Significance of Magnetic Field on Carreau Dissipative Flow Over a Curved Porous Surface with Activation Energy
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Copyright © 2021 by American Scientific Publishers Journal of Nanofluids
All rights reserved. Vol. 10, pp. 75–82, 2021
Printed in the United States of America (www.aspbs.com/jon)
Significance of Magnetic Field on Carreau
Dissipative Flow Over a Curved Porous
Surface with Activation Energy
Gadamsetty Revathi1 , Jayachandra Babu Macherla2 , Chakravarthula Sivakrishnam Raju3, ∗ ,
Rohit Sharma3 , and Ali J. Chamkha4
1
Department of Mathematics, Gokaraju Rangaraju Institute of Engineering and Technology, Bachupally 500090,
Hyderabad, India
2
Department of Mathematics, S.V.A Govt. College, Srikalahasti 517644, India
3
Department of Mathematics, GITAM University, Bangalore 562163, Karnataka, India
4
Faculty of Engineering, Kuwait College of Science and Technology, Doha District, 35004 Kuwait
This paper theoretically clarifies the impact of pertinent parameters, including viscous dissipation on the flow
of Carreau fluid through a permeable arched elongating sheet. Flow describing equations are metamorphosed
as ODEs and executed using the combination of shooting and Runge-Kutta strategies. Consequences are elu-
cidated using tables and graphs. We discovered that (a) an appreciable decline in the concentration against
ARTICLE
temperature difference and reaction rate parameters (b) curvature parameter and porosity parameters regis-
tered opposite behaviour to each other on velocity profile (c) there is a reduction in the heat transfer rate with
larger Eckert number and curvature parameters (d) Biot number ameliorates the temperature and local Nusselt
number (e) Schmidt number and IP: 192.168.39.211
activation energyOn: Sun, 26 Sep
parameters are 2021 08:10:04
showing different behaviours on local Sher-
wood number. And also, magnetic Copyright: American
field and porosity Scientific Publishers
parameters minimize the velocity and surface drag force
and Biot number ameliorates the temperature. Delivered
Further, by Ingenta
present results are validated with the earlier outcomes
and perceived an acceptable agreement.
KEYWORDS: Carreau Fluid, Curved Stretching Sheet, Shooting Procedure, Curvature Parameter, Porosity Parameter,
Activation Energy Parameter.
1. INTRODUCTION including molten plastics and pulps, which are ultimately
Extrusion is a process in the industries, dealing with mate- propelled in factories analogous to usual Newtonian flu-
rials including polymers, plastics. In recent times, extru- ids. Sarpkaya1 started the work on the non-Newtonian
sion cooking has become a significant food processing fluid flow amongst two parallel planes with magnetic field.
activity. The greater part of the pertinent materials in these Tomita2 obtained the relation among the Reynolds number
procedures are non-Newtonian, with a shear rate reliant on and the boundary layer thickness after applying the bound-
viscosity, and hence carry on considerably not quite the ary layer theory concept to the non-Newtonian fluid flow
same as Newtonian fluids, for example, air and water. The at the high Reynold’s number. Huang3 presented numeri-
word “non-Newtonian” is an exceptionally wide one which cal solutions for the laminar non-Newtonian flow through
envelope an enormous assortment of fluids with basi- a porous annulus with the aid of perturbation and quasi-
cally dissimilar rheological features. Blood, ketchup, paint, linearization methods. Chandrupatla and Sastri4 and Hanks
jams, palm oil are a few instances of non-Newtonian flu- and Larsen5 demonstrated power-law fluid flows over dif-
ids. Non-Newtonian fluids have been exposed to numerous ferent geometries. One of their discoveries is, pseudoplas-
investigations regarding the energy transport and forecast tic fluids are superior functioning fluids in heat exchange
of drag force over 50 years. This is due to the expanded apparatus than Newtonian fluids. Rajagopal et al.6 anal-
use of non-Newtonian fluids in the industry, with examples ysed the behaviour of skin friction in different situations
in the examination of Falkner-Skan flow across a wedge.
