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Exact solutions for different vorticity functions of couple stress fluids

In this paper, inverse solutions are obtained for the class of 2D steady incompressible couple stress fluid flows. This class consists of flows for which the vorticity distribution is given by ▽2ψ=ψ+ƒ(x,y). The solutions are obtained by applying the inverse method which makes certain hypotheses regarding the form of the velocity field and pressure but without making any regarding the boundaries of the domain occupied by the fluid. Inverse solutions are derived for three different forms of ƒ(x,y).