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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 nanofluids and water when γ = 0.5, λ = -0.53, and φ = 0.1.
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Figure 8: Temperature profiles for different nanofluids and water when γ = 0.5, λ = -0.53, and φ = 0.1.

Mentions: Figure 6 displays the variation of the skin friction coefficient (1/(1-φ)2.5)f"(0) with λ when γ = 0.5 for water, Cu-water and Ag-water nanofluids, while the respective local Nusselt number -(knf/kf)θ'(0) is shown in Figure 7. In general, for a particular value of λ, the skin friction coefficient of Cu-water nanofluid is higher than that of Ag-water nanofluid and that of water for the upper branch solutions, while the skin friction coefficient of Ag-water nanofluid is higher than that of Cu-water nanofluid and that of water for the lower branch solutions. Further, Figure 7 shows that Cu-water nanofluid has the highest local Nusselt number compared with Ag-water nanofluid and water for the upper branch solutions. From this observation, the heat transfer rate at the surface of Cu-water nanofluid is higher than that of Ag-water nanofluid even though Ag has higher thermal conductivity than the thermal conductivity of Cu as presented in Table 1. However, the difference in heat transfer rate at the surface is small. On the other hand, Ag-water nanofluid has the highest local Nusselt number compared with Cu-water nanofluid and water for the lower branch solutions. The corresponding temperature profiles that support the results obtained in Figure 7 when λ = -0.53 is shown in Figure 8.


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 nanofluids and water when γ = 0.5, λ = -0.53, and φ = 0.1.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 8: Temperature profiles for different nanofluids and water when γ = 0.5, λ = -0.53, and φ = 0.1.
Mentions: Figure 6 displays the variation of the skin friction coefficient (1/(1-φ)2.5)f"(0) with λ when γ = 0.5 for water, Cu-water and Ag-water nanofluids, while the respective local Nusselt number -(knf/kf)θ'(0) is shown in Figure 7. In general, for a particular value of λ, the skin friction coefficient of Cu-water nanofluid is higher than that of Ag-water nanofluid and that of water for the upper branch solutions, while the skin friction coefficient of Ag-water nanofluid is higher than that of Cu-water nanofluid and that of water for the lower branch solutions. Further, Figure 7 shows that Cu-water nanofluid has the highest local Nusselt number compared with Ag-water nanofluid and water for the upper branch solutions. From this observation, the heat transfer rate at the surface of Cu-water nanofluid is higher than that of Ag-water nanofluid even though Ag has higher thermal conductivity than the thermal conductivity of Cu as presented in Table 1. However, the difference in heat transfer rate at the surface is small. On the other hand, Ag-water nanofluid has the highest local Nusselt number compared with Cu-water nanofluid and water for the lower branch solutions. The corresponding temperature profiles that support the results obtained in Figure 7 when λ = -0.53 is shown in Figure 8.

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