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. 2012;7(11):e49499.
doi: 10.1371/journal.pone.0049499. Epub 2012 Nov 15.

MHD free convective boundary layer flow of a nanofluid past a flat vertical plate with Newtonian heating boundary condition

Mohammed J Uddin  1 , Waqar A Khan, Ahmed I Ismail
Affiliations

MHD free convective boundary layer flow of a nanofluid past a flat vertical plate with Newtonian heating boundary condition

Mohammed J Uddin et al. PLoS One. 2012.

Abstract

Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Flow configuration and coordinate system.
Figure 2
Figure 2. Effects of several parameters on dimensionless velocity profiles.
Figure 3
Figure 3. Effects of several parameters on dimensionless temperature profiles.
Figure 4
Figure 4. Effects of several parameters on dimensionless concentration profiles.
Figure 5
Figure 5. Effects of several parameters on dimensionless heat transfer rate.
Figure 6
Figure 6. Effects of several parameters on dimensionless mass transfer rate.
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