Four-stage Lobatto analysis on 3D magneto-hydrodynamic radiative non-newtonian nanofluid flow and heat transportation over a stretchable surface under Brownian motion and thermophorsis impact.

Viscous dissipation and thermal radiation are essential in governing the dynamics of boundary layer flow, particularly in high-temperature engineering systems such as gas turbines, combustion engines, and industrial furnaces. Thermal radiation emerges as a primary factor of heat transfer under such conditions, while viscous dissipation contributes to the transformation of kinetic energy into thermal energy through internal frictional forces within the fluid. The present study investigates the three dimensional magneto-hydrodynamic (MHD) flow of a radiative Eyring-Powell nanofluid towards a stretchable, porous surface. The governing equations, initially formulated as partial differential equations (PDEs), are reduced to a set of coupled ordinary differential equations (ODEs) through similarity transformations. These transformed equations are numerically solved using MATLAB bvp5c solver. A detailed parametric analysis is performed to examine the impact of key dimensionless quantities, including slip parameter, Lewis number, Eckert number, thermophoresis parameter, magnetic field strength and Brownian motion parameter, on velocity profile, temperature profile and concentration distributions. The analysis reveals that the fluid velocity decreases with an increase in the magnetic field strength, whereas it exhibits an increasing trend with higher values of the Eyring-Powell fluid parameter. This paper convers the following key points:•Modeled the dynamical flow equation for hybrid Eyring-Powell nanofluid.•Analyzed the magnetic force impact on the velocity curve.•Graphical interpretations are presented, highlighting the effects of physical parameters.