Exploring the dynamics of magnetized Casson nanofluid flow across an extended porous surface with non-uniform heat generation

This analysis addresses the impacts of variable thermal conductivity on the magnetic hydrodynamic motion of Casson nanofluid via an infinite porous sheet with non-uniform heat sources. Stretching sheets and convective circumstances are also considered in the initial boundary conditions. The combination of ethylene glycol and oxide nanoparