Time-dependent three-dimensional Oldroyd-B nanofluid flow due to bidirectional movement of surface with zero mass flux

Unsteady three-dimensional flow of an incompressible Oldroyd-B nanomaterial is reported in this article. The origin of flow is time-dependent surface spreading in lateral directions transversely taking nanoparticles with zero mass flux. The formulated partial differential system is reframed by similarity variables into ordinary differential system. The obtained system is solved by the process of homotopy analysis for dimensional temperature and concentration of nanoparticles. Physical parameter behavior on temperature and concentrations of nanoparticles is examined using graph and tabular data. The surface temperature is also measured and evaluated, and it is found that the temperature is reduced for greater unsteadiness parameter values. We found that the higher beta(1) enhances the curves of nanoparticle concentration and temperature while these curves retard for the incrementing values of beta(2). The increasing nature of Brownian movement N-b and Lewis number Le corresponds to lower profiles of nanoparticles concentration.