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International Journal of Research in Engineering and Applied Sciences(IJREAS)
Available online at http://euroasiapub.org
Vol. 11 Issue 05, May-2021 ISSN (O): 2249-3905, ISSN(P): 2349-6525 | Impact Factor: 7.196 |
International Journal of Research in Engineering & Applied Sciences
Email:- editorijrim@gmail.com, http://www.euroasiapub.org
An open access scholarly, online, peer-reviewed, interdisciplinary, monthly, and fully refereed journals
1
Magnetic effects on free convection flow of Nano fluids through porous
medium past an infinite vertical plate in slip flow regime in the presence of
variable heat source and variable suction
Dr Rajendra Kumar Dhal
*Dr Banamali Jena
**Mr P M Sreekumar
J.N.V. Hadgarh, Keonjhar, Odisha- 758023
Email: dhal.rajendra@gmail.com
*J.N.V. Goshala, Sambalpur, Odisha- 768024
Email:banamalijena@rediffmail.com
**J.N.V. Joura, Morena, MP-476221
Email:pmsreekumar63@gmail.com
ABSTRACT: Magnetic effects on free convection flow of nano fluid through porous medium
past an infinite vertical plate in slip flow regime in the presence of both variable heat source
and variable suction for water- Cu and water - Al2O3 has been studied. The influences of the
various parameters on the flow field, Heat field, mean value of skin friction and tangential
value of phase angle are extensively discussed from graphs and tables.
KEY WORDS: MHD, Free convection, Heat Transfer, variable Heat Source, slip flow regime,
variable Suction, nano fluid, porous medium.
1.INTRODUCTION: Free convection fluids like oil, water and ethylene glycol have poor heat
transfer capacity due to their poor thermal conductivity. To enhance the thermal conductivity of
these fluids, investigatorshave added nano particles (nano size) of base metals (Al, Cu), Oxides
(Al2O3, TiO2), Nitriles (AlN, SiN) and Carbides (SiC), etc. to base fluids. Thus the convective
heat transfer of the base liquids will increase. Nano fluids contribute to lower heat exchanger
size because of their thermal and flow characteristics. Hence, nano fluids are used in
microelectronics and in chips of computer devices.Nano fluids in the presence or absence of
magnetic field have enumerable applications in the industries due to unique chemical and
physical properties of nanometer sized materials. Sundry utilizations of nano fluids, the cooling
applications of nano fluids incorporate silcon mirror cooling, electronics cooling, vehicle
International Journal of Research in Engineering and Applied Sciences(IJREAS)
Available online at http://euroasiapub.org
Vol. 11 Issue 05, May-2021 ISSN (O): 2249-3905, ISSN(P): 2349-6525 | Impact Factor: 7.196 |
International Journal of Research in Engineering & Applied Sciences
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cooling, transformer cooling and so on, are some bright instances. The hypothesis of nano fluid
was first presented by S. U. S. Choi and has been a field of dynamic research area for two
decades. Choi et. al. [1] has demonstrated experimentally that the injection of nano particles
enhances the themal conductivity of the fluid. Buongiorno [2] developed a mathematical model
for nanofluid and explored its various transport mechanisms of nano fluids. Mahian et. al. [3]
have discussed the irreversible analysis of the vertical annulus using water-TiO2 fluid with
MHD flow effects. Shehzad et. al. [4] have studied the MHD mixed convective peristaltic
motion of nano fluid with joule heating and thermophoresis effects. Venkataramanaiah et. al.
[5] have clarified about the nano particles effect on MHD boundary layer flow of Williamson
fluid over a stretching sheet. Zubair et. al. [6] have discussed the Heat and Mass Transfer
analysis of MHD Nano fluid flow with Radiative Heat Effects in the presence of Spherical Au-
Metallic Nano particles.Khan et. al. [7] have discoursed about the MHD Williamson nano fluid
with chemical reaction. Thumma et. al. [8] have investigated about the numerical study of heat
source on dissipative magnetic nano fluid flow from a non linear inclined stretching surface.
Vedavathi et. al. [9] have discussed on heat transfer on MHD nano fluid flow over a semi
infinite flat plate embedded in a porous medium with radiation absorption, heat source and
diffusion thermo effect. Mohyud-Din et. al. [10] have presented a study of heat and mass
transfer on magnetohydrodynamic (MHD) flow of nano particles. D Vidyanandha Babu [11]
has studied the effect of Dufour and thermal radiation on convection radiative nano fluid flow
with suction and heat source. Govardhan et. al. [12] have studied on Heat and Mass transfer in
MHD Nano fluid over a STretching Surface along with Viscous Dissipation effect.
