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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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Temperature profiles for different nanofluids.
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Related In: Results  -  Collection


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fig5: Temperature profiles for different nanofluids.

Mentions: Figures 5–7 show the effects of various parameters on the temperature profile. In general, the maximum fluid temperature is achieved at the plate surface due to the convectional heating but decreases exponentially to zero far away from the plate surface satisfying the free stream conditions. As expected, at the plate surface, Cu-water has the highest temperature and a greater thermal boundary layer thickness than the other two nanofluids, as seen in Figure 5. This is in accordance with the earlier observation, since the Cu-water nanofluid is more likely to absorb more heat from the plate surface owing to its close proximity to the hot surface. It is observed from Figure 6, that increasing Ha, φ, Bi, and Ec leads to an increase in both the fluid temperature and the thermal boundary layer thickness. This can be attributed to the additional heating due resistance of fluid flow as a result of the magnetic field, the presence of the nanoparticle, the increased rate at which the heat moves from the hot fluid to the plate and the additional heating as a result of the viscous dissipation.


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)

Temperature profiles for different nanofluids.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig5: Temperature profiles for different nanofluids.
Mentions: Figures 5–7 show the effects of various parameters on the temperature profile. In general, the maximum fluid temperature is achieved at the plate surface due to the convectional heating but decreases exponentially to zero far away from the plate surface satisfying the free stream conditions. As expected, at the plate surface, Cu-water has the highest temperature and a greater thermal boundary layer thickness than the other two nanofluids, as seen in Figure 5. This is in accordance with the earlier observation, since the Cu-water nanofluid is more likely to absorb more heat from the plate surface owing to its close proximity to the hot surface. It is observed from Figure 6, that increasing Ha, φ, Bi, and Ec leads to an increase in both the fluid temperature and the thermal boundary layer thickness. This can be attributed to the additional heating due resistance of fluid flow as a result of the magnetic field, the presence of the nanoparticle, the increased rate at which the heat moves from the hot fluid to the plate and the additional heating as a result of the viscous dissipation.

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