∗
Chaoyang and Chuanjing7 explained the heat transfer char-
Author to whom correspondence should be addressed.
Emails: rchakrav@gitam.edu, sivaphd90@gmail.com acteristics of non-Newtonian fluid flow in two cases (natu-
Received: 12 April 2021 ral and forced convection) in porous media. Prasad et al.8
Accepted: 11 May 2021 considered elongating sheet as a geometry and elucidated
J. Nanofluids 2021, Vol. 10, No. 1 2169-432X/2021/10/075/008 doi:10.1166/jon.2021.1768 75Significance of Magnetic Field on Carreau Dissipative Flow Over a Curved Porous Surface with Activation Energy Revathi et al.
the visco-elastic flow. They remarked that the visco-elastic progressively noticeable on local shear stress. Shah et al.34
parameter escalates the mass transfer rate. Xu and Liao9 explored the Williamson fluid flow by a permeable elon-
applied HAM to provide the outcomes for the MHD gating sheet. By considering heat source/sink and elon-
non-Newtonian fluid flow triggered via an impulsively gating sheet, Hosseinzadeh et al.35 numerically scrutinised
stretching plate. By considering stretching sheet, several the nanofluid flow. Later several researchers36–44 explained
researchers10–13 scrutinized distinct non-Newtonian fluid different MHD fluid flows over a stretching sheet with sev-
flows. Their findings include a point that the entropy gen- eral parameters including Peclet number. In all the above
eration function upsurges up to a firm distance from the examinations, the stretching sheet is viewed as flat, and
sheet with the rise in the magnetic parameter. Santhosh and mathematical modelling is completed utilizing cartesian
Raju14–15 considered exponential stretching sheet and scru- coordinates. But, one can complete the same modelling by
tinized different Carreau fluid flows with various param- obtaining the governing equations with the aid of curvi-
eters including thermal radiation. Later, Maleki et al.16 linear coordinates system, when curved stretched sheet
elucidated the non-Newtonian nanofluid flow through a is considered. Flow over a curved stretching sheet has
porous surface and observed that for injection and suc- gained ample influences in the examination of boundary
tion cases, the utilization of nanoparticles does not sig- layer flow because of its amazing importance in engi-
nificantly affect heat transfer. Further, some authors17–22
neering and manufacturing segments, for example, making
deliberated diverse non-Newtonian fluid flows over differ-
of paper crafts, wire drawing, rubber sheets manufactur-
ent geometries. Khan et al.23 elucidated Carreau fluid flow
ing, and so forth. Rosca and Pop45 performed a numeri-
with Cattaneo-Christov heat flux by a shrinking/stretching
cal study on the viscid flow through a permeable arched
cylinder. They observed an escalation in the surface drag
contracting/elongating sheet and discovered that the suc-
forice with larger magnetic field parameter. Madhu et al.24
tion parameter upsurges the shrinking parameter. Naveed
used FEM (Finite Element Method) to resolve the math-
et al.46–47 deliberated different flows across the same geom-
ARTICLE
ematical model to examine the Carreau fluid flow in an
inclined microchannel with entropy generation optimiza- etry and witnessed that the material parameter exhibit dif-
tion. They detected the reduction in the entropy genera- ferent behaviour on fluid temperature and velocity. Imtiaz
tion at the right and left phase of the channel. Recently, et al.48 provided convergent series solutions to discuss
IP: 192.168.39.211 On: Sun, 26outcomes
the Sep 2021of08:10:04
their work and found that the curvature
various researchers25–27 considered distinct geometries
Copyright: and Scientific
American Publishers
inspected Carreau fluid flow with Joule heating as parameter
one of by Ingenta
Delivered raises the temperature. Recently, Kumar et al.49
50
the parameter. and Taseer et al. explained different fluid flows across a
The stretching sheet is utilized for polymer expulsion curved stretching sheet with several parameters, including
procedures, which is prepared with the mixture of both thermal radiation.