In this problem, we try to investigate the Magnetic effects on free convection flow of nano fluid
through porous medium past an infinite vertical plate in slip flow regime in the presence of
variable heat source and variable suction both for water-Cu and Water-Al2O3.
2. FORMULATION OF PROBLEM: An unsteady free convection two dimensional flow of an
incompressible, electrically conducting viscous nano fluid through porous medium past an
infinite vertical plate in slip flow regime in the presence of chemical reaction, variable heat
International Journal of Research in Engineering and Applied Sciences(IJREAS)
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source and variable suction is considered. Let ๐โฒ axis is taken along the plate in vertical upward
direction and ๐โฒ axis is normal to the plate. A uniform magnetic field strength H0 is applied
normal to the plate. Initially, sorrounding temperature is ๐โโฒ . Also, the temperature at the plate
is ๐๐คโฒ . For ๐ก โฒ โฅ 0, the temperature and mass concentration changes periodically. As the plate is
infinite along ๐โฒ axis, so all the physical quantities are in dependentof ๐ฅโฒ and are the functions
of ๐ฆโฒ and ๐ก โฒonly. It is assumed that viscous dissipation and joulean dissipation are neglected,
density varies in the body force term and variable heat source is taken as ๐ฃ0
2
๐๐ 1 + ๐๐ต๐๐๐ โฒ ๐ก โฒ
.
Then by usual Boussinesq's approximation the unsteady flow is governed by the following
equations.
Equation of Continuity:
๐๐ฃ โฒ
๐๐ฆ โฒ= 0 โน ๐ฃ โฒ = โ๐0 1 + ๐๐ด๐๐๐ โฒ๐ก โฒ (1)
The Equation of Motion:
๐๐ข โฒ
๐๐ก โฒโ ๐0 1 + ๐๐ด๐๐๐ โฒ๐ก โฒ
๐๐ข โฒ
๐๐ฆ โฒ=
๐๐๐
๐๐๐
๐2๐ข โฒ
๐๐ฆ โฒ2 + ๐ ๐ฝ ๐๐ ๐ โฒ โ ๐โโฒ + ๐ ๐ฝ๐ ๐๐ ๐ถ โฒ โ ๐ถโ
โฒ โ๐๐ต0
2๐ข โฒ
๐๐๐โ
๐ข โฒ
๐พโฒ(2)
The Energy Equation:
๐๐ โฒ
๐๐ก โฒโ ๐0 1 + ๐๐ด๐๐๐ โฒ๐ก โฒ
๐๐ โฒ
๐๐ฆ โฒ=
๐๐๐
๐๐ถ๐ ๐๐
๐2๐โฒ
๐๐ฆ โฒ2โ
๐02
๐๐ 1 + ๐๐ต๐๐๐ โฒ๐ก โฒ ๐ โฒ โ ๐โ
โฒ (3)
with the following boundary conditions
๐ก > 0: ๐ขโฒ = ๐ฟโฒ
๐๐ข โฒ
๐๐ฆ โฒ, ๐ โฒ = ๐๐ค
โฒ + ๐ ๐๐คโฒ โ ๐โ
โฒ ๐๐๐ โฒ๐กโฒ๐๐ก๐ฆ = 0,
๐ขโฒ = 0 , ๐ โฒ = ๐โโฒ ๐๐ก๐ฆ โ โ
(4)
where ๐๐๐ is the dynamic viscosity,๐๐๐ is the thermal diffusivity,๐๐๐ is the effective density,
๐๐ถ๐ ๐๐
is the heat capacity and ๐ฝ ๐๐ is the coefficient of volumetric expansion of heat of nano
fluid. They are defind as
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๐๐๐ =๐๐
1โ๐ 2.5 ,๐๐๐ = 1 โ ๐ ๐๐ + ๐๐๐ , ๐๐ถ๐ ๐๐
= 1 โ ๐ ๐๐ถ๐ ๐
+ ๐ ๐๐ถ๐ ๐ ,
๐๐๐ = ๐๐ + 2๐๐ โ 2๐ ๐๐ โ ๐๐
๐๐ + 2๐๐ + 2๐ ๐๐ โ ๐๐ ๐๐ , ๐ฝ ๐๐ = 1 โ ๐ ๐ฝ ๐ + ๐ ๐ฝ ๐
๐ is the electrical conductivity of the fluid, g is the acceleration due to gravity and ๐is the
volume of nano fluid.
