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Non-alignment stagnation-point flow of a nanofluid past a permeable stretching/shrinking sheet: Buongiorno's model.

Hamid RA, Nazar R, Pop I - Sci Rep (2015)

Bottom Line: The main purpose of the present paper is to examine whether the non-alignment function has the effect on the problem considered when the fluid suction and injection are imposed.The numerical results are shown in the tables and the figures.It is worth mentioning that dual solutions are found to exist for the shrinking sheet.

View Article: PubMed Central - PubMed

Affiliation: Institute of Engineering Mathematics, Universiti Malaysia Perlis, Perlis, Malaysia.

ABSTRACT
The paper deals with a stagnation-point boundary layer flow towards a permeable stretching/shrinking sheet in a nanofluid where the flow and the sheet are not aligned. We used the Buongiorno model that is based on the Brownian diffusion and thermophoresis to describe the nanofluid in this problem. The main purpose of the present paper is to examine whether the non-alignment function has the effect on the problem considered when the fluid suction and injection are imposed. It is interesting to note that the non-alignment function can ruin the symmetry of the flows and prominent in the shrinking sheet. The fluid suction will reduce the impact of the non-alignment function of the stagnation flow and the stretching/shrinking sheet but at the same time increasing the velocity profiles and the shear stress at the surface. Furthermore, the effects of the pertinent parameters such as the Brownian motion, thermophoresis, Lewis number and the suction/injection on the flow and heat transfer characteristics are also taken into consideration. The numerical results are shown in the tables and the figures. It is worth mentioning that dual solutions are found to exist for the shrinking sheet.

No MeSH data available.


Related in: MedlinePlus

Streamlines for two-dimensional shrinking sheet when λ = −0.5 and c = 0.5 for different values of s: (a) s = 0.2 (suction) (b) s = 0 (impermeable); (c) s = −0.2 (injection).
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f11: Streamlines for two-dimensional shrinking sheet when λ = −0.5 and c = 0.5 for different values of s: (a) s = 0.2 (suction) (b) s = 0 (impermeable); (c) s = −0.2 (injection).

Mentions: Furthermore, in this problem the second solution is found to exist in the shrinking region where the critical values λa are for s = 0.2, λb for s = 0 and λc for s = −0.2 as reported in the Figs 2, 3, 4, 5. The values for the critical numbers are shown in the Table 5. It is observed that λa > λb > λc. Not only that, for the second solution, the suction and injection parameters have the same effects as in the first solution. On the other hand, the streamlines for the present problem are shown in Figs 10 and 11 for the two-dimensional stretching and shrinking sheets, respectively. One can see that in both sheets, the suction parameter causes the flows being drag into the center. The fluid flows are also reduced. Meanwhile, when the fluid is injected through the surface, more flows are formed as shown in Figs 10(c) and 11(c).


Non-alignment stagnation-point flow of a nanofluid past a permeable stretching/shrinking sheet: Buongiorno's model.

Hamid RA, Nazar R, Pop I - Sci Rep (2015)

Streamlines for two-dimensional shrinking sheet when λ = −0.5 and c = 0.5 for different values of s: (a) s = 0.2 (suction) (b) s = 0 (impermeable); (c) s = −0.2 (injection).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4594122&req=5

f11: Streamlines for two-dimensional shrinking sheet when λ = −0.5 and c = 0.5 for different values of s: (a) s = 0.2 (suction) (b) s = 0 (impermeable); (c) s = −0.2 (injection).
Mentions: Furthermore, in this problem the second solution is found to exist in the shrinking region where the critical values λa are for s = 0.2, λb for s = 0 and λc for s = −0.2 as reported in the Figs 2, 3, 4, 5. The values for the critical numbers are shown in the Table 5. It is observed that λa > λb > λc. Not only that, for the second solution, the suction and injection parameters have the same effects as in the first solution. On the other hand, the streamlines for the present problem are shown in Figs 10 and 11 for the two-dimensional stretching and shrinking sheets, respectively. One can see that in both sheets, the suction parameter causes the flows being drag into the center. The fluid flows are also reduced. Meanwhile, when the fluid is injected through the surface, more flows are formed as shown in Figs 10(c) and 11(c).

Bottom Line: The main purpose of the present paper is to examine whether the non-alignment function has the effect on the problem considered when the fluid suction and injection are imposed.The numerical results are shown in the tables and the figures.It is worth mentioning that dual solutions are found to exist for the shrinking sheet.

View Article: PubMed Central - PubMed

Affiliation: Institute of Engineering Mathematics, Universiti Malaysia Perlis, Perlis, Malaysia.

ABSTRACT
The paper deals with a stagnation-point boundary layer flow towards a permeable stretching/shrinking sheet in a nanofluid where the flow and the sheet are not aligned. We used the Buongiorno model that is based on the Brownian diffusion and thermophoresis to describe the nanofluid in this problem. The main purpose of the present paper is to examine whether the non-alignment function has the effect on the problem considered when the fluid suction and injection are imposed. It is interesting to note that the non-alignment function can ruin the symmetry of the flows and prominent in the shrinking sheet. The fluid suction will reduce the impact of the non-alignment function of the stagnation flow and the stretching/shrinking sheet but at the same time increasing the velocity profiles and the shear stress at the surface. Furthermore, the effects of the pertinent parameters such as the Brownian motion, thermophoresis, Lewis number and the suction/injection on the flow and heat transfer characteristics are also taken into consideration. The numerical results are shown in the tables and the figures. It is worth mentioning that dual solutions are found to exist for the shrinking sheet.

No MeSH data available.


Related in: MedlinePlus