polymer sheets and metal. By considering stretching sur- From the above conversation, it is completely clear that
face as a geometry, several researchers analysed the char- the impression of activation energy parameter on Carreau
acteristics of heat transfer and flow because of its extensive fluid flow through an arched elongating sheet with viscous
scope of uses in engineering and industries problems. dissipation and Schmidt number is not explored up until
Instances of such procedures regarding polymers incorpo- this point. In this manner, the goal of the present work
rate cooling of filaments, glass blowing, synthetic fibers, is to make such an endeavour. Numerical solution of the
hot rolling and so forth. In all the procedures referenced problem is gotten by utilizing the combination of Runge-
above, the final product relies upon the rate of heat transfer Kutta and shooting strategies. Results are disclosed via
and surface drag force at the surface. In 1961, Sakiadis28 plots and table in two cases. To approve the precision of
provided the boundary layer equations of motion for lam- our investigation, an examination is made with the past
inar flow on a continuous solid surface. This work was work by Ahmad et al.51 and all outcomes are found in
extended by Crane29 to a stretching sheet in 1970, who acceptable agreement.
solved energy equation with various values of Prandtl
number. Gupta and Gupta30 considered the same geom-
etry and elucidated the features of two transports (heat, 2. FORMULATION
mass) of the flow. They perceived that the temperature A steady, incompressible 2D Carreau fluid flow across a
declines with the rise in blowing. Hassanien and Gorla 31 arched elongating sheet. Elongated velocity of the sheet is
used generalised Newton’s method to explain the influ- denoted by uw = ds. Arched elongating sheet is nestled in
ence of several parameters on the common profiles in the a circle or radius R. B0 is the intensity of the magnetic
inspection of micropolar fluid flow through an elongating field, which is enforced in r-direction. It is presumed that
sheet. Majeed et al.32 discovered that the Prandtl number C and Cw designate the ambient and surface concentra-
lowers the temperature in the analysis of ferromagnetic tion while T and Tw designate the ambient and surface
viscoelastic flow. Hussain et al.33 mentioned that, contrast temperatures respectively. Flow geometry is presented in
with fluid parameter, magnetic field parameter impact is Figure 1.
76 J. Nanofluids, 10, 75–82, 2021Revathi et al. Significance of Magnetic Field on Carreau Dissipative Flow Over a Curved Porous Surface with Activation Energy
with the conditions
⎫
u 0 s = uw v0 s = 0 ⎪
⎪
⎪
⎪
⎪
T ⎪
⎪
−k = h Tw − T C 0 s = Cw ⎪
⎬
r r=0
(6)
⎪
⎪
u r s → 0
u r s
→ 0 T r s → T ⎪
⎪
⎪
⎪
r ⎪
⎪
⎭
C r s → C as r →
Here u component of velocity in s direction, v component
of velocity in r direction, n power law index parameter, m
fitted rate constant , k∗ Boltzmann constant, electrical
conductivity, kinematic viscosity, fluid density, per-
meability of the porous medium, fluid relaxation time, T
fluid temperature, Cp specific heat capacitance, k thermal
Fig. 1. Flow geometry of the present problem. conductivity, C fluid concentration, k1 chemical reaction
rate, Dm molecular diffusivity, E1 activation energy param-
With these presumptions, flow driven equations are eter, h convective heat transfer coefficient.
