In presented in the forms of graphs and tables.

In this section we analyze
simulated numerical results of pertinent controlling parameters namely thermal
Grashof number (Gr), Eckert number (Ec), Viscosity parameter (

), nanoparticle volume fraction (

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), Skin friction coefficient (Cf), Nusselt number (Nu)
and dimensionless time ‘t’ on velocity
field components and temperature distributions which are presented in the forms
of graphs and tables. Kerosene oil is chosen as conventional base fluid with
Copper (Cu), Titanium oxide (TiO2), Alumina (Al2O3), Cobalt (Co) nanoparticles. In this study we have considered the
nanoparticle volume fraction in the range of

 as
sedimentation takes place when the nanoparticle volume fraction exceeds eight
percent. Also, we assumed Spherical shaped nanoparticles with thermal
conductivity and dynamic viscosity shown in Model I in Table 2 (see Hamilton R L and Crosser O K(1962), Loganathan et al. (2013)). The Prandtl number, Pr
of the base fluid is kept constant at 23. When

 this study reduces the governing equations to those of a
regular fluid i.e. nanoscale characteristics are eliminated.

The
influence of controlling parameters Grashof number (Gr), Eckert number (Ec), Viscosity
parameter (

) on velocity components and temperature distributions
are demonstrated in figures 4 and 5, respectively. It is observed from figure 4
that the velocity of Alumina (Al2O3)
– kerosene nanofluid increases with increase in thermal Grashof number (Gr) which coincides physically since

represents the relative influence of thermal buoyancy
force and viscous force in the boundary layer regime. An increase in the value
of thermal Grashof number has the tendency to induce much flow in the boundary
layer due to the effect of thermal buoyancy. In Figure 5, the growing
temperature is observed with increasing thermal Grashof number; this is
expected since the terms linked to the Grashof number act as a strong heat
source in momentum equation. Moreover, it is observed in figures that the
velocity and temperature decrease with an increase in

. It is physically evident that the primary assumption
in  boundary-layer definition says that
boundary-layer thickness is supposed to be practically very thin (according to
the boundary layer assumption presented by prandtal in 1904). Applying suction
at the vertical surface causes to draw the amount of fluid into the surface and
consequently the boundary-layer gets thinner and also the momentum
boundary-layer and thermal boundary-layer get depressed by increasing the
suction parameter

. As shown on the graph, considering the values used,
increase in Eckert number causes the velocity to reduce without any change in
the momentum boundary layer thickness. The Eckert number, Ec, expresses the relationship between the kinetic energy in the
flow and the enthalpy. It embodies the conversion of kinetic energy into
internal energy by work done against the viscous fluid stresses, and this
energy is dissipated as heat. Greater viscous dissipate heat, therefore causes
a rise in the temperature as observed in Figure 5.

Figure 3. Transient Velocity
profiles for different Gr, Ec,

 

Figure 4. Transient temperature
profiles for different Gr, Ec,

Figure
5 and 6 portrays the velocity components and temperature distributions of
kerosene -Al2O3
 nanofluid for various values of

, t. It is expected that velocity and temperature
enhances with rise in time. Further, the velocity of kerosene -Al2O3 nanofluid is
less than that of pure  kerosene (

= 0) for all values of time t. However kerosene -Al2O3 nanofluid
temperature is more than that of pure kerosene (

= 0). We observe that in figure 5 the velocity
components of  the kerosene alumina
nanofluid reduces with in the boundary-layer with the progress in nanoparticle
volume fraction

. Physically it is true since addition of the
nanoparticles make the fluid more viscous as a consequence the motion of the
fluid slows down. Henceforth we observe from figure 6 that temperature
distribution of kerosene-alumina nanofluid depreciates with rise in
nanoparticle volume fraction

which results in the decrease of boundary-layer thickness.

 

Figure
5. Transient velocity profiles for different

,t

                                                                                                                                               

Figure 6 Transient temperature
profiles for different

,t

Table
1 exhibits the values of Nusselt number for various types of nano-fluids when
Pr=23.004. Nusselt number rises due to rise in thermal grashof number this
effect is due to the rise in surface heat flux which accelerates development of
the flow and the largest enhancement in the heat is obtained. It is also
observed that nusselt number increases with increase in suction parameter

. Nusselt number depreciates with rise of Eckert
number this is due to the fact that dimensionless surface temperature increases
due to dissipation which increases the thermal boundary-layer thickness and
decreases the nusselt number. It is noted that the thermal conductivity of
nanofluid is a function of thermal conductivity of both base fluid and
nanoparticles. Increase of nanoparticle volume fraction, results in increase in
the conductive heat transfer coefficient and consequently heat transfer
enhancement take place. These effects are clearly seen from table 1 for all
nanofluids. Nusselt number increases with progression of time for all
nanofluids.

