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Numerical study of boundary layer flow and heat transfer of oldroyd-B nanofluid towards a stretching sheet.

Nadeem S, Ul Haq R, Akbar NS, Lee C, Khan ZH - PLoS ONE (2013)

Bottom Line: In the present article, we considered two-dimensional steady incompressible Oldroyd-B nanofluid flow past a stretching sheet.The effects of various parameters, namely, Deborah numbers [Formula: see text] and [Formula: see text], Prandtl parameter [Formula: see text], Brownian motion [Formula: see text], thermophoresis parameter [Formula: see text] and Lewis number [Formula: see text], on flow and heat transfer are investigated.To see the validity of the present results, we have made the comparison of present results with the existing literature.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan.

ABSTRACT
In the present article, we considered two-dimensional steady incompressible Oldroyd-B nanofluid flow past a stretching sheet. Using appropriate similarity variables, the partial differential equations are transformed to ordinary (similarity) equations, which are then solved numerically. The effects of various parameters, namely, Deborah numbers [Formula: see text] and [Formula: see text], Prandtl parameter [Formula: see text], Brownian motion [Formula: see text], thermophoresis parameter [Formula: see text] and Lewis number [Formula: see text], on flow and heat transfer are investigated. To see the validity of the present results, we have made the comparison of present results with the existing literature.

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Variation of velocity, temperature and nanoparticles fraction for various values of .
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pone-0069811-g002: Variation of velocity, temperature and nanoparticles fraction for various values of .

Mentions: The nonlinear coupled ordinary differential equations (7)–(9) subject to the boundary conditions (10)–(12) have been solved numerically using the fourth-fifth order Runge-Kutta-Fehlberg method. Figs. 1, 2, 3, 4, 5, and 6 illustrate the behavior of emerging parameters such relaxation time constant , retardation time constant , Prandtl parameter , Brownian parameter , thermophoresis parameter and Lewis number on velocity profile , temperature profile and mass fraction function . Fig. 1, depicts the variation of on , and . Since is a function of relaxation time and due to viscoelastic properties of fluid it always resist the motion of the fluid. As a result, the velocity profile and boundary layer thickness are decreasing function of . On the other hand, both temperature profile and mass fraction function increases with an increase in Deborah number (see Fig. 1). Physical behavior of Fig. 2 is due to an increase in retardation time of any material enhances the flow. Consequently, with an increase of velocity profile increases and both temperature and mass fraction function decreases (see Fig. 2). Thus, it concluded that and have opposite results on , and due to relaxation and retardation times, respectively (see Fig. 1 and 2).


Numerical study of boundary layer flow and heat transfer of oldroyd-B nanofluid towards a stretching sheet.

Nadeem S, Ul Haq R, Akbar NS, Lee C, Khan ZH - PLoS ONE (2013)

Variation of velocity, temperature and nanoparticles fraction for various values of .
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3755006&req=5

pone-0069811-g002: Variation of velocity, temperature and nanoparticles fraction for various values of .
Mentions: The nonlinear coupled ordinary differential equations (7)–(9) subject to the boundary conditions (10)–(12) have been solved numerically using the fourth-fifth order Runge-Kutta-Fehlberg method. Figs. 1, 2, 3, 4, 5, and 6 illustrate the behavior of emerging parameters such relaxation time constant , retardation time constant , Prandtl parameter , Brownian parameter , thermophoresis parameter and Lewis number on velocity profile , temperature profile and mass fraction function . Fig. 1, depicts the variation of on , and . Since is a function of relaxation time and due to viscoelastic properties of fluid it always resist the motion of the fluid. As a result, the velocity profile and boundary layer thickness are decreasing function of . On the other hand, both temperature profile and mass fraction function increases with an increase in Deborah number (see Fig. 1). Physical behavior of Fig. 2 is due to an increase in retardation time of any material enhances the flow. Consequently, with an increase of velocity profile increases and both temperature and mass fraction function decreases (see Fig. 2). Thus, it concluded that and have opposite results on , and due to relaxation and retardation times, respectively (see Fig. 1 and 2).

Bottom Line: In the present article, we considered two-dimensional steady incompressible Oldroyd-B nanofluid flow past a stretching sheet.The effects of various parameters, namely, Deborah numbers [Formula: see text] and [Formula: see text], Prandtl parameter [Formula: see text], Brownian motion [Formula: see text], thermophoresis parameter [Formula: see text] and Lewis number [Formula: see text], on flow and heat transfer are investigated.To see the validity of the present results, we have made the comparison of present results with the existing literature.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan.

ABSTRACT
In the present article, we considered two-dimensional steady incompressible Oldroyd-B nanofluid flow past a stretching sheet. Using appropriate similarity variables, the partial differential equations are transformed to ordinary (similarity) equations, which are then solved numerically. The effects of various parameters, namely, Deborah numbers [Formula: see text] and [Formula: see text], Prandtl parameter [Formula: see text], Brownian motion [Formula: see text], thermophoresis parameter [Formula: see text] and Lewis number [Formula: see text], on flow and heat transfer are investigated. To see the validity of the present results, we have made the comparison of present results with the existing literature.

Show MeSH
Related in: MedlinePlus