given as:47 With the transmutations47
u ⎫
v R + r + R = 0
u = dsf ⎪
(1) uw
= r p = d s P
2 2 ⎪
⎪
ARTICLE
r s ⎪
s ⎪
⎪
⎪
⎪
u p R √ ⎬
u = (2) v = − d f
R+r r r +R (7)
⎪
⎪
IP: 192.168.39.211 On: Sun, 26 Sep 2021 ⎪
⎪
T =08:10:04
Copyright: American Scientific Publishers −T + Tw + T ⎪
⎪
⎪
u u u vu ⎪
⎭
v+ R+ Delivered by Ingenta C = −C + Cw + C
r s R + r R+r
2 Eq. (1) is trivially satisfied, the Eqs. (2)–(5) metamor-
P R u u 1 1 u
=− + + − phosed as:
s R + r r 2 r R + r R + r R + r
n−1/2 2
2 u u u u 1 dP f 2
× 1+ + + = (8)
r r r 2 r R + r d +K
2
1 u u
− 2
n − 1
R+r R+r r 2K 1 n−3/2
P = f + f 1 + We2 f 2
+K +K
u u n−3/2 u
× 1+ 2 − B02 u − (3) K
r r × 1 + nWe2 f 2 + ff − f 2
+K
2
T 1 T k T T 1 1 1
v + Ru = + + ff − f
r R+r s Cp r 2 r r + R +K + K2
2
u − M + f (9)
+ (4)
Cp r
K
C R C C 2
1 C + Pr f + + Pr Ecf 2 = 0 (10)
v + u = Dm + +K +K
r r + R s r 2 r + R r
K
m + Scf + − Sc 1 + m
T E1 +K +K
− k1
2
exp −
T k∗T
E
× exp − =0 (11)
× C − C (5) 1 +
J. Nanofluids, 10, 75–82, 2021 77Significance of Magnetic Field on Carreau Dissipative Flow Over a Curved Porous Surface with Activation Energy Revathi et al.
and conditions (6) metamorphosed as rs (wall shear stress), jw (heat flux) and qw (heat flux)
⎫ are specified as
df ⎪
⎪
f = 0 =1 ⎪ ⎛ ⎞
d =0 ⎪
⎪
⎪ 2 n−1/2
⎪
⎪ u u u
⎪
⎪ rs = ⎝ 1 + 2
− ⎠
d ⎪
⎪
⎪ r r R + r
= − 1 − Bi ⎪
⎪
d =0 ⎬
r=0
(12) C T
= 1 ⎪
at = 0
⎪ jw = − Dm qw = − k (16)
⎪
⎪ r r
⎪
⎪
r=0 r=0
df d2f ⎪
⎪
→0 → 0 → 0 ⎪
⎪ and their non-dimensional forms are designated as:
⎪
⎪
⎪ n−1∗05 ⎫
2
d d
⎪
⎪
⎭ ⎪
⎪
→ 0 as → Res 1/2 Cfs = 1 + f 2 We2 ⎪
⎪
⎪
⎪
⎪
Curvature parameter K, Weissenberg parameter We, poros- 1 ⎪
⎬
×f − f =0
ity parameter , Prandtl number Pr, Schmidt number K (17)
⎪
⎪
Sc, temperature difference parameter , Eckert number Res −1/2 Shs = − =0 ⎪
⎪
⎪
⎪
Ec reaction rate parameter , activation energy param- ⎪
⎪
−1/2 ⎭
eter E, magnetic field parameter M, Biot number Bi are Res Nus = − =0
designed as:
⎫ where Res = suw / (Reynold’s number).
d 2
duw 2 ⎪
⎪
K=R We = = ⎪
⎪
⎪
⎪
d ⎪
⎪ 3. DISCUSSION
⎪
⎪
Cp T − T ⎪
⎪ Equations (10)–(11), (15) with conditions (12) are puzzled
⎪
ARTICLE
Pr = Sc = = w ⎪
⎪ out numerically by executing the combination of Runge-
k Dm T ⎪
⎬
Kutta and shooting strategies by taking K = 2 Sc = 06,
uw 2 k1 2 E1 ⎪ (13) n = 05 = 05 Ec = 03 = 15 = 01 Pr = 071
Ec = = E= ⎪
⎪
Cp Tw − T ⎪
k ∗ T ⎪ = Sep = 05 M = 15 Bi = 05. Consequences are
d 192.168.39.211
IP: ⎪
⎪ On: Sun,m26 05 E 2021 08:10:04
⎪
⎪ Scientific Publishersand tables in two cases i.e., We = 05
elucidated by plots
⎪
Copyright: American
⎪
⎪
⎪
Delivered by We = 0. In both cases, we witnessed the same impact
Ingenta
and
B0 2
h ⎪
⎪
d ⎪
⎭ (increasing or decreasing).
