Finite difference simulation for numerical investigation of Powell–Eyring hybrid nanofluid with thermal radiation and viscous dissipation effects

This study conducts a comprehensive numerical investigation of Powell–Eyring hybrid nanofluids (PE-HNF) convective flow with linear thermal radiation and viscous dissipation over a permeable and non-uniformly stretched flat plate. The hybrid nanofluid is represented by dispersing copper (Cu) and aluminum oxide (Al 2 O 3 ) nanoparticles in a water-based fluid. The governing boundary layer equations are transformed to an analogous non-linear system of ordinary differential equations through a similarity transformation. We discretize the equations and then solve them numerically using the MATLAB finite difference method, the similarity variable is handled with forward differencing and the spatial coordinates are handled with central differencing. The study presents the physical effects for 6 scenarios with changing stretching parameter ( M ), material parameter ( Z ), Eckert number ( Ec ), Prandtl number ( Pr ) and radiation parameter ( Nr ). We find the velocity declines as surface stretching increases while non-Newtonian effects cause a greater fluid motion. Furthermore, there is a relatively higher study sensitivity of temperature profiles to viscous heating, resistance due to thermal diffusion, and absorption of radiative heat. For thermal transport performance, PE-HNF outperforms base fluid and mono-nanofluids. We represented the study with 2D/3D bar plots and heat maps. This will demonstrate how well we are able to capture complex thermo-fluid flow behaviors models. To assist in thermal expansion of heat transfer performance, we proved the low cost and efficient results of using PE-HNF. We also proved that our finite difference method is a reliable program as well. This article presents a unique and potentially effective combination of hybrid nanoparticles, non-Newtonian rheology, entropy modelling, and FDM simulation, representing a new avenue for thermal system design based on the utilization of developing nanofluids. The hybrid nanofluid has introduced demonstrated thermal performance improvements in comparison with base and mono-nanofluids. The format of the study included the mathematical framework, the numerical framework using finite difference implementation, the graphical results and review of comparisons across six physical situations, and then discussion of practical applications and conclusions.