Research Papers: Fundamental Issues and Canonical Flows

Some Exact Analytical Solutions for Two-Dimensional Flow 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

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 12, 2014; final manuscript received April 12, 2015; published online June 15, 2015. Assoc. Editor: Sharath S. Girimaji.

J. Fluids Eng 137(10), 101206 (Oct 01, 2015) (9 pages) Paper No: FE-14-1660; doi: 10.1115/1.4030491 History: Received November 12, 2014; Revised April 12, 2015; Online June 15, 2015

This investigation deals with some exact analytical solutions of the incompressible second grade fluid by using the method based on the separation of variables. In many cases, this method can derive exact analytical solutions easier than other methods. A family of solutions is derived in this paper, which governs scientific and engineering experimentations. The derived solutions represent the flows having streamlines as a family of ellipses, parabolas, concentric circles, and rectangular hyperbolas. From practical point of view, these flows have applications in many manufacturing processes in industry. Some physical features of the derived solutions are also illustrated by their contour plots.

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Grahic Jump Location
Fig. 1

Contour plot of (a) ψ1, (b) ψ2, (c) ψ3, and (d) ψ5

Grahic Jump Location
Fig. 2

Contour plot of (a) ψ6, (b) ψ7, (c) ψ8, and (d) ψ9

Grahic Jump Location
Fig. 3

Contour plot of (a) ψ10, (b) ψ11, (c) ψ12, and (d) ψ13

Grahic Jump Location
Fig. 4

Contour plot of (a) ψ14, (b) ψ15, (c) ψ16, and (d) ψ17

Grahic Jump Location
Fig. 5

Contour plot of (a) ψ18, (b) ψ19, (c) ψ20, and (d) ψ21

Grahic Jump Location
Fig. 6

Contour plot of (a) ψ22 and (b) ψ23



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