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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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Physical model and the coordinate system.
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Figure 1: Physical model and the coordinate system.

Mentions: Consider a two-dimensional steady boundary layer shear flow over a stretching/shrinking sheet in a laminar and incompressible nanofluid of ambient temperature T∞. The fluid is a water-based nanofluid containing two type of nanoparticles, either Cu (copper) or Ag (silver). The nanoparticles are assumed to have a uniform shape and size. Moreover, it is assumed that both the fluid phase and nanoparticles are in thermal equilibrium state. Figure 1 describes the physical model and the coordinate system, where the x and y axes are measured along the surface of the sheet and normal to it, respectively. Following Magyari and Weidman [41], it is assumed that the velocity of the moving stretching/shrinking sheet is uw(x) = Uw(x/L)1/3 and the velocity outside the boundary layer (potential flow) is ue(y) = βy, where β is the constant strain rate. We also assume that the bottom surface of the stretching/shrinking surface is heated by convection from a base (water) fluid at temperature Tf, which provides a heat transfer coefficient hf (see [36]). Under the boundary layer approximations, the basic equations are (see [17,42]),(1)(2)(3)


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)

Physical model and the coordinate system.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Physical model and the coordinate system.
Mentions: Consider a two-dimensional steady boundary layer shear flow over a stretching/shrinking sheet in a laminar and incompressible nanofluid of ambient temperature T∞. The fluid is a water-based nanofluid containing two type of nanoparticles, either Cu (copper) or Ag (silver). The nanoparticles are assumed to have a uniform shape and size. Moreover, it is assumed that both the fluid phase and nanoparticles are in thermal equilibrium state. Figure 1 describes the physical model and the coordinate system, where the x and y axes are measured along the surface of the sheet and normal to it, respectively. Following Magyari and Weidman [41], it is assumed that the velocity of the moving stretching/shrinking sheet is uw(x) = Uw(x/L)1/3 and the velocity outside the boundary layer (potential flow) is ue(y) = βy, where β is the constant strain rate. We also assume that the bottom surface of the stretching/shrinking surface is heated by convection from a base (water) fluid at temperature Tf, which provides a heat transfer coefficient hf (see [36]). Under the boundary layer approximations, the basic equations are (see [17,42]),(1)(2)(3)

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