This thesis aims at understanding and improving the existing knowledge in the area of generalized Newtonian fluids. The main focus in this work is given to the mathematical modeling and computation of three dimensional flow of Carreau rheological model that can describe both the shear thinning and shear thickening characteristics of fluids. Consequently, three dimensional boundary layer equations for both steady and unsteady cases are established. Utilizing Boussinesq estimates the governing flow and heat transfer expressions of Carrau fluid model influenced by a bidirectional stretched surface have been framed. The appropriate conversions reformed the modeled partial differential equations (PDEs) into ordinary differential equations (ODEs) and results are established both numerically as well as analytically by employing bvp4c scheme and homotopy analysis method (HAM), respectively. The performance of influential parameters for shear thinning-thickening cases are graphed, tabulated and conferred. Additionally, a comparative study has been reported in both graphical and tabular forms with available literature. The consideration of non-Newtonian fluids have noteworthy utilizations in the area of energy, deferrals, genetic disciplines, polymer clarification, imitation fibers compound inventions, geophysics and refined materials, etc. Regardless of such attentions, various researchers are still affianced to scrutinize further the streams of non-Newtonian fluids. The contributions in this thesis include mathematical modeling of Carreau fluid in three dimension with elucidations of results of considered problems. The results for the velocity, temperature and concentration fields for both shear thinning-thickening cases are reported. The results showed that the velocity components have conflicting performance for the local Weissenberg numbers for shear thinning and shear thickening cases. It was also noted that the enhancing values of the power law exponent intensify the fluid velocities for both instances. Further, the temperature of Carrau fluid for shear thinning case intensifies for higher estimation of the local Weissenberg numbers; however, for shear thickening fluid a different behavior is observed.