Unsteady Boundary Layer Flow Over a Permeable Stretching/Shrinking Cylinder Immersed in Nanofluid

Abstract

In this study, the unsteady boundary layer flow over a stretching/shrinking cylinder immersed in copper (Cu)-water nanofluid with the presence of suction effect is analyzed. The governing partial differential equations are converted to ordinary differential equations using similarity transformation. The bvp4c solver in Matlab software is applied to solve the system of ordinary differential equations where the numerical solutions are obtained and presented graphically. The study aims to investigate the effects of nanoparticle volume fraction, the unsteadiness parameter, the stretching/shrinking parameter on the velocity and temperature gradients. It is found that the dual solutions are obtained in a specific range of these parameters for both stretching and shrinking cylinders. Besides, a high volume of the nanoparticles in the base fluid increases the velocity gradient and decreases the temperature gradient at the surface. Also, increasing nanoparticle volume fraction in the base fluid expands the range of solutions, which denotes the boundary layer separation from the surface has been delayed. The stability analysis is performed by introducing a new dimensionless variable to determine the stability of the solutions. In this phase, the smallest eigenvalue obtained shows that the first solution is stable and physically realizable while the second solution is not stable.