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Fundamental Issues and Canonical Flows

# Flow and Heat Transfer of Powell–Eyring Fluid Over a Stretching Surface: A Lie Group Analysis

[+] Author and Article Information
Mudassar Jalil

Department of Mathematics,
COMSATS Institute of Information Technology,
e-mail: mudassarjalil@yahoo.com

Saleem Asghar

Department of Mathematics,
COMSATS Institute of Information Technology,
Department of Mathematics,
King Abdulaziz University,
Jeddah 21589, Saudi Arabia

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 28, 2012; final manuscript received July 23, 2013; published online September 9, 2013. Assoc. Editor: Sharath S. Girimaji.

J. Fluids Eng 135(12), 121201 (Sep 09, 2013) (6 pages) Paper No: FE-12-1410; doi: 10.1115/1.4025097 History: Received August 28, 2012; Revised July 23, 2013

## Abstract

In this study, the flow and heat transfer of Powell–Eyring fluid over a permeable stretching surface is examined. By using Lie group analysis, the symmetries of the equations are found. Four finite parameter and one infinite parameter Lie group of transformations are obtained. Similarity transformations for the problem are derived with help of these symmetries. The governing system of partial differential equations is transformed to a system of ordinary differential equations by using the similarity transformations. These equations are solved numerically using the Keller-box method. A comparison is performed with analytical results as well as previously published work, and an excellent agreement is observed between the results. The effects of governing parameters on the velocity and temperature profiles, the skin friction, and local Nusselt number are analyzed and discussed. It is observed that both the skin friction and local Nusselt number increase due to an increase in suction/injection parameter fw. The effects of the Prandtl number Pr, temperature power index m, and fluid parameter ε are found to increase the local Nusselt number whereas the effect of the fluid parameter δ is to decrease it. The obtained results elucidate that the skin friction reduces with increase in ε while opposite behavior is noticed for increasing values of δ.

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## References

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## Figures

Fig. 1

Effects of ε on similar velocity f ′(η) when δ = 0.1 and fw = 0.5

Fig. 2

Effects of δ on similar velocity f ′(η) when ε = 0.1 and fw = 0.5

Fig. 3

Effects of fw on similar velocity f ′(η) when ε = 0.1 and δ = 0.1

Fig. 8

Effects of fw on θ(η) when Pr = m = ε = 1.0 and δ = 0.1

Fig. 4

Effects of ε on θ(η) when Pr = m = 1.0, δ = 0.1, and fw = 0.5

Fig. 5

Effects of δ on θ(η) when Pr = m = ε = 1.0 and fw = 0.5

Fig. 6

Effects of Pr on θ(η) when m = ε = 1.0, δ = 0.1, and fw = 0.5

Fig. 7

Effects of m on θ(η) when Pr = ε = 1.0, δ = 0.1, and fw = 0.5

Fig. 9

Effects of Pr on Rex-1/2Nu for m when ε = 1.0, fw = 0.5, and δ = 0.1

Fig. 10

Effects of Pr on Rex-1/2Nu for fw when m = ε = 1.0 and δ = 0.1

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