Let us introduce the dimensionless quantities
๐ข =
๐ข โฒ
๐0 , ๐ก =
๐02๐ก โฒ
๐๐ , ๐ฆ =
๐0๐ฆ โฒ
๐๐ , ๐ =
๐ โฒโ๐โโฒ
๐๐คโฒ โ๐โ
โฒ , ๐บ๐ =๐ ๐ฝ ๐๐๐ ๐๐ค
โฒ โ๐โโฒ
๐03 ,
๐๐ =๐๐ ๐๐ถ๐
๐
๐๐ , ๐ =
๐๐๐๐ต02
๐๐๐02 , ๐ =
๐ โฒ
๐03 ๐๐ , ๐พ =
๐พโฒ๐02
๐๐ , ๐ =
๐0๐ฟโฒ
๐๐
(5)
where Gr is the Grashof number, K is permeability of porous medium, M is magnetic
parameter, Pr is Prandtl number, h is rarefraction parameter, A is suction parameter and B is
heat source parameter.
Substituting equation (5) in equations (2) to (3) with boundary condition (4), we have
๐๐ข
๐๐กโ 1 + ๐๐ด๐๐๐๐ก
๐๐ข
๐๐ฆ= ๐0
๐2๐ข
๐๐ฆ 2 โ ๐1๐๐ข โ1
๐พ๐ข + ๐2๐บ๐๐(6)
๐๐
๐๐กโ 1 + ๐๐ด๐๐๐๐ก
๐๐
๐๐ฆ=
1
๐๐๐3
๐2๐
๐๐ฆ 2 โ 1 + ๐๐ต๐๐๐๐ก ๐ (7)
with boundary conditions
๐ข = hโu
โy, ๐ = 1 + ๐๐๐๐๐ก at ๐ฆ = 0
๐ข = 0, ๐ โ 0, as๐ฆ โ โ (8)
3. METHOD OF SOLUTION:
Assuming small amplitude oscillation๐ โช 1, we can represent the velocity u and temperature
๐near the plate as follows
๐ข = ๐ข0 ๐ฆ + ๐๐ข1 ๐ฆ ๐๐๐๐ก
๐ฝ = ๐ฝ๐ ๐ + ๐๐ฝ๐ ๐ ๐๐๐๐ (9)
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Substituting (9) in (6) to (8) and equating the coefficient of harmonic and non harmonic terms
with neglecting the coefficient of ๐2, we get
๐0 ๐ข0โฒโฒ + ๐ข0
โฒ โ ๐1๐ + 1
๐พ ๐ข0 = โ๐บ๐๐2๐0 (10)
๐0๐ข1โฒโฒ + ๐ข1
โฒ โ ๐๐ + ๐1๐ + 1
๐พ ๐ข1 = โ๐ข0
โฒ ๐ด โ ๐บ๐๐2๐1 (11)
๐3๐0โฒโฒ + ๐๐๐0
โฒ โ ๐๐๐0 = 0 (12)
๐3๐1โฒโฒ + ๐๐๐1
โฒ โ ๐๐ 1 + ๐๐ ๐1 = ๐๐๐ต๐0 โ ๐๐๐ด๐0โฒ (13)
with the following boundary conditions
๐ข0 = hโu0
โy, ๐ข1 = h
โu1
โy, ๐0 = 1, ๐1 = 1 at ๐ฆ = 0
๐ข0 = 0, ๐ข1 = 0, ๐0 = 0, ๐1 = 0 at๐ฆ โ โ (14)
Solving the equations (10) to (13) using boundary condition (14) and (9), we get
u = b2 eโa2y โ b1 e
โa1y + b8eโa4y + b5eโa2y + b6eโa1y + b7 eโa3y ฯตeiฯt (15)
ฮธ = eโa1y + b4eโa3y + b3eโa1y ฯตeiฯt (16) The non-
dimensional skin friction
๐0 = ๐๐ข
๐๐ฆ
๐ฆ=0
= โ๐2๐2 + ๐1๐1 + โ๐4๐8 โ ๐2๐5 โ ๐1๐6 โ ๐3๐7 ๐๐๐๐๐ก
= โ๐2๐2 + ๐1๐1 + ๐๐๐๐๐ก ๐น๐ + ๐๐น๐ = ๐๐ + ๐ ๐น ๐๐ ๐๐ก +๐ผ (17)
where ๐น = ๐น๐2 + ๐น๐
2 , ๐ก๐๐๐ผ =๐น๐
๐น๐ , ๐๐ = โ๐2๐2 + ๐1๐1 Is the skin friction of mean velocity
and F= โ๐4๐8 โ ๐2๐5 โ ๐1๐6 โ ๐3๐7
The non-dimensional Nusselt number
๐๐ข = โ ๐๐
๐๐ฆ
๐ฆ=0
= ๐1 + ๐3๐4 + ๐1๐3 ๐๐๐๐๐ก = ๐1 + ๐๐๐๐๐ก ๐1 + ๐๐2
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=๐1 + ๐ ๐๐๐ ๐๐ก +๐ฝ (18)
