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 (

), 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.