Computational fluid dynamics is used to study two distinct areas of engineering interest: microfluidic systems involving superhydrophobic surfaces and blood pumps. Superhydrophobic surfaces, which can induce slip at fluid-solid interfaces, are modeled using mixed free-shear and no-slip boundary conditions. Despite remarkable effort to include the effects of surface topology and various flow and physical properties in models describing fluid slip over these surfaces, the mathematical description of flow over mixed slip boundaries is still incomplete. Critical configurations of roughness necessary to achieve drag reduction in micro-channels are established. The effects of roughness shape and size on drag for both Newtonian and non-Newtonian fluid flow are also considered in depth. Based on these findings, similarity theory is used to develop a model to describe drag reduction as a function of channel geometry. The principles used in the development of these models are then applied to the more complicated system of a centrifugal blood pump. The effects of the non-Newtonian rheological behavior, hematocrit, temperature, and turbulence on pump performance and subsequent blood damage is quantified over a wide range of operating conditions.