magnetic effects on free convection flow of nano fluids

International Journal of Research in Engineering and Applied Sciences(IJREAS)

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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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An open access scholarly, online, peer-reviewed, interdisciplinary, monthly, and fully refereed journals

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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: [email protected]

*J.N.V. Goshala, Sambalpur, Odisha- 768024

Email:[email protected]

**J.N.V. Joura, Morena, MP-476221

Email:[email protected]

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

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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









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source and variable suction is considered. Let 𝑋′ axis is taken along the plate in vertical upward

direction and 𝑌′ axis is normal to the plate. A uniform magnetic field strength H0 is applied

normal to the plate. Initially, sorrounding temperature is 𝑇∞′ . Also, the temperature at the plate

is 𝑇𝑤′ . For 𝑡 ′ ≥ 0, the temperature and mass concentration changes periodically. As the plate is

infinite along 𝑋′ axis, so all the physical quantities are in dependentof 𝑥′ and are the functions

of 𝑦′ and 𝑡 ′only. 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 𝑣0

2

𝜈𝑓 1 + 𝜖𝐵𝑒𝑖𝜔 ′ 𝑡 ′

.

Then by usual Boussinesq's approximation the unsteady flow is governed by the following

equations.

Equation of Continuity:

𝜕𝑣 ′

𝜕𝑦 ′= 0 ⟹ 𝑣 ′ = −𝑉0 1 + 𝜖𝐴𝑒𝑖𝜔 ′𝑡 ′ (1)

The Equation of Motion:

𝜕𝑢 ′

𝜕𝑡 ′− 𝑉0 1 + 𝜖𝐴𝑒𝑖𝜔 ′𝑡 ′

𝜕𝑢 ′

𝜕𝑦 ′=

𝜇𝑛𝑓

𝜌𝑛𝑓

𝜕2𝑢 ′

𝜕𝑦 ′2 + 𝑔 𝛽 𝑛𝑓 𝑇 ′ − 𝑇∞′ + 𝑔 𝛽𝑐 𝑛𝑓 𝐶 ′ − 𝐶∞

′ −𝜎𝐵0

2𝑢 ′

𝜌𝑛𝑓−

𝑢 ′

𝐾′(2)

The Energy Equation:

𝜕𝑇 ′

𝜕𝑡 ′− 𝑉0 1 + 𝜖𝐴𝑒𝑖𝜔 ′𝑡 ′

𝜕𝑇 ′

𝜕𝑦 ′=

𝑘𝑛𝑓

𝜌𝐶𝑝 𝑛𝑓

𝜕2𝑇′

𝜕𝑦 ′2−

𝑉02

𝜈𝑓 1 + 𝜖𝐵𝑒𝑖𝜔 ′𝑡 ′ 𝑇 ′ − 𝑇∞

′ (3)

with the following boundary conditions

𝑡 > 0: 𝑢′ = 𝐿′

𝜕𝑢 ′

𝜕𝑦 ′, 𝑇 ′ = 𝑇𝑤

′ + 𝜖 𝑇𝑤′ − 𝑇∞

′ 𝑒𝑖𝜔 ′𝑡′𝑎𝑡𝑦 = 0,

𝑢′ = 0 , 𝑇 ′ = 𝑇∞′ 𝑎𝑡𝑦 → ∞

(4)

where 𝜇𝑛𝑓 is the dynamic viscosity,𝑘𝑛𝑓 is the thermal diffusivity,𝜌𝑛𝑓 is the effective density,

𝜌𝐶𝑝 𝑛𝑓

is the heat capacity and 𝛽 𝑛𝑓 is the coefficient of volumetric expansion of heat of nano

fluid. They are defind as









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𝜇𝑛𝑓 =𝜇𝑓

1−𝜙 2.5 ,𝜌𝑛𝑓 = 1 − 𝜙 𝜌𝑓 + 𝜙𝜌𝑠 , 𝜌𝐶𝑝 𝑛𝑓

= 1 − 𝜙 𝜌𝐶𝑝 𝑓

+ 𝜙 𝜌𝐶𝑝 𝑠,

𝑘𝑛𝑓 = 𝑘𝑠 + 2𝑘𝑓 − 2𝜙 𝑘𝑓 − 𝑘𝑠

𝑘𝑠 + 2𝑘𝑓 + 2𝜙 𝑘𝑓 − 𝑘𝑠 𝑘𝑓 , 𝛽 𝑛𝑓 = 1 − 𝜙 𝛽 𝑓 + 𝜙 𝛽 𝑠

𝜎 is the electrical conductivity of the fluid, g is the acceleration due to gravity and 𝜙is the

volume of nano fluid.

