In this thesis, I investigated the fundamental aspects of nanofluids including nanoparticles, base fluids, and their production processes. The applications of nanofluids in science, engineering and nanotechnology are widely discussed. The basic equations of fluid dynamics and boundary layer analysis are also presented which then extended for nanofluid modeling. A detailed literature survey is carried out to explore the heat and mass transfer characteristics of nanofluids in various geometries. I developed a three dimensional physical model which investigates the axisymmetric stagnation-point flow and heat transfer characteristics over a moving surface with anisotropic slip in a nanofluid considering various thermal and nanoparticles volume fraction conditions. The nonlinear coupled governing equations are made dimensionless using similarity transformations. These nondimensional similarity equations are solved numerically using the function bvp4c from the computer algebra software Matlab. Similarity solutions for the dimensionless velocity, temperature and nanoparticles volume fraction are displayed graphically whereas the rate of shear stress, rate of heat and mass transfer are presented in a tabular form for different model parameters namely: slip parameter, Prandtl number, Lewis number, stretching/shrinking parameter, Brownian diffusion parameter, and thermophoresis parameter. Asymptotic behavior of the solutions for large slip and stability analysis of the numerical solutions are also presented. It is found that the anisotropic slip significantly controls the shear stress, heat and mass transfer of a nanofluid. I also found that slip on the surface actively influences the nanofluid velocity. It is noticeable that heat and mass transfer in a nanofluid depend substantially on the types of the surface conditions. It is more realistic to apply a convective surface condition and zero normal flux of the nanoparticles due to thermophoresis on the boundary modeling with nanofluid. Stability analysis guaranteed that the obtained solutions are stable, hence physically realizable.