where ๐ = ๐12 + ๐2
2๐ก๐๐๐ฝ =๐2
๐1, ฯ
0=
1
1โฯ 2.5 1โฯ +ฯฯsฯf
, ฯ1
=1
1โฯ +ฯฯsฯf
,
๐2 = 1 โ ฯ + ฯฮฒs
ฮฒf
, ๐3 = ๐๐ +2๐๐โ2๐ ๐๐โ๐๐
๐๐ +2๐๐+2๐ ๐๐โ๐๐
1โ๐ +๐ ๐๐ถ๐
๐ ๐๐ถ๐
๐
,
๐1 =๐๐+ ๐๐ 2+4๐3๐๐
2๐3, ๐2 =
1+ 1+4๐0 ๐1๐+ 1
๐พ
2๐0 , ๐3 =
๐๐+ ๐๐2+4๐๐๐3 1+๐๐
2๐3,
๐4 =1 + 1 + 4 ๐0 ๐๐ + ๐1๐ +
1
๐พ
2๐0 , ๐1 =
๐1๐บ๐
๐0๐12 โ ๐1 โ ๐๐1๐ +
1
๐พ
, ๐2
=๐1 1 + ๐๐1
1 + ๐๐2, ๐3 =
๐๐๐ต + ๐๐๐ด๐1
๐3๐12 โ ๐๐๐1 โ ๐๐ 1 + ๐๐
,
๐4 = โ๐3, ๐5 =๐ด๐2
๐0๐22 โ ๐2 โ ๐๐ + ๐1๐ +
1
๐พ
, ๐6 = โ ๐ด๐1๐2 + ๐บ๐๐2
๐0๐12 โ ๐1 โ ๐๐ + ๐1๐ +
1
๐พ
,
๐7 = โ๐บ๐๐2๐4
๐0๐32 โ ๐3 โ ๐๐ + ๐1๐ +
1
๐พ
, ๐8 = โ ๐๐3๐5 + ๐๐1๐6 + ๐๐3๐7 + ๐5 + ๐6 + ๐7
1 + ๐๐4
4. RESULT AND DISCUSSION:
In this paper, Magnetic effects on free convection flow of nano fluid through porous medium
past an infinite vertical plate in slip flow regime in the presence of variable heat source and
variable suction has been compared between water-Cu and water-Al2O3. The effect of the
parameters Gr, M, K, Pr, A, B, ๐ and h on flow characteristics have been studied and shown by
means of graphs and tables. In order to have physical correlation, we choose suitable values of
flow parameters and values of parameters for two different nano fluids in table-1. The graph of
heat and velocities are taken w.r.t. to distance y. The mean value of shearing stress and tangent
value of phase angle are shown in table.
International Journal of Research in Engineering and Applied Sciences(IJREAS)
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Velocity Profile: The velocity profiles are depicted in Fig 1-7. Figure-1 shows the effects of the
parameter M on velocity profile at any point of the fluid when Pr = 6.86, K = 2, A = 2, B = 2,
Gr = 2, t = 0.5, ฯ = 0.05and h = 0.2. It is noticed that the velocity decreases with the increase
of Magnetic parameter (M). Initially, the velocity of water-Cu nano fluid is more than the
water-Al2O3 nano fluid.
Figure-(2) shows the effects of the parameter K on velocity profile at any point of the fluid
when Pr = 6.86, M = 2, A = 2, B = 2, Gr = 2, t = 0.5, ฯ = 0.05and h = 0.2. It is noticed that the
velocity increases with the increase of permeability of porous medium (K). Initially the velocity
of water-Cu nano fluid is more than water-Al2O3 nano fluid.
