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In current pagination the flow problems involving shear rate dependent nonlinear viscosity have been treated successfully in the sense of space discretization and solvers. The stable finite element pair Q2/P1disc is employed to approximate the velocity and pressure spaces independently. Discretized form of non-linear expressions is linearized by implementing Newton’s procedure and the resulting systems are solved using a geometric multigrid approach. The flow generated by way of driven cavity and by an obstacle are very important benchmarks of computational fluid dynamics. In current pagination shear rate reliant viscosity model renowned as Carreau Yasuda fluid is capitalized. The obtained results are demonstrated and analyzed with the help of velocity and viscosity plots. In addition, we have produced new reference data for kinetic energy (K.E) for driven cavity problem and drag and lift coefficients for circular obstacle problem. The obtained results for driven cavity problem reveal the fact that K.E is an increasing function of the relaxation parameter (λ) and power law exponent (n) whereas a decreasing function of the model parameter (a). For the case of flow around obstacle the drag coefficient (CD) and the lift coefficient (CL) show strong dependence on (λ) and (n), however a weak dependence on the parameter (a). Keywords: Carreau yasuda fluid, Driven-cavity problem, Flow around obstacle, Multigrid method, Finite element method