Due to the lack of heat transfer rate of traditional fluids like water, ethylene, kerosene oil and some others, scientists over the year have made efforts to improve the thermal properties of these traditional fluids based on the idea of nanofluids. In this manuscript, we have used different available models for thermal conductivity of nanofluids to analyze the behavior of velocity and temperature profiles. The base fluid mostly considered is water, while Copper (Cu) and the carbon nanotubes (CNT) have been utilized as the nanoparticles. thermal conductivity have been employed in particular. The flows passing through nonparallel walls, stretching sheet problems and the flow over a wedge have been keen areas of focus in the manuscript. A novel analysis for the flow of nanofluids in converging/diverging channels when the walls are stretching/shrinking has also been included. Also, the squeezing flow of nanofluids in a channel with lower stretching wall has also been studied. The influence of magnetic field on the flow and heat transfer of nanofluids is also studied. In some of the problems, Brownian motion and thermophoresis effects are also considered. The radiation effects have also been included in modeling the problems using Buongiorno servations laws used to model the physical problems have been used. Employing suitable similarity transformations, the equations that govern the flow are transformed to a set of nonlinear ordinary differential equations. Some analytical as well as numerical schemes have been used for the solution purpose. The results thus obtained are compared with some of the existing ones, and the agreement between the solutions is highlighted in the form of tables. Variations in velocity, temperature and concentration profiles with respect to the parameters involved are simulated graphically with the help of different mathematical software.