int. Commun. Heat Mass Transfer
,
25
(
2
), pp.
289
295
.
19.
Badruddin
,
I. A.
,
Zainal
,
Z. A.
,
Aswatha Narayana
,
P. A.
,
Seetharamu
,
K. N.
, and
Siew
,
L. W.
,
2006
, “
Free Convection and Radiation for a Vertical Wall With Varying Temperature Embedded in a Porous Medium
,”
Int. J. Therm. Sci.
,
45
(
5
), pp.
487
493
.
20.
Mahmoud
,
M. A. A.
,
2012
, “
Radiation Effect on Free Convection of a Non-Newtonian Fluid Over a Vertical Cone Embedded in a Porous Medium With Heat Generation
,”
J. Appl. Mech. Tech. Phys.
,
53
(
5
), pp.
743
750
.
21.
Moradi
,
A.
,
Ahmadikia
,
H.
,
Hayat
,
T.
, and
Alsaedi
,
A.
,
2013
, “
On Mixed Convection-Radiation Interaction About an Inclined Plate Through a Porous Medium
,”
Int. J. Therm. Sci.
,
64
, pp.
129
136
.
22.
Tai
,
B. C.
, and
Char
,
M. I.
,
2010
, “
Soret and Dufour Effects on Free Convection Flow of Non-Newtonian Fluids Along a Vertical Plate Embedded in a Porous Medium With Thermal Radiation
,”
Int. Commun. Heat Mass Transfer
,
37
(
5
), pp.
480
483
.
23.
Minkowycz
,
W. J.
, and
Cheng
,
P.
,
1982
, “
Local Non-Similar Solutions for Free Convective Flow With Uniform Lateral Mass Flux in Porous Medium
,”
Lett. Heat Mass Transfer
,
9
(3), pp.
159
168
.
24.
Yih
,
K. A.
,
1997
, “
The Effect of Uniform Lateral Mass Flux on Free Convection About a Vertical Cone Embedded in a Saturated Porous Medium
,”
Int. Commun. Heat Mass Transfer
,
24
(
8
), pp.
1195
1205
.
25.
Yih
,
K. A.
,
1998
, “
Uniform Lateral Mass Flux Effect on Natural Convection of Non-Newtonian Fluids Over a Cone in Porous Media
,”
Int. Commun. Heat Mass Transfer
,
25
(
7
), pp.
959
968
.
26.
Chamkha
,
A. J.
, and
Ben-Nakhi
,
A.
,
2008
, “
MHD Mixed Convection–Radiation Interaction Along a Permeable Surface Immersed in a Porous Medium in the Presence of Soret and Dufour's Effects
,”
Heat Mass Transfer
,
44
, pp.
846
856
.
27.
Kumari
,
M.
, and
Nath
,
G.
,
2009
, “
Natural Convection From a Vertical Cone in a Porous Medium Due to the Combined Effects of Heat and Mass Diffusion With Non-Uniform Wall Temperature/Concentration or Heat/Mass Flux and Suction/Injection
,”
Int. J. Heat Mass Transfer
,
52
(
13–14
), pp.
3064
3069
.
28.
Rashad
,
A. M.
,
EL-Hakiem
,
M. A.
, and
Abdou
,
M. M. M.
,
2011
, “
Natural Convection Boundary Layer of a Non-Newtonian Fluid About a Permeable Vertical Cone Embedded in a Porous Medium Saturated With a Nanofluid
,”
Comput. Math. Appl.
,
62
(
8
), pp.
3140
3151
.
29.
Yih
,
K. A.
,
2012
, “
Uniform Blowing/Suction and Soret/Dufour Effects on Heat and Mass Transfer by Natural Convection About a Vertical Cone in Porous Media: UWT/UWC
,”
J. Air Force Inst. Technol., Taiwan
,
11
(
1
), pp.
109
120
.
30.
Huang
,
C. J.
,
2016
, “
Lateral Mass Flux and Thermal Radiation on Natural Convection Heat and Mass Transfer From a Vertical Flat Plate in Porous Media Considering Soret/Dufour Effects
,”
J. King Saud Univ. Sci.
(in press).
31.
Christopher
,
R. V.
, and
Middleman
,
S.
,
1965
, “
Power-Law Flow Through a Packed Tube
,”
Ind. Eng. Chem. Fundam.
,
4
(
4
), pp.
424
426
.
32.
Dharmadhirkari
,
R. V.
, and
Kale
,
D. D.
,
1985
, “
Flow of Non-Newtonian Fluids Through Porous Media
,”
Chem. Eng. Sci.
,
40
(
3
), pp.
527
529
.
33.
Cebeci
,
T.
, and
Bradshaw
,
P.
,
1984
,
Physical and Computational Aspects of Convective Heat Transfer
,
Springer-Verlag
,
New York
.
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