Let us introduce the dimensionless quantities

𝑢 =

𝑢 ′

𝑉0 , 𝑡 =

𝑉02𝑡 ′

𝜐𝑓 , 𝑦 =

𝑉0𝑦 ′

𝜐𝑓 , 𝜃 =

𝑇 ′−𝑇∞′

𝑇𝑤′ −𝑇∞

′ , 𝐺𝑟 =𝑔 𝛽 𝑓𝜐𝑓 𝑇𝑤

′ −𝑇∞′

𝑉03 ,

𝑃𝑟 =𝜈𝑓 𝜌𝐶𝑝

𝑓

𝑘𝑓 , 𝑀 =

𝜎𝜈𝑓𝐵02

𝜌𝑓𝑉02 , 𝜔 =

𝜔 ′

𝑉03 𝜐𝑓 , 𝐾 =

𝐾′𝑉02

𝜈𝑓 , 𝑕 =

𝑉0𝐿′

𝜈𝑓

(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

𝜕𝑢

𝜕𝑡− 1 + 𝜖𝐴𝑒𝑖𝜔𝑡

𝜕𝑢

𝜕𝑦= 𝜙0

𝜕2𝑢

𝜕𝑦 2 − 𝜙1𝑀𝑢 −1

𝐾𝑢 + 𝜙2𝐺𝑟𝜃(6)

𝜕𝜃

𝜕𝑡− 1 + 𝜖𝐴𝑒𝑖𝜔𝑡

𝜕𝜃

𝜕𝑦=

1

𝑃𝑟𝜙3

𝜕2𝜃

𝜕𝑦 2 − 1 + 𝜖𝐵𝑒𝑖𝜔𝑡 𝜃 (7)

with boundary conditions

𝑢 = h∂u

∂y, 𝜃 = 1 + 𝜖𝑒𝑖𝜔𝑡 at 𝑦 = 0

𝑢 = 0, 𝜃 → 0, as𝑦 → ∞ (8)

3. METHOD OF SOLUTION:

Assuming small amplitude oscillation𝜖 ≪ 1, we can represent the velocity u and temperature

𝜃near the plate as follows

𝑢 = 𝑢0 𝑦 + 𝜖𝑢1 𝑦 𝑒𝑖𝜔𝑡

𝜽 = 𝜽𝟎 𝒚 + 𝝐𝜽𝟏 𝒚 𝒆𝒊𝝎𝒕 (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 𝜖2, we get

𝜑0 𝑢0′′ + 𝑢0

′ − 𝜑1𝑀 + 1

𝐾 𝑢0 = −𝐺𝑟𝜑2𝜃0 (10)

𝜑0𝑢1′′ + 𝑢1

′ − 𝑖𝜔 + 𝜑1𝑀 + 1

𝐾 𝑢1 = −𝑢0

′ 𝐴 − 𝐺𝑟𝜑2𝜃1 (11)

𝜑3𝜃0′′ + 𝑃𝑟𝜃0

′ − 𝑃𝑟𝜃0 = 0 (12)

𝜑3𝜃1′′ + 𝑃𝑟𝜃1

′ − 𝑃𝑟 1 + 𝑖𝜔 𝜃1 = 𝑃𝑟𝐵𝜃0 − 𝑃𝑟𝐴𝜃0′ (13)

with the following boundary conditions

𝑢0 = h∂u0

∂y, 𝑢1 = h

∂u1

∂y, 𝜃0 = 1, 𝜃1 = 1 at 𝑦 = 0

𝑢0 = 0, 𝑢1 = 0, 𝜃0 = 0, 𝜃1 = 0 at𝑦 → ∞ (14)

Solving the equations (10) to (13) using boundary condition (14) and (9), we get

u = b2 e−a2y − b1 e

−a1y + b8e−a4y + b5e−a2y + b6e−a1y + b7 e−a3y ϵeiωt (15)

θ = e−a1y + b4e−a3y + b3e−a1y ϵeiωt (16) The non-

dimensional skin friction

𝜏0 = 𝜕𝑢

𝜕𝑦

𝑦=0

= −𝑎2𝑏2 + 𝑎1𝑏1 + −𝑎4𝑏8 − 𝑎2𝑏5 − 𝑎1𝑏6 − 𝑎3𝑏7 𝜖𝑒𝑖𝜔𝑡

= −𝑎2𝑏2 + 𝑎1𝑏1 + 𝜖𝑒𝑖𝜔𝑡 𝐹𝑟 + 𝑖𝐹𝑖 = 𝜏𝑚 + 𝜖 𝐹 𝑒𝑖 𝜔𝑡 +𝛼 (17)