M= Bi =
d k
With the help of Eq. (9), Eq. (8) can be rewritten as 3.1. Concentration Profile
n−3/2 It is witnessed from Figure 2 that larger Sc mini-
1 + We2 f 2 1 + nWe2f 2 f iv + 1 + We2 f 2 mizes the fluid concentration. Typically, escalation in Sc
2f n−5∗05 leads to the deceleration in mass diffusivity of the fluid.
× 1 + nWe2 f 2 + 1 + f 2We2 n − 3 Figure 3 affirms that E ameliorates fluid concentration.
+K
From Figure 4, it is emphasized that larger mini-
1
× 1 + f 2We2 n f We2 f f + f mizes the concentration. It is noticed that profiles are
K +
1 f 1 f 1 1
− + − Solid : Non-newtonian fluid
K + K + K + K + K +
2
0.9 Dashed : Newtonian fluid
1 K 0.8
× f f − f f K − −ff + f 2
K + K + 0.7
Sc = 0.5,0.6,0.7 0.29
K 1
− ff − M + 0.6
K + + K2 0.28
( )
0.5
f
× f + =0 0.4 0.27
(14)
+K
0.3 0.26
Surface drag force Cfs , Sherwood number Shs , Nusselt
0.2 1 1.05 1.1
numbers Nus are characterized as (Naveed et al. [46])
0.1
rs sjw
Cfs = Shs =
u2w Dm Cw − C 0
0 0.5 1 1.5 2 2.5 3 3.5 4
sqw
Nus = (15)
k Tw − T Fig. 2. Outcome of Sc on concentration.
78 J. Nanofluids, 10, 75–82, 2021Revathi et al. Significance of Magnetic Field on Carreau Dissipative Flow Over a Curved Porous Surface with Activation Energy
1 4
Solid : Non-newtonian fluid Solid : Non-newtonian fluid
0.9
Dashed : Newtonian fluid 3.5 Dashed : Newtonian fluid
0.8
3
0.7 E = 1,1.6,3
0.6 0.29 2.5 Ec = 1,1.5,2
0.28
( )
( )
0.5
2
0.27
0.4
0.26
1.5
0.3 0.25
0.2 1
1 1.05 1.1 1.15
0.1
0.5
0
0 0.5 1 1.5 2 2.5 3 3.5 4 0
0 0.5 1 1.5 2 2.5 3 3.5 4
Fig. 3. Outcome of E on concentration.
Fig. 6. Outcome of Ec on temperature.
1
0.6
Solid : Non-newtonian fluid
0.9
Dashed : Newtonian fluid
Solid : Non-newtonian fluid
0.8 0.5 Dashed : Newtonian fluid
ARTICLE
= 0.3,0.6,0.9
0.7
0.31 0.4
0.6
K = 1,1.6,3
( )
0.5 0.3
( )
IP: 192.168.39.211 On: Sun, 260.3Sep 2021 08:10:04
0.4 0.29
Copyright: American Scientific Publishers
0.3
Delivered by Ingenta
0.2
0.28
1 1.05 1.1 1.15
0.2
0.1
0.1
0
0 0.5 1 1.5 2 2.5 3 3.5 4 0
0 0.5 1 1.5 2 2.5 3 3.5 4
Fig. 4. Outcome of on concentration.
Fig. 7. Outcome of K on temperature.
1 0.9
Solid : Non-newtonian fluid
0.9 0.8 Solid : Non-newtonian fluid
Dashed : Newtonian fluid
Dashed : Newtonian fluid
0.8
0.7
0.7
0.6
Bi = 1,1.5,2
0.6 = 1,2,3 0.3
0.5
( )
( )
0.5
0.29
0.4
0.4
0.28 0.3
0.3
0.27 0.2
0.2
1 1.05 1.1 0.1
0.1
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4
Fig. 5. Outcome of on concentration. Fig. 8. Outcome of Bi on temperature.