 

 

 

 

 

Table 1. Values of Nusselt number for different
types of nanofluids when Pr =23.004

Gr

Ec

t

Cu-
kerosene
 


kerosene
 

Ag-
kerosene
 

-kerosene
 

Co-kerosene
 

5

0.2

0.9

0.04

0.5

0.8002

1.689

0.3612

1.6123

0.8522

10

0.2

0.9

0.04

0.5

1.0306

2.0298

0.5753

1.9499

1.0756

15

0.2

0.9

0.04

0.5

1.3822

2.4545

0.9304

2.3747

1.4166

5

0.3

0.9

0.04

0.5

1.6361

2.6037

1.1217

2.5157

1.7035

5

0.4

0.9

0.04

0.5

2.6513

3.6788

2.0658

3.5801

2.7347

5

0.2

0.3

0.04

0.5

5.232

5.4671

4.9972

5.4266

5.2784

5

0.2

0.9

0.02

0.5

1.4661

1.921

1.2424

1.8826

1.4915

5

0.2

0.9

0

0.5

2.1494

2.1494

2.1494

2.1494

2.1494

5

0.2

0.9

0.04

1

1.4931

2.1717

1.1857

2.1146

1.5225

5

0.2

0.9

0.04

1.5

2.0045

2.5186

1.7499

2.4721

2.0322

 

Table
2 explain the values of Skin-friction coefficient respectively for various
types of nano-fluids when Pr=23.004. It is found that skin-friction coefficient
for all nano-fluids increases enhances with rise in thermal grashof number Gr.
Physically it is true that as buoyancy increases which enhances the shear
stress as a result skin-friction increases. Increasing the value of suction
parameter the velocity and temperature of the nano-fluids are found to increase
in the boundary-layer region. The physical explanation for such behavior is the
heated fluid is pushed towards the wall where the buoyancy forces can act to
enhance the nano-fluid due to high influence of the viscosity. This effects as
to decrease the wall shear stress that is skin-friction coefficient. As
nanoparticle volume fraction

 increases the
skin-friction coefficient reduces. Skin-friction coefficient progresses with
progressing time. The negative value of skin-friction indicates that there
occurs a reversal flow in the win city of the moving plate. Physically it
agrees the fact that as a motion of fluid is due to plate moving in the
vertical direction against the gravitational field.

 

 

Table 2. Values of Skin friction coefficient for
different types of nanofluids when Pr = 23.004.

Gr

Ec

t

Cu-kerosene

-kerosene

Ag-kerosene

-kerosene

Co-kerosene

5

0.2

0.9

0.04

0.5

-0.5494

-0.4499

-0.5653

-0.4543

-0.5537

10

0.2

0.9

0.04

0.5

0.0705

0.1379

0.0795

0.1366

0.0609

15

0.2

0.9

0.04

0.5

0.704

0.7293

0.7418

0.7317

0.6889

5

0.3

0.9

0.04

0.5

-0.6799

-0.5678

-0.6985

-0.5729

-0.6844

5

0.4

0.9

0.04

0.5

-0.8179

-0.6914

-0.8398

-0.6972

-0.8226

5

0.2

0.3

0.04

0.5

-0.8531

-0.7356

-0.8789

-0.7422

-0.8555

5

0.2

0.9

0.02

0.5

-0.4465

-0.3968

-0.4544

-0.399

-0.4487

5

0.2

0.9

0

0.5

-0.3466

-0.3466

-0.3466

-0.3466

-0.3466

5

0.2

0.9

0.04

1

-0.0021

0.065

-0.0038

0.0629

-0.0082

5

0.2

0.9

0.04

1.5

0.3195

0.3694

0.3285

0.3688

0.3113

 

6 Conclusions

The
heat transfer augmentation of Kerosene-Alumina nano-fluid past an impulsive
motion of vertical porous plate under the influence of viscous dissipation using Tiwari-Das nanofluid model with Bossiness
approximation is investigated numerically using Galerkin finite element
technique. The main results are summarized as follows

(1)   The
Kerosene-Alumina nano-fluid velocity component increases with increasing Gr, t
and decreases with increasing Ec,

 and

.

(2)   The
Kerosene-Alumina nano-fluid temperature distribution increases with Gr, Ec, t and
decreases with

 and

.  

(3)  
As the thermal
Grashof number increased, the skin-friction coefficient and the Nusselt number
at the surface increased for all nanofluids namely, aluminium oxide, copper,
titanium oxide, silver and cobalt.

(4)   As time progressed, the skin-friction coefficient and the Nusselt
number at the surface increased for all nanofluids namely, aluminium oxide,
copper, titanium oxide, silver and cobalt.

(5)   The skin-friction coefficient at the surface increased and the
Nusselt number decreased for all nanofluids namely, aluminium oxide, copper, titanium
oxide silver and cobalt with the increase in Eckert number.

(6)   As the nanoparticle volume fraction increased, the skin-friction
coefficient decreased and the Nusselt number increased at the surface for all
nanofluids namely, aluminium oxide, copper, titanium oxide, silver and cobalt.

(7)  
 The
skin-friction coefficient at the surface decreased and the Nusselt number increased
for all nanofluids namely, aluminium oxide, copper, titanium oxide silver and
cobalt with the increase in Suction parameter

.

(8)  
Kerosene-Alumina nano-fluid attains maximum heat transfer rate and Kerosene-Silver attains minimum heat transfer rate when compared with the other nanofluids for all values of Gr, Ec,

, t,

. This confirms that
use of nanofluids achieves significant enhancement in heat transfer rates, and
demonstrates the importance of utilizing nanofluids for improving industrial
cooling processes.