Implementation of shooting technique for Buongiorno nanofluid model driven by a continuous permeable surface

The current investigation focuses on the thermal characteristics and heat and mass transfer in the context of their applications. There has been a lot of interest in the utilization of non-Newtonian liquids in various engineering and biological fields. Having such considerable attention on non-Newtonian liquids, the goal is to investigate the flow nature of viscoelastic nanoliquid flow driven by a permeable stretchable surface considering the Buongiorno nanofluid model with suction or injection and mixed convection. This model includes Brownian diffusion, thermophoresis, and radiation effects. The thermal boundary layer theories established the constitutive flow equations, that is, the momentum, diffusion balance, and energy expressions. The established partial differential equations are diminished to dimensionless coupled ordinary differential equations by taking the assistance of proper transformations of nonlinearities. An efficient and validated numerical algorithm is implemented as a computational technique where Mathematica 11.0 environment, a programming tool, is developed for fluid dynamics. The convergence standard had also been recognized for the precision of the relevant parameters by using boundary postulates. The impact of embedded physical quantities of practical interest is examined and offered via the plotted graphs. In addition, the impression of system parameters on drag force, heat, and mass flow coefficient with three-dimensional graphs is also debated.