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Research Papers

An Explicit Analytic Solution of Steady Three-Dimensional Stagnation Point Flow of Second Grade Fluid Toward a Heated Plate

[+] Author and Article Information
Ahmer Mehmood1

Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistanahmerqau@yahoo.co.uk

Asif Ali

Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan

1

Corresponding author. Present address: Department of Mathematics (FBAS), International Islamic University Islamabad, Pakistan.

J. Appl. Mech 75(6), 061003 (Aug 15, 2008) (8 pages) doi:10.1115/1.2957597 History: Received June 12, 2006; Revised January 25, 2007; Published August 15, 2008

We present a purely analytic solution to the steady three-dimensional viscous stagnation point flow of second grade fluid over a heated flat plate moving with some constant speed. The analytic solution is obtained by a newly developed analytic technique, namely, homotopy analysis method. By giving a comparison with the existing results, it is shown that the obtained analytic solutions are highly accurate and are in good agreement with the results already present in literature. Also, the present analytic solution is uniformly valid for all values of the dimensionless second grade parameter α. The effects of α and the Prandtl number Pr on velocity and temperature profiles are discussed through graphs.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 8

ℏ-curves of θ(η) plotted at the 12th order of approximation

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Figure 9

Effect of the parameter α on temperature distribution at a fixed value of the Prandtl number Pr

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Figure 10

Effect of the Prandtl number Pr on temperature distribution at a fixed value of the parameter α

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Figure 1

ℏ-curves of h(η) plotted for different values of the parameter α

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Figure 2

ℏ-curves of f(η) plotted for different values of the parameter α

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Figure 3

Comparison between the analytic solution and the numerical data

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Figure 4

Effect of the parameter α on velocity distribution at aU∕x=0.01

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Figure 5

Effect of the parameter α on velocity distribution at aU∕x=0.5

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Figure 6

Effect of the parameter α on nondimensional velocity h′(η)

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Figure 7

Effect of the parameter α on nondimensional velocity h(η)

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