Finite element analysis of copper nanoparticles in Boger fluid: Effects of dynamic inter-particle spacing, nanolayer thermal conductivity, nanoparticles diameter, and thermal radiation over a stretching sheet

Abstract This study explores the magnetohydrodynamic (MHD) boundary layer flow of a water-based Boger nanofluid over a stretching sheet, with particular focus on the influences of nanoparticle diameter, nanolayer effects, and thermal radiation. The primary aim is to examine how variations in nanoparticle size and nanolayer thickness affect the hydrothermal behavior of the nanofluid. The model also incorporates the contributions of viscous dissipation and Joule heating within the heat transfer equation. The governing momentum and energy equations are converted into dimensionless partial differential equations (PDEs) using appropriate similarity variables and are numerically solved using the finite element method (FEM) implemented in MATLAB. Extensive validation of this method confirms its reliability and accuracy in numerical solutions. The findings reveal that increasing the diameter of copper nanoparticles significantly enhances the velocity profile, with a more pronounced effect observed at wider inter-particle spacings. A higher solvent volume fraction leads to decreased velocity and temperature distributions, while a greater relaxation time ratio improves velocity and temperature profiles due to the increased elastic response of the fluid. Moreover, enhancements in the magnetic parameter, thermal radiation, and Eckert number lead to an elevation in temperature profiles. Furthermore, higher nanolayer thickness reduces the temperature profile, whereas particle radius yields the opposite outcome.