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On Comparison of Series and Numerical Solutions for Flow of Eyring-Powell Fluid with Newtonian Heating And Internal Heat Generation/Absorption.

Hayat T, Ali S, Farooq MA, Alsaedi A - PLoS ONE (2015)

Bottom Line: The governing non-linear analysis of partial differential equations is reduced into the ordinary differential equations using similarity transformations.The resulting problems are computed for both series and numerical solutions.Both solutions are found in an excellent agreement.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad, 44000, Pakistan.

ABSTRACT
In this paper, we have investigated the combined effects of Newtonian heating and internal heat generation/absorption in the two-dimensional flow of Eyring-Powell fluid over a stretching surface. The governing non-linear analysis of partial differential equations is reduced into the ordinary differential equations using similarity transformations. The resulting problems are computed for both series and numerical solutions. Series solution is constructed using homotopy analysis method (HAM) whereas numerical solution is presented by two different techniques namely shooting method and bvp4c. A comparison of homotopy solution with numerical solution is also tabulated. Both solutions are found in an excellent agreement. Dimensionless velocity and temperature profiles are plotted and discussed for various emerging physical parameters.

No MeSH data available.


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Variation of γ on θ.
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pone.0129613.g008: Variation of γ on θ.

Mentions: Tables 2 and 3 are presented to analyze the comparison of HAM and numerical solutions for various values of embedding parameters for −f″(0) and −θ′(0) respectively. A comparative study of these two tables shows an excellent agreement. Our interest further is concerned with the influence of parameters ε, δ, γ, λ and Pr on the velocity and temperature fields. Hence we draw the Figs 3–12 for such objective. Figs 3 and 4 are plotted to examine the variations of δ and ε on the velocity field. We see from (Fig 3) that the velocity decreases when δ is increased. The influence of parameter ε on the velocity is quite opposite to that of δ (See Fig 4). Effects of heat source (λ > 0) and sink (λ < 0) on the temperature are analyzed in the Figs 5 and 6. As expected, (Fig 5) illustrates that there is rise in temperature when λ > 0. However, the temperature decreases when λ < 0. Effects of Pr on temperature is plotted in (Fig 7). Here the temperature decreases when we increase the Prandtl number Pr. This is because of the reason that an increase in Pr decreases the thermal conductivity of the fluid and consequently the temperature decreases. (Fig 8) displays the effects of conjugate parameter γ on temperature θ(η). It is observed that temperature is an increasing function of. (Fig 9). Show the variation of δ on skin friction coefficient when other parameters are kept fixed. It is noticed that skin friction coefficient increases by increasing parameter δ. Figs 10, 11 and 12 respectively plot the variation of Pr, (λ > 0) and (λ < 0) on the local Nusselt number. These Figs. Witness that the local Nusselt number increases by increasing Pr and λ < 0. However, the behavior of λ > 0 is reverse when compare with Pr and λ < 0.


On Comparison of Series and Numerical Solutions for Flow of Eyring-Powell Fluid with Newtonian Heating And Internal Heat Generation/Absorption.

Hayat T, Ali S, Farooq MA, Alsaedi A - PLoS ONE (2015)

Variation of γ on θ.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4581858&req=5

pone.0129613.g008: Variation of γ on θ.
Mentions: Tables 2 and 3 are presented to analyze the comparison of HAM and numerical solutions for various values of embedding parameters for −f″(0) and −θ′(0) respectively. A comparative study of these two tables shows an excellent agreement. Our interest further is concerned with the influence of parameters ε, δ, γ, λ and Pr on the velocity and temperature fields. Hence we draw the Figs 3–12 for such objective. Figs 3 and 4 are plotted to examine the variations of δ and ε on the velocity field. We see from (Fig 3) that the velocity decreases when δ is increased. The influence of parameter ε on the velocity is quite opposite to that of δ (See Fig 4). Effects of heat source (λ > 0) and sink (λ < 0) on the temperature are analyzed in the Figs 5 and 6. As expected, (Fig 5) illustrates that there is rise in temperature when λ > 0. However, the temperature decreases when λ < 0. Effects of Pr on temperature is plotted in (Fig 7). Here the temperature decreases when we increase the Prandtl number Pr. This is because of the reason that an increase in Pr decreases the thermal conductivity of the fluid and consequently the temperature decreases. (Fig 8) displays the effects of conjugate parameter γ on temperature θ(η). It is observed that temperature is an increasing function of. (Fig 9). Show the variation of δ on skin friction coefficient when other parameters are kept fixed. It is noticed that skin friction coefficient increases by increasing parameter δ. Figs 10, 11 and 12 respectively plot the variation of Pr, (λ > 0) and (λ < 0) on the local Nusselt number. These Figs. Witness that the local Nusselt number increases by increasing Pr and λ < 0. However, the behavior of λ > 0 is reverse when compare with Pr and λ < 0.

Bottom Line: The governing non-linear analysis of partial differential equations is reduced into the ordinary differential equations using similarity transformations.The resulting problems are computed for both series and numerical solutions.Both solutions are found in an excellent agreement.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad, 44000, Pakistan.

ABSTRACT
In this paper, we have investigated the combined effects of Newtonian heating and internal heat generation/absorption in the two-dimensional flow of Eyring-Powell fluid over a stretching surface. The governing non-linear analysis of partial differential equations is reduced into the ordinary differential equations using similarity transformations. The resulting problems are computed for both series and numerical solutions. Series solution is constructed using homotopy analysis method (HAM) whereas numerical solution is presented by two different techniques namely shooting method and bvp4c. A comparison of homotopy solution with numerical solution is also tabulated. Both solutions are found in an excellent agreement. Dimensionless velocity and temperature profiles are plotted and discussed for various emerging physical parameters.

No MeSH data available.


Related in: MedlinePlus