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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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ℏθ curve for temperature.
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pone.0129613.g002: ℏθ curve for temperature.

Mentions: In this section, Eqs (7) and (8) subject to the boundary conditions (9) are solved using homotopy analysis method. We choose auxiliary parameters ℏf and ℏθ for the functions ƒ and g respectively. The convergence of the obtained series solutions strictly depends upon these parameters. In order to obtain the permissible values of auxiliary parameters, we have plotted ℏ -curves in the Figs 1 and 2 for ε = 0.1 = δ = γ, λ = 0.2 and Pr = 1.0. (Fig 1) depicts that the range for acceptable value of ℏf is from −1.6 to –0.25. Fig 2 shows that the appropriate range for ℏθ is from –2.4 to –0.8.


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)

ℏθ curve for temperature.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0129613.g002: ℏθ curve for temperature.
Mentions: In this section, Eqs (7) and (8) subject to the boundary conditions (9) are solved using homotopy analysis method. We choose auxiliary parameters ℏf and ℏθ for the functions ƒ and g respectively. The convergence of the obtained series solutions strictly depends upon these parameters. In order to obtain the permissible values of auxiliary parameters, we have plotted ℏ -curves in the Figs 1 and 2 for ε = 0.1 = δ = γ, λ = 0.2 and Pr = 1.0. (Fig 1) depicts that the range for acceptable value of ℏf is from −1.6 to –0.25. Fig 2 shows that the appropriate range for ℏθ is from –2.4 to –0.8.

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