This dissertation emphasis on axi-symmetric flow of Newtonian fluid, rate type fluids and nanofluids between two infinite stretching disks. The modeling of said problems is done in cylindrical coordinates. Applied magnetic field, mixed convection, viscous dissipation, joule heating and heat source/sink are taken into account in various cases. Heat transfer, chemical and material composition analysis of flow between stretching disks have been analyzed under different boundary conditions; such as slip boundary conditions and convective boundary conditions. It is also important to mention that the second order slip and second order temperature jump is also studies on both disk surfaces with homogenous and heterogeneous reactions. The Brownian motion and thermophoresis effects are investigated in the presence of radiation effect for Maxwell and Oldroyd-B nanofluids. The mathematical modeling of problem statement results in partial differential equations, which further transformed to coupled nonlinear ordinary differential equations using similarity transformations. The reliability and flexibility of homotopy analysis method has encouraged us to find the solution of system of coupled nonlinear ordinary differential equations. The convergence of derived series solutions is ensured using ℏ-curves. The numerical values of skin friction, Nusselt number and Sherwood number are discussed through tables and graphs. The effects of other important parameters like Archimedes number, Eckert number, Prandtl number, Biot number, Schmidt number and Brownian motion parameters on velocity, pressure, temperature and concentration profiles are discussed and analyzed graphically