Abstract
The unsteady boundary layer flow and thermal transportation analysis of an incompressible Oldroyd-B nanofluid driven by stretching cylinder is scrutinized with analytically approach in this study. The governing unsteady boundary layer equations (PDEs) are first established, and then these PDEs are converted into highly nonlinear ordinary differential equations (ODEs) using appropriate similarity transformations. The obtained equations are then solved in the form of series solutions via homotopy analysis method (HAM) for the velocity, temperature, and concentration fields. Additionally, the convergence analysis of the analytic series solutions is discussed. The model under consideration predicts the features of both the relaxation and retardation times effects. The aspects of thermophoresis and Brownian motion characteristics due to nanoparticles are studied by employing Buongiorno's model. The findings demonstrated that when the curvature parameter increases, the velocity, temperature, and concentration distributions near the cylinder's surface enhanced. Moreover, the velocity profile, for relaxation and the retardation times parameters, showed the opposite behavior. Also, the unsteadiness parameter enhanced the fluid velocity. The comparison of some current and old results is remarkable.