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Combined effect of buoyancy force and Navier slip on MHD flow of a nanofluid over a convectively heated vertical porous plate.

Mutuku-Njane WN, Makinde OD - ScientificWorldJournal (2013)

Bottom Line: A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique.Three different water-based nanofluids containing copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are taken into consideration.Graphical results are presented and discussed quantitatively with respect to the influence of pertinent parameters, such as solid volume fraction of nanoparticles (φ), magnetic field parameter (Ha), buoyancy effect (Gr), Eckert number (Ec), suction/injection parameter (f w ), Biot number (Bi), and slip parameter ( β ), on the dimensionless velocity, temperature, skin friction coefficient, and heat transfer rate.

View Article: PubMed Central - PubMed

Affiliation: Mechanical Engineering Department, Cape Peninsula University of Technology, P.O. Box 1906, Bellville 7635, South Africa.

ABSTRACT
We examine the effect of magnetic field on boundary layer flow of an incompressible electrically conducting water-based nanofluids past a convectively heated vertical porous plate with Navier slip boundary condition. A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique. Three different water-based nanofluids containing copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are taken into consideration. Graphical results are presented and discussed quantitatively with respect to the influence of pertinent parameters, such as solid volume fraction of nanoparticles (φ), magnetic field parameter (Ha), buoyancy effect (Gr), Eckert number (Ec), suction/injection parameter (f w ), Biot number (Bi), and slip parameter ( β ), on the dimensionless velocity, temperature, skin friction coefficient, and heat transfer rate.

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Velocity profiles with increasing Gr, β, and fw.
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fig4: Velocity profiles with increasing Gr, β, and fw.

Mentions: Figures 2–4 illustrate the effects of various thermophysical parameters on the nanofluids velocity profiles. Generally, it is noted that the fluid velocity increases gradually from zero at the plate surface to the free stream prescribed value far away from the plate satisfying the boundary conditions. Figure 2 shows that the momentum boundary layer thickness for Cu-water nanofluid is smaller than the rest of the nanofluids consequently, Cu-water nanofluid tends to flow closer to the convectively heated plate surface and serves as a better coolant than the other nanofluids. It is observed in Figures 3 and 4 that an increase in the magnetic field intensity (Ha), nanoparticle volume fraction (φ), Eckert number (Ec), Grashof number (Gr), and the suction/injection parameter (fw) causes an overshoot of the fluid velocity towards the plate surface hence decreasing both the momentum boundary layer thickness and the fluid velocity. From the physics of the problem, an increase in the magnetic field intensity leads to an increase in the Lorentz force which is a retarding force to the transport phenomena. This retarding force can control the nanofluids velocity which is useful in numerous applications such as magneto hydrodynamic power generation and electromagnetic coating of wires and metal. We also note that the fluid velocity at the plate surface increases with an increase in the slip parameter (β). This is in agreement with the fact that higher β implies an increase in the lubrication and slipperiness of the surface.


Combined effect of buoyancy force and Navier slip on MHD flow of a nanofluid over a convectively heated vertical porous plate.

Mutuku-Njane WN, Makinde OD - ScientificWorldJournal (2013)

Velocity profiles with increasing Gr, β, and fw.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3814100&req=5

fig4: Velocity profiles with increasing Gr, β, and fw.
Mentions: Figures 2–4 illustrate the effects of various thermophysical parameters on the nanofluids velocity profiles. Generally, it is noted that the fluid velocity increases gradually from zero at the plate surface to the free stream prescribed value far away from the plate satisfying the boundary conditions. Figure 2 shows that the momentum boundary layer thickness for Cu-water nanofluid is smaller than the rest of the nanofluids consequently, Cu-water nanofluid tends to flow closer to the convectively heated plate surface and serves as a better coolant than the other nanofluids. It is observed in Figures 3 and 4 that an increase in the magnetic field intensity (Ha), nanoparticle volume fraction (φ), Eckert number (Ec), Grashof number (Gr), and the suction/injection parameter (fw) causes an overshoot of the fluid velocity towards the plate surface hence decreasing both the momentum boundary layer thickness and the fluid velocity. From the physics of the problem, an increase in the magnetic field intensity leads to an increase in the Lorentz force which is a retarding force to the transport phenomena. This retarding force can control the nanofluids velocity which is useful in numerous applications such as magneto hydrodynamic power generation and electromagnetic coating of wires and metal. We also note that the fluid velocity at the plate surface increases with an increase in the slip parameter (β). This is in agreement with the fact that higher β implies an increase in the lubrication and slipperiness of the surface.

Bottom Line: A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique.Three different water-based nanofluids containing copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are taken into consideration.Graphical results are presented and discussed quantitatively with respect to the influence of pertinent parameters, such as solid volume fraction of nanoparticles (φ), magnetic field parameter (Ha), buoyancy effect (Gr), Eckert number (Ec), suction/injection parameter (f w ), Biot number (Bi), and slip parameter ( β ), on the dimensionless velocity, temperature, skin friction coefficient, and heat transfer rate.

View Article: PubMed Central - PubMed

Affiliation: Mechanical Engineering Department, Cape Peninsula University of Technology, P.O. Box 1906, Bellville 7635, South Africa.

ABSTRACT
We examine the effect of magnetic field on boundary layer flow of an incompressible electrically conducting water-based nanofluids past a convectively heated vertical porous plate with Navier slip boundary condition. A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique. Three different water-based nanofluids containing copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are taken into consideration. Graphical results are presented and discussed quantitatively with respect to the influence of pertinent parameters, such as solid volume fraction of nanoparticles (φ), magnetic field parameter (Ha), buoyancy effect (Gr), Eckert number (Ec), suction/injection parameter (f w ), Biot number (Bi), and slip parameter ( β ), on the dimensionless velocity, temperature, skin friction coefficient, and heat transfer rate.

Show MeSH
Related in: MedlinePlus