Nature is abundant with the examples of flows involving non-Newtonian fluids. Such flows are widely encountered in many industrial and technology applications, such as melts of polymers, biological solutions, paints, tars, asphalts and glues etc. Moreover, non-Newtonian nanofluids are also widely encountered in many industrial and technology applications such as nuclear reactors, transportation industry (an automobiles, trucks, and airplanes), micro-electromechanical systems, electronics and instrumentation etc. This book deals an incompressible, non-Newtonian and non-Newtonian nanofluid. It is well known that getting an analytic solution of a nonlinear coupled partial differential equation is often more difficult as compared to getting a numerical solution. This book provides analytical solutions by using the methods like lie algebra, perturbation and homotopy techniques. In many cases solution obtains are compared with each other and existing results. Convergence of the obtained series solutions has been discussed explicitly and the recurrence formulae for finding the coefficients are also given. The role of pertinent parameters is illustrated graphically in each case.