where 𝐹 = 𝐹𝑟2 + 𝐹𝑖

2 , 𝑡𝑎𝑛𝛼 =𝐹𝑖

𝐹𝑟 , 𝜏𝑚 = −𝑎2𝑏2 + 𝑎1𝑏1 Is the skin friction of mean velocity

and F= −𝑎4𝑏8 − 𝑎2𝑏5 − 𝑎1𝑏6 − 𝑎3𝑏7

The non-dimensional Nusselt number

𝑁𝑢 = − 𝜕𝜃

𝜕𝑦

𝑦=0

= 𝑎1 + 𝑎3𝑏4 + 𝑎1𝑏3 𝜖𝑒𝑖𝜔𝑡 = 𝑎1 + 𝜖𝑒𝑖𝜔𝑡 𝑆1 + 𝑖𝑆2









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=𝑎1 + 𝑄 𝜖𝑒𝑖 𝜔𝑡 +𝛽 (18)

where 𝑄 = 𝑆12 + 𝑆2

2𝑡𝑎𝑛𝛽 =𝑆2

𝑆1, ϕ

0=

1

1−ϕ 2.5 1−ϕ +ϕρsρf

, ϕ1

=1

1−ϕ +ϕρsρf

,

𝜙2 = 1 − ϕ + ϕβs

βf

, 𝜙3 = 𝑘𝑠+2𝑘𝑓−2𝜙 𝑘𝑓−𝑘𝑠

𝑘𝑠+2𝑘𝑓+2𝜙 𝑘𝑓−𝑘𝑠

1−𝜙 +𝜙 𝜌𝐶𝑝

𝑠 𝜌𝐶𝑝

𝑓

,

𝑎1 =𝑃𝑟+ 𝑝𝑟 2+4𝜑3𝑃𝑟

2𝜑3, 𝑎2 =

1+ 1+4𝜑0 𝜑1𝑀+ 1

𝐾

2𝜑0 , 𝑎3 =

𝑃𝑟+ 𝑃𝑟2+4𝑃𝑟𝜑3 1+𝑖𝜔

2𝜑3,

𝑎4 =1 + 1 + 4 𝜑0 𝜔𝑖 + 𝜑1𝑀 +

1

𝐾

2𝜑0 , 𝑏1 =

𝑎1𝐺𝑟

𝜑0𝑎12 − 𝑎1 − 𝜔𝜑1𝑀 +

1

𝐾

, 𝑏2

=𝑏1 1 + 𝑕𝑎1

1 + 𝑕𝑎2, 𝑏3 =

𝑃𝑟𝐵 + 𝑃𝑟𝐴𝑎1

𝜑3𝑎12 − 𝑃𝑟𝑎1 − 𝑃𝑟 1 + 𝑖𝜔

,

𝑏4 = −𝑏3, 𝑏5 =𝐴𝑏2

𝜑0𝑎22 − 𝑎2 − 𝜔𝑖 + 𝜑1𝑀 +

1

𝐾

, 𝑏6 = − 𝐴𝑏1𝑎2 + 𝐺𝑟𝜑2

𝜑0𝑎12 − 𝑎1 − 𝜔𝑖 + 𝜑1𝑀 +

1

𝐾

,

𝑏7 = −𝐺𝑟𝜑2𝑏4

𝜑0𝑎32 − 𝑎3 − 𝜔𝑖 + 𝜑1𝑀 +

1

𝐾

, 𝑏8 = − 𝑕𝑎3𝑏5 + 𝑕𝑎1𝑏6 + 𝑕𝑎3𝑏7 + 𝑏5 + 𝑏6 + 𝑏7

1 + 𝑕𝑎4

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, 𝜑 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.









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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, φ = 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, φ = 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,φ = 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,φ = 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 parameter𝜑 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 𝜑 . 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 φ = 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, 𝜑 = 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 𝜑 =

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 𝜑 = 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 𝜑 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 𝜑 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 𝜑 . But the

Tangent value of phase angle increases with the increase of volume fraction of nano fluid 𝜑 ,









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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

2.064X10−4 9.8X10−6 8.5X10−6

4 Thermal

diffusivity

0.613 401 40

Table-2

When B=2 and Sc=6.8 Mean value of

shearing

stress 𝜏𝑚

For

Al2 O3 -water

Mean value

of shearing

stress 𝜏𝑚

Cu-Water

Tangent

value of

phase

angle

𝑡𝑎𝑛𝛼

Cu-Water

Tangent

value of

phase

angle

𝑡𝑎𝑛𝛼

Al2 O3 -









10

water

Initially

h=0.2,M=5,K=2,A

=2, Gr=2,𝜑 =

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

𝜑

= 0.09

1.1059 1.3759 0.1636 0.1439

𝜑

= 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, 𝝋 = 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, 𝝋 = 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, 𝝋 = 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, 𝝋 = 0.05 and h = 0.2.









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Fig-(5): Effect of 𝝋 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 𝝋 = 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, 𝝋 = 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 𝝋 =0.05.









18

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 𝝋 = 0.05.









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Fig-(10): Effect of 𝝋 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 𝜑.

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 𝜑. But the tangent value of phase angle

increases with the increase of 𝜑, 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.

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