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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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Flow configuration and coordinate system.
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fig1: Flow configuration and coordinate system.

Mentions: The steady laminar incompressible two-dimensional MHD boundary layer flow of an electrically conducting water-based nanofluid past a convectively heated porous vertical semiinfinite flat plate under the combined effects of buoyancy forces and Navier slip is considered. The nanofluids contain three different types of nanoparticles: Cu, Al2O3, and TiO2. Let the x-axis be taken along the direction of plate, and let y-axis be normal to it. The left side of the plate is assumed to be heated by convection from a hot fluid at temperature Tf, which provides a heat transfer coefficient hf, while the right surface is subjected to a stream of an electrically conducting cold nanofluid at temperature T∞ in the presence of a transverse magnetic field of strength B0 applied parallel to the y-axis, as shown in Figure 1. The induced magnetic field due to the motion of the electrically conducting fluid is negligible. It is also assumed that the external electrical field is zero and that the electric field due to the polarization of charges is negligible (see Table 1).


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)

Flow configuration and coordinate system.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig1: Flow configuration and coordinate system.
Mentions: The steady laminar incompressible two-dimensional MHD boundary layer flow of an electrically conducting water-based nanofluid past a convectively heated porous vertical semiinfinite flat plate under the combined effects of buoyancy forces and Navier slip is considered. The nanofluids contain three different types of nanoparticles: Cu, Al2O3, and TiO2. Let the x-axis be taken along the direction of plate, and let y-axis be normal to it. The left side of the plate is assumed to be heated by convection from a hot fluid at temperature Tf, which provides a heat transfer coefficient hf, while the right surface is subjected to a stream of an electrically conducting cold nanofluid at temperature T∞ in the presence of a transverse magnetic field of strength B0 applied parallel to the y-axis, as shown in Figure 1. The induced magnetic field due to the motion of the electrically conducting fluid is negligible. It is also assumed that the external electrical field is zero and that the electric field due to the polarization of charges is negligible (see Table 1).

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