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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 Nusselt number with  for various values of  when .
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pone-0069811-g007: Variation of Nusselt number with for various values of when .

Mentions: Physically it is observed that an increase in the elastic parameter, the resistance to fluid flow will increase. Table 1 illustrates an excellent agreement of the present results with Khan and Pop [17] in the absence of non-Newtonian parameters and . As expected, it is found from Fig. 3, that both temperature and nanoparticle concentration profiles exert the decreasing behavior with the influence of Pr. Fig. 4 shows that both temperature and nanoparticle concentration have the same behavior when it is compared with Fig. 3 for higher values of . Consequently, boundary layer thickness decreases indefinitely with an increase in . Effects of Brownian motion and thermophoresis parameters on temperature profile and mass fraction function are shown in Figs. 5 and 6. It is observed that for higher values of both and , the temperature profile rises. On the other hand Fig. 5, shows opposite behavior for mass fraction function when it is compare with Fig. 6, for increasing values of both and . In the absence of both nanoparticles and non-Newtonian effects there is an excellent agreement of the present results with Wang [4] (see Table 2). The effects of elastic parameter, Prandtl parameter, Brownian parameter, thermophoresis parameter and Lewis number on the Nusselt number and Sherwood number are presented in Figs. 7, 8, 9, and 10. It is seen from Fig. 7, 8 and Table 3 that the Nusselt number decreases with increasing for both cases when is less or greater than for . Figs. 9 and 10 and Table 3 show the variation in dimensionless mass transfer rates vs parameter for the selected values of other parameters. The dimensionless mass transfer rates decrease with the increase in . Finally, high Prandtl fluid has a low thermal conductivity reducing conduction which results in an increase in the heat transfer rate at the surface of sheet.


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 Nusselt number with  for various values of  when .
© Copyright Policy
Related In: Results  -  Collection

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

pone-0069811-g007: Variation of Nusselt number with for various values of when .
Mentions: Physically it is observed that an increase in the elastic parameter, the resistance to fluid flow will increase. Table 1 illustrates an excellent agreement of the present results with Khan and Pop [17] in the absence of non-Newtonian parameters and . As expected, it is found from Fig. 3, that both temperature and nanoparticle concentration profiles exert the decreasing behavior with the influence of Pr. Fig. 4 shows that both temperature and nanoparticle concentration have the same behavior when it is compared with Fig. 3 for higher values of . Consequently, boundary layer thickness decreases indefinitely with an increase in . Effects of Brownian motion and thermophoresis parameters on temperature profile and mass fraction function are shown in Figs. 5 and 6. It is observed that for higher values of both and , the temperature profile rises. On the other hand Fig. 5, shows opposite behavior for mass fraction function when it is compare with Fig. 6, for increasing values of both and . In the absence of both nanoparticles and non-Newtonian effects there is an excellent agreement of the present results with Wang [4] (see Table 2). The effects of elastic parameter, Prandtl parameter, Brownian parameter, thermophoresis parameter and Lewis number on the Nusselt number and Sherwood number are presented in Figs. 7, 8, 9, and 10. It is seen from Fig. 7, 8 and Table 3 that the Nusselt number decreases with increasing for both cases when is less or greater than for . Figs. 9 and 10 and Table 3 show the variation in dimensionless mass transfer rates vs parameter for the selected values of other parameters. The dimensionless mass transfer rates decrease with the increase in . Finally, high Prandtl fluid has a low thermal conductivity reducing conduction which results in an increase in the heat transfer rate at the surface of sheet.

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