Significance of sinusoidal wall temperature, natural convection, nanoparticle diameter, and nanolayer in water flow subject to a vertical plate via Finite element analysis

This present exploration aims to investigate the significance of the roles played by nanoparticles, diameter variations, nanolayer, sinusoidal surface temperature and natural convection on the boundary layer MHD flow of fluid across vertical plate. Our aim is to scrutinize the numerical outputs of the developed problem and explore how the interplay of nanolayer mechanism and nanoparticles diameter effects the dynamics of hydrothermal pattern along with flow. The governing equations of energy and momentum are converted into dimensionless form by using appropriate transformation. By using Finite element method (FEM) in MATLAB, the solution of final non-linear equations is obtained. This method has been extensively verified to certify the accuracy and reliability in numerical outcomes. Heat transfer augments with higher values of nanoparticle concentration, while shear stress has opposite trend. The temperature distribution profile has significant reducing behavior against greater values of nano particles diameter, while nanolayer thickness yields opposite outcomes. The amplifies in the amplitude of oscillation of the surface temperature increases heat transfer rate and shear stress. To ensure the validity of present outcomes, a comprehensive comparison with existing outcomes is conducted and found an excellent relationship between them. The findings of this study can contribute to enhancing or improving the efficiency of nanofluids, and the insights gained may support the advancement of thermal management in various modern techniques.