J. Nanofluids, 10, 75–82, 2021 79Significance of Magnetic Field on Carreau Dissipative Flow Over a Curved Porous Surface with Activation Energy Revathi et al.
1 1
0.9 0.9 Solid : Non-newtonian fluid
Solid : Non-newtonian fluid
Dashed : Newtonian fluid
Dashed : Newtonian fluid
0.8 0.8
0.7 0.7
0.6 0.6
M = 1,2,3
f'( )
0.5 0.5 = 1,2.5,5
f'( )
0.4 0.4
0.3 0.3
0.2 0.2
0.1 0.1
0
0
0 0.5 1 1.5 2 2.5 3 3.5 4
0 0.5 1 1.5 2 2.5 3 3.5 4
Fig. 9. Outcome of M on velocity. Fig. 11. Outcome of on velocity.
appearing predominant in the case of We = 05 compared the resistance to the flow. So, M minimizes the velocity
to the other. Figure 5 affirms that lowers the same (Fig. 9). Figure 10 enlightens the change in velocity with
(concentration). curvature parameter. Surface radius becomes higher with
the escalation in K. So, fluid velocity ameliorates. Step-
ARTICLE
3.2. Temperature Profile up in porosity parameter () leads to the creation of large
amount of porous spaces, which offers more resistance to
Eckert number initiate the action of transmutation of shear
the flow. Figure 11 affirms the same. We detected that pro-
forces into heat, which affirms the result in Figure 6 (incre-
files are appearing more prominent in case of Newtonian
ment). Note that, there is an increase in the radius ofOn:
IP: 192.168.39.211 the Sun, 26 Sep 2021 08:10:04
fluid.
surface with the raise in K. So, thickness of theAmerican
Copyright: thermal Scientific Publishers
boundary layer ameliorates, which in turn, aid toDelivered
enhance by Ingenta
the temperature (Fig. 7). Figure 8 reported that Bi inten- Table I. Numerical values of surface drag force for different
sify the temperature. Typically, quantity of heat transferred parameters.
to the fluid flow escalates with the larger Biot number. Res 05 Cfs
M K Non-newtonian fluid Newtonian fluid
3.3. Velocity Profile
Due to Lorentz force (which arises owing to the trans- 1 −2033689 −2027294
2 −2366173 −2336660
fer of energy among electric and magnetic fields dur- 3 −2668236 −2601716
ing the movement of fluid), there is an escalation of 1 −3326969 −3329360
16 −2619560 −2630139
3 −2108216 −2102186
1
1 −2517283 −2507122
0.9 Solid : Non-newtonian fluid 25 −2952692 −2877835
Dashed : Newtonian fluid 5 −3670820 −3388083
0.8
0.7
Table II. Values of heat transfer rate for various parameters.
0.6
K = 1,1.6,3
Res −05 Nus
f'( )
0.5
0.4
Ec K Bi Non-newtonian fluid Newtonian fluid
0.3
1 −0561973 −0403660
1.5 −1002414 −0766904
0.2 2 −1442856 −1130162
1 0284893 0291394
0.1
16 0265666 0270980
0 3 0242414 0247375
0 0.5 1 1.5 2 2.5 3 3.5 4 1 0339792 0375680
17 0426244 0473511
3 0505929 0564515
Fig. 10. Outcome of K on velocity.
80 J. Nanofluids, 10, 75–82, 2021Revathi et al. Significance of Magnetic Field on Carreau Dissipative Flow Over a Curved Porous Surface with Activation Energy
Table III. Values of mass transfer rate for various parameters. • An appreciable decline has been noticed in the con-
centration against temperature difference and reaction rate
Res −05 Shs
parameters.
E Sc Non-newtonian fluid Newtonian fluid • Temperature ameliorates with larger Eckert number.
