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Research Papers: Fundamental Issues and Canonical Flows

Some Exact Solutions to Equations of Motion of an Incompressible Second Grade Fluid

[+] Author and Article Information
Saif Ullah

Department of Mathematics,
Government College University,
Lahore 54000, Pakistan
e-mail: dr.saifullah@gcu.edu.pk

Irsa Maqbool

Department of Mathematics,
Government College University,
Lahore 54000, Pakistan

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 27, 2013; final manuscript received June 5, 2014; published online September 10, 2014. Editor: Malcolm J. Andrews.

J. Fluids Eng 137(1), 011205 (Sep 10, 2014) (4 pages) Paper No: FE-13-1752; doi: 10.1115/1.4027826 History: Received December 27, 2013; Revised June 05, 2014

In this paper, we derive some exact solutions of the equations governing the steady plane motions of an incompressible second grade fluid. For this purpose, the vorticity and stream functions both are expressed in terms of complex variables and complex functions. The derived solutions represent the flows having streamlines as a family of ellipses, parabolas, concentric circles, and rectangular hyperbolas. Some physical features of the derived solutions are also illustrated by their contour plots.

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Figures

Grahic Jump Location
Fig. 1

Contour plot of ψ when I = (a1 + ıa2)ln z

Grahic Jump Location
Fig. 2

Contour plot of ψ when I = (b1 + ıb2)z2

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