Poiseuille Flow of the Suspension of Gold Nanoparticles in Second-grade Fluid: Analytical Solutions

The Poiseuille flows have been extensively restricted to Newtonian fluids through a channel, and the significance of such flows has spanned several industries, from chemical industries to engineering applications. The restriction to Newtonian flows has impacted the further advancement in the study of Poiseuille flow and as a result, studies on Poiseuille flows have been neglected for decades. In this study, the Poiseuille flow of the second-grade nanofluid fluid is considered. The base fluid is the viscoelastic Second-grade fluid, a fluid that is both shear-thinning and shear-thickening under different conditions and whose applications can be found in polymer processing and cosmetic production. This study invokes the general assumptions of Poiseuille flow, which reduces the governing equations to ordinary differential equations. The results from simulating the model show that the velocity drops as both the second-grade fluid parameter and the volume fraction increase. The flow rate increases with increasing channel width.