1 1332499 1332984 • Activation energy parameter enriches fluid
1.6 1228297 1229217 concentration.
3 1108869 1110796 • Curvature parameter and porosity parameters registered
03 0992120 0992695 opposite behaviour to each other on velocity profile.
06 1109992 1109990
09 1213103 1212626
• Porosity parameter minimizes the surface drag force.
05 1099404 1099640 • Observed shrink in the heat transfer rate with larger Ec
06 1180963 1181203 and K.
07 1256366 1256603 • Biot number ameliorates the temperature and local Nus-
1 1153483 1148888 selt number.
2 1255083 1247237
3 1337163 1327150
• Eckert number lessens the heat transfer rate.
• Schmidt number and activation energy parameters are
showing different behaviours on local Sherwood number.
Table IV. Validation of present results with the previous results for skin
friction.
References and Notes
−Res 05 Cfs (skin friction) 1.
T. Sarpkaya, A. I. Ch. E. J. 7, 324 (1961).
2.
Y. Tomita, Bulletin of JSME 4, 77 (1961).
K M Ahmad et al.51 Present study 3.
C. L. Huang, J. Math. Anal. Appl. 59, 130 (1977).
5 02 05 153300 1533000 4.
R. C. Ashok and V. M. K. Sastri, Numer. Heat Transf. Part B: Fun-
ARTICLE
10 141300 1413000 daments: An Int. J. Comp. Methodology 1, 243 (1978).
20 135700 1357000 5. R. W. Hanks and K. M. Larsen, Ind. Eng. Chem. Fundam. 18, 33
10 0 05 132800 1328000 (1979).
02 141300 1413000 6. K. R. Rajagopal, A. S. Gupta, and T. Y. Na, Int. J. Non-Linear
04 IP: 192.168.39.211
149300 On: Sun, 26Mechanics
1493000 Sep 2021 18, 313 (1983).
08:10:04
7.
Copyright: American Scientific Publishers Chuanjing, Int. J. Heat Fluid Flow 10, 160
W. Chaoyang and T.
(1989).
Delivered by Ingenta
8. K. V. Prasad, S. Abel, and P. S. Datti, Int. J. Non-Linear Mech.
From Table I, it is understandable that porosity and mag- 38, 651 (2003).
netic field parameters are decreasing functions of surface 9. H. Xu and S. Liao, J. Non-Newtonian Fluid Mech. 129, 46 (2005).
drag force in contrast to curvature parameter. Table II clari- 10. T. Javed, N. Ali, Z. Abbas, and M. Sajid, Chemical Eng. Commun.
200, 327 (2013).
fies that Eckert number and curvature parameters minimize 11. S. Nadeem, R. U. Haq, N. S. Akbar, and Z. H. Khan, Alexandria
the local Nusselt number but Biot number step-up the Eng. J. 52, 577 (2013).
same. Table III elucidate that Schmidt number, tempera- 12. M. M. Rashidi, S. Bagheri, E. Momoniat, and N. Freidoonimehr, Ain
ture difference parameter and reaction rate parameters are Shams Eng. J. 8, 77 (2017).
13. M. Jayachandra Babu and N. Sandeep, Alexandria Eng. J. 55, 2193
having the same impact (raise) on local Sherwood number
(2016).
in contrast to activation energy parameter. Table IV dis- 14. H. B. Santhosh and C. S. K. Raju, Journal of Nanofluids 7, 72
plays the correlation among the present outcomes and the (2018).
previous outcomes (for the numerical estimations of fric- 15. H. B. Santhosh and C. S. K. Raju, Journal of Nanofluids 7, 1130
tion factor). We found a respectable understanding. This (2018).
16. H. Maleki, M. R. Safaei, A. A. A. A. Alreashed, and A. Kasaeian,
decides the aptness of the present investigation. J. Thermal Anal. Calorimetry 135, 1655 (2019).
17. A. Hussain, S. Akbar, L. Sarwar, S. Nadeem, and Z. Iqbal, Heliyon
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