In the present paper, we have studied three fundamental flows namely Couette, Poiseuille and generalized Couette flows of an incompressible Casson fluid between parallel plates using slip boundary conditions. The equations governing the flow of Casson fluid are non-linear in nature. Analytical solutions of the non-linear governing equations with non-linear boundary conditions are obtained for each case. The effect of the various parameters on the velocity and volume flow rate for each problem is studied and the results are presented through graphs. It is observed that, the presence of Casson number decreases the velocity and volume flow rate of the fluid. Increasing of slip parameter increases the velocity and volume flow rate in both Poiseuille and generalized Couette flows

Recent studies in nanoscience and technology have emphasized the significance of the nanofluid in biomedical engineering like drug targeting systems, biotherapy and treatment of cancer. The present article is opted to analyze the impact of copper and diamond nanoparticles on peristaltic pumping of couple stress nanofluid regulated by the electro-magneto-hydrodynamic mechanism in a vertical microchannel. The influences of thermal radiation, convective and slip boundary conditions are also considered. In this study, the blood is treated as a coupled stress fluid, nanoparticles with four types of shapes (sphere, platelet, blade and cylinder) have been taken into account. The lubrication approach is carried out for mathematical modeling. The resulting non-linear system of equations has been solved analytically. The impacts of pertinent parameters on shear stress, velocity, temperature, heat transfer rate and entropy generation are shown through pictorial representations. From the current study, it is observed that the couple stress parameter reduces velocity and enhances pressure gradient and shear stress of nanofluid. The entropy generation enhances with sphere-shaped nanoparticles. Magnetic field strength reduces the bolus size. The thermal radiation diminishes the rate of heat transfer and nanofluid temperature increases with heat generation effects.