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Boundary layer flow past a stretching/shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a nanofluid.

Yacob NA, Ishak A, Pop I, Vajravelu K - Nanoscale Res Lett (2011)

Bottom Line: The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically by a Runge-Kutta-Fehlberg method with shooting technique.Two types of nanofluids, namely, Cu-water and Ag-water are used.It is found that the heat transfer rate at the surface increases with increasing nanoparticle volume fraction while it decreases with the convective parameter.

View Article: PubMed Central - HTML - PubMed

Affiliation: Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania. popm.ioan@yahoo.co.uk.

ABSTRACT
The problem of a steady boundary layer shear flow over a stretching/shrinking sheet in a nanofluid is studied numerically. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically by a Runge-Kutta-Fehlberg method with shooting technique. Two types of nanofluids, namely, Cu-water and Ag-water are used. The effects of nanoparticle volume fraction, the type of nanoparticles, the convective parameter, and the thermal conductivity on the heat transfer characteristics are discussed. It is found that the heat transfer rate at the surface increases with increasing nanoparticle volume fraction while it decreases with the convective parameter. Moreover, the heat transfer rate at the surface of Cu-water nanofluid is higher than that at the surface of Ag-water nanofluid even though the thermal conductivity of Ag is higher than that of Cu.

No MeSH data available.


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Temperature profiles for different values of γ when λ = -0.5 and φ = 0.2 for Ag-water nanofluid.
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Figure 9: Temperature profiles for different values of γ when λ = -0.5 and φ = 0.2 for Ag-water nanofluid.

Mentions: The temperature profiles of Ag-water nanofluid for different values of convective parameter γ when φ = 0.2 is presented in Figure 9. It is observed that the surface temperature increases with an increase in γ for both solution branches, and in consequence, decreases the local Nusselt number. It can be seen that from the convective boundary conditions (9), the value of θ(0) approaches 1, as γ → ∞. Further, the convective parameter γ as well as the Prandtl number Pr has no influence on the flow field, which is clear from Equations 7-9. Finally, it is worth mentioning that all the velocity and temperature profiles presented in Figures 4, 5, 7, 8, and 9 satisfy the far-field boundary conditions (9) asymptotically, thus supporting the validity of the numerical results obtained.


Boundary layer flow past a stretching/shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a nanofluid.

Yacob NA, Ishak A, Pop I, Vajravelu K - Nanoscale Res Lett (2011)

Temperature profiles for different values of γ when λ = -0.5 and φ = 0.2 for Ag-water nanofluid.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3211401&req=5

Figure 9: Temperature profiles for different values of γ when λ = -0.5 and φ = 0.2 for Ag-water nanofluid.
Mentions: The temperature profiles of Ag-water nanofluid for different values of convective parameter γ when φ = 0.2 is presented in Figure 9. It is observed that the surface temperature increases with an increase in γ for both solution branches, and in consequence, decreases the local Nusselt number. It can be seen that from the convective boundary conditions (9), the value of θ(0) approaches 1, as γ → ∞. Further, the convective parameter γ as well as the Prandtl number Pr has no influence on the flow field, which is clear from Equations 7-9. Finally, it is worth mentioning that all the velocity and temperature profiles presented in Figures 4, 5, 7, 8, and 9 satisfy the far-field boundary conditions (9) asymptotically, thus supporting the validity of the numerical results obtained.

Bottom Line: The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically by a Runge-Kutta-Fehlberg method with shooting technique.Two types of nanofluids, namely, Cu-water and Ag-water are used.It is found that the heat transfer rate at the surface increases with increasing nanoparticle volume fraction while it decreases with the convective parameter.

View Article: PubMed Central - HTML - PubMed

Affiliation: Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania. popm.ioan@yahoo.co.uk.

ABSTRACT
The problem of a steady boundary layer shear flow over a stretching/shrinking sheet in a nanofluid is studied numerically. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically by a Runge-Kutta-Fehlberg method with shooting technique. Two types of nanofluids, namely, Cu-water and Ag-water are used. The effects of nanoparticle volume fraction, the type of nanoparticles, the convective parameter, and the thermal conductivity on the heat transfer characteristics are discussed. It is found that the heat transfer rate at the surface increases with increasing nanoparticle volume fraction while it decreases with the convective parameter. Moreover, the heat transfer rate at the surface of Cu-water nanofluid is higher than that at the surface of Ag-water nanofluid even though the thermal conductivity of Ag is higher than that of Cu.

No MeSH data available.


Related in: MedlinePlus