In this dissertation, the boundary layer analysis of non-Newtonian nanofluid flows over unsteady, stretching permeable surface was investigated. The Williamson, Carreau, and tangent hyperbolic nanofluid flow models were considered either over stretching cylindrical surface or axisymmetric disk. The conservation laws of mass, momentum, energy, and concentration served as the basis to formu- late the governing boundary value problems of the flow regimes. Using the appropriate linearization and similarity techniques, the coupled nonlinear partial differential equations were converted into a system of initial value problems. The system of initial value problems were then solved numerically using higher order Runge-Kutta methods with the shooting technique. The Python programming language was used to carry out the computations. The methods employed and the programming language implemented have been validated with formerly published articles. The impacts of different non-dimentsionalized parameters on velocity, temperature, concentration, skin friction, rate of mass and heat transfers, entropy generation were investigated for different non-Newtonian nano fluid flows. The main results revealed that the velocity decreases as the Weinberg number, Forchheimer number, and unsteady parameters increase. The temperature of the non-Newtonian nanofluids rises with an increase in magnetic parameter, heat generation parameter, thermophoresis parameter, and Eckert number. A thinner concentration boundary layer is observed for destructive chemical reaction parameter, Schmidt number, and Eckert number. Both the rates of heat and mass transfers are initiated for an increase in magnetic parameter, porosity parameter, thermophoresis parameter, Eckert number, and Prandtl number. The irreversibility of heat in the Carreau nanofluid flow over a stretching cylinder is initiated by an increase in the radiation parameter, Eckert number, and Prandtl number. However, the energy irreversibility due to radiation to the total entropy generation decreases along the wall as the Weissenberg number increases.