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The unsteady and incompressible flow of non-Newtonian fluid through composite stenosis is investigated in the present study. The micropolar fluid is treated as a blood flow model. Mild stenosis and slip velocity are also taken into account. The governing equations are given in cylindrical coordinates system. Analytic solutions of velocity and volumetric flow flux are developed interms of modified Bessel functions. The expressions for the impedance (flow resistance) λ , the wall shear stress distribution in the stenotic region T w and the shearing stress at the stenosis throat T s are also given. Impact of involved pertinent parameters is sketched and examined by the resistance of impedance and shear stress. The stream lines are also made for different sundry parameters.

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In this paper, we initiate the novel concept of complex intuitionistic fuzzy subgroups and prove that every complex intuitionistic fuzzy subgroup generates two intuitionistic fuzzy subgroups. We extend this ideology to define the concept of level subsets of complex intuitionistic fuzzy set and discuss its various fundamental algebraic characteristics. We also show that the level subset of the complex intuitionistic fuzzy subgroups is a subgroup. Furthermore, we investigate the homomorphic image and preimage of complex intuitionistic fuzzy subgroup under group homomorphism. Moreover, we prove that the product of two complex intuitionistic fuzzy subgroups is also a complex intuitionistic fuzzy subgroup and develop some new results about direct product of complex intuitionistic fuzzy subgroups.INDEX TERMS Complex intuitionistic fuzzy set, Complex intuitionistic fuzzy subgroup, Level subsets, Product of complex intuitionistic fuzzy sets, Product of complex intuitionistic fuzzy subgroups.

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