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.
Some Exact Solutions to Equations of Motion of an Incompressible Second Grade Fluid
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.
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Ullah, S., and Maqbool, I. (September 10, 2014). "Some Exact Solutions to Equations of Motion of an Incompressible Second Grade Fluid." ASME. J. Fluids Eng. January 2015; 137(1): 011205. https://doi.org/10.1115/1.4027826
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