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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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Effects of increasing φ, Bi, and Ha on local Nusselt number.
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fig12: Effects of increasing φ, Bi, and Ha on local Nusselt number.

Mentions: Figures 8–13 demonstrate the effects of the various pertinent parameters at the plate surface for both the skin friction coefficient and the local Nusselt number (rate of heat transfer). The presence of nanoparticle in the convectional fluid leads to an increase in the skin friction, as seen in Figure 8, where increasing the nanoparticle volume fraction increases the skin friction for the three nanoparticles (Cu, Al2O3, and TiO2) used, with Cu-water exhibiting the highest increment. This is as expected, since Cu-water moves closer to the plate surface leading to an elevation in the velocity gradient at the plate surface. As expected, increasing Ha, Gr, Ec, and fw leads to an increase in the skin friction coefficient, while an increase in β reduces the skin friction coefficient as shown in Figures 9 and 10. There is an increase in the rate of heat transfer with an increase in φ, Bi, and fw as seen in Figures 11-12, with Al2O3 exhibiting the highest increment. The converse is seen with increasing Ha as shown in Figure 13.


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)

Effects of increasing φ, Bi, and Ha on local Nusselt number.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig12: Effects of increasing φ, Bi, and Ha on local Nusselt number.
Mentions: Figures 8–13 demonstrate the effects of the various pertinent parameters at the plate surface for both the skin friction coefficient and the local Nusselt number (rate of heat transfer). The presence of nanoparticle in the convectional fluid leads to an increase in the skin friction, as seen in Figure 8, where increasing the nanoparticle volume fraction increases the skin friction for the three nanoparticles (Cu, Al2O3, and TiO2) used, with Cu-water exhibiting the highest increment. This is as expected, since Cu-water moves closer to the plate surface leading to an elevation in the velocity gradient at the plate surface. As expected, increasing Ha, Gr, Ec, and fw leads to an increase in the skin friction coefficient, while an increase in β reduces the skin friction coefficient as shown in Figures 9 and 10. There is an increase in the rate of heat transfer with an increase in φ, Bi, and fw as seen in Figures 11-12, with Al2O3 exhibiting the highest increment. The converse is seen with increasing Ha as shown in Figure 13.

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