Present thesis addresses the nanofluid flow between two plates, viz. vertical parallel plates, horizontal parallel plates, and inclined plates. These problems are usually governed by nonlinear partial differential equations, which may be converted into nonlinear ordinary differential equations with the aid of appropriate similarity variables. It may not always be possible to get analytical solutions to these nonlinear differential equations. As such, different semi-analytical and numerical methods viz, homotopy perturbation method, optimal homotopy analysis method, Adomian decomposition method, Galerkin&rsquos method, and least square method, are applied here to handle corresponding governing differential equations. Further, it may be noted that a small change in the value of nanoparticle volume fraction or any other parameter may affect the velocity and/or temperature profiles of nanofluid. So, it will be important and challenging to study nanofluid flow problems by considering parameters such as nanoparticle volume fraction as uncertain. In this regard, this thesis also aims to investigate the above-mentioned nanofluid problems in uncertain environment. The homotopy perturbation and Adomian decomposition methods have been extended with the aid of the double parametric concept of fuzzy numbers to handle these uncertain differential equations. This investigation also introduces the inverse problems related to nanofluid flow models. Accordingly, the inclined angle has been computed for a known velocity profile in the crisp case, and the required fuzzy volume fraction for a known fuzzy velocity in the uncertain case.