Figure-(3) shows the effect of the parameter Gr on velocity profile at any point of the fluid
when Pr = 6.68, M = 2, A = 2, B = 2, K = 2, t = 0.5,ฯ = 0.05and h = 0.2. It is noticed that the
velocity increases with the increase of Grashof number (Gr).
Figure-(4) shows the effect of the parameter A on velocity profile at any point of the fluid,
when Pr = 6.86, M = 2, K = 2, B = 2, Gr = 2, t = 0.5,ฯ = 0.05and h = 0.2. It is noticed that the
velocity increases with the increase of Suction parameter (A). Initially, the velocity of water-Cu
nano fluid is more than water-Al2O3 nano fluid.
Figure-(5) shows the effect of the parameter๐ on velocity profile at any point of the fluid, when
Pr = 6.86, M = 2, K = 2, A = 2, B = 2, Gr = 2, t = 0.5 and h = 0.2. It is noticed that the velocity
increases with the increase of volume fraction of nano fluid ๐ . The velocity of water-Cu nano
fluid is more than water-Al2O3 nano fluid near the plate.
Figure-(6) shows the effect of the parameter h on velocity profile at any point of the fluid, when
Pr = 6.86, M = 2, K = 2, A = 2, B = 2, Gr = 2, t = 0.5 and ฯ = 0.05.It is noticed that the
velocity increases with the increase of rarefaction parameter (h). The velocity of water-Cu nano
fliuid is more than water-Al2O3 nano fluid near the plate.
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Figure-(7) shows the effect of the parameter B on velocity profile at any point of the fluid,
when Pr = 6.86, M = 2, K = 2, A = 2, Gr = 2, t = 0.5, ๐ = 0.05, and h = 0.2. It is noticed that
the velocity increases slowly with the increase of Source parameter (B). The velocity of water-
Cu nano fluid is more than water-Al2O3 nano fluid near the plate.
Heat Profile: The heat profiles are depicted in Fig 8-10. Figure-(8) shows the effect of the
parameter B on heat profile at any point of the fluid, when Pr = 6.86, A = 2, t = 0.5 and ๐ =
0.05. It is noticed that the temperature slowly rises in the increase of heat source (B).The heat
of water-Cu nano fluid is less than the water- Al2O3 at every point of the flow field.
Figure-(9) shows the effect of the parameter A on heat profile at any point of the fluid, when Pr
= 6.86, B = 2, t = 0.5 and ๐ = 0.05. It is noticed that the temperature slowly falls with the
increase of Suction Parameter (A). The heat of water-Cu nano fluid is less than water-Al2O3
nano fluid at every point of the flow field.
Figure-(10) shows the effect of the parameter ๐ on heat profile at any point of the fluid, when
Pr = 6.86, A = 2, B = 2. It is noticed that the temperature rises with the increase of heat source
(B). The heat of water-Cu nano fluid is less than water-Al2O3 nano fluid at every point of the
flow field, but the rate of rise of heat of water-Cu nano fluid is more than water-Al2O3nano
fluid.
Skin Friction: The mean value of shearing stress and Tangent value of phase angle is depicted
in Table-(2), which illustrates the effects of the parameters M, K, Gr, A, h and ๐ on mean value
of shearing stress and Tangent value of phase angle at the plate. It is noticed that Mean value of
skin friction at plate decreases with the increase of magnetic parameter (M), Suction parameter
(A) and rarefaction parameter (h), where as decreases with the increase of permeability of
porous medium (K), Grashof number (Gr) and volume fraction of nano fluid ๐ . But the
Tangent value of phase angle increases with the increase of volume fraction of nano fluid ๐ ,
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magnetic parameter (M) and Suction parameter (A), where as decreases with the increase of
permeability of porous medium (K) and rarefaction parameter (h).
Table-1
Sl.no parameters Base fluid
(water)
Nano
particles
( Cu)
Nano
particles
(Al2O3
1 Density 997.1 8933 3970
2 Specific heat at
constant
pressure
4179 386 765
3 coefficient of
volumetric
expansion
2.064X10โ4 9.8X10โ6 8.5X10โ6
4 Thermal
diffusivity
0.613 401 40
Table-2
When B=2 and Sc=6.8 Mean value of
shearing
stress ๐๐
For
Al2 O3 -water
Mean value
of shearing
stress ๐๐
Cu-Water
Tangent
value of
phase
angle
๐ก๐๐๐ผ
Cu-Water
Tangent
value of
phase
angle
๐ก๐๐๐ผ
Al2 O3 -
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water
Initially
h=0.2,M=5,K=2,A
=2, Gr=2,๐ =
0.05
M=5 1.1026 1.3481 0.1581 0.1402
M=7 1.0188 1.2384 0.1629 0.1414
M=8 0.9530 1.1920 0.1653 0.1428
K=3 1.1433 1.3946 0.1544 0.1365
K=5 1.2124 1.4658 0.1482 0.1296
A=4 1.1026 1.3456 0.3022 0.2645
A=6 1.1026 1.3419 0.4469 0.3893
Gr=4 2.2053 2.6965 0.1581 0.1402
Gr=6 3.3079 4.0451 0.1581 0.1402
h=0.4 0.8162 0.9631 0.1616 0.1467
H=0.6 0.6479 0.7474 0.1641 0.1411
๐
= 0.09
1.1059 1.3759 0.1636 0.1439
๐
= 0.1
1.1084 1.4616 0.1691 0.1476
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Fig-(1): Effect of M on Velocity profile for water-Cu and water-Al2O3nano fluid, when Pr
= 6.86, K = 2, A = 2, B = 2, Gr = 2, t = 0.5, ๐ = 0.05 and h = 0.2.
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Fig-(2): Effect of K on Velocity profile for water-Cu and water-Al2O3 nano fluid, when Pr
= 6.86, M= 2, A = 2, B = 2, Gr = 2, t = 0.5, ๐ = 0.05 and h = 0.2.
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Fig-(3): Effect of Gr on Velocity profile of water-Cu and water-Al2O3 nano fluid, when Pr
= 6.86, K = 2, M = 2, A = 2, B = 2, t = 0.5, ๐ = 0.05 and h = 0.2.
Fig-(4): Effect of A on velocity profile of water-Cu and water-Al2O3 nano fluid, when Pr =
6.86, M = 2, K = 2, B = 2, Gr = 2, t = 0.5, ๐ = 0.05 and h = 0.2.
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Fig-(5): Effect of ๐ on Velocity profile of water-Cu and water-Al2O3 nano fluid, when Pr
= 6.86, M = 2, K = 2, A = 2, B = 2, Gr = 2, t = 0.5 and h = 0.2.
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Fig-(6): Effect of h on Velocity profile of water-Cu and water-Al2O3 nano fluid, Pr =
6.86, M = 2, K = 2, A = 2, B = 2, Gr = 2, t = 0.5 and ๐ = 0.05.
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Fig-(7): Effect of B on Velocity profile of water-Cu and water-Al2O3 nano fluid, when Pr =
6.86, M = 2, K = 2, A = 2, Gr = 2, t = 0.5, ๐ = 0.05 and h = 0.2.
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Fig-(8): Effect B on Heat profile of water-Cu and water-Al2O3 nano fluid, when Pr = 6.86,
A = 2, t = 0.5 and ๐ =0.05.
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Fig-(9): Effect of A on Heat profile for water-Cu and water-Al2O3 nano fluid, when Pr =
6.86, B = 2, t = 0.5 and ๐ = 0.05.
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Fig-(10): Effect of ๐ on Heat profile of water-Cu and water-Al2O3 nano fluid, when Pr =
6.86, B = 2, t = 0.5 and A = 2.
6. CONCLUSION:
The following results are obtained due to the magnetic effects on free convection flow of nano
fluid through porous medium past an infinite vertical plate in slip flow regime in the presence
of variable heat source and variable suction:
i. The velocities of both water-Cu and water-Al2O3 nano fluids decrease with the increase
in M, but increases with the increase of other parameters. Also velocity of water-Cu nano
fluid is more than the water-Al2O3 nano fluid near the plate.
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ii. Heat diminishes with the enhancement of the value of suction parameter (A), but rises
with the increase of B and ๐.
iii. Mean value of Skin friction at the plate decreases with the increase of M, A and h, where
as increases with the increase of K, Gr and ๐. But the tangent value of phase angle
increases with the increase of ๐, M and A, where as decreases with the increase of K and
h. No change is marked in case of increase in Gr.
iv. Both mean value of Skin friction and tangent value of phase angle is more in case of
water-Cu nano fluid than water-Al2O3 nano fluid for all parameters.
Reference
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Available online at http://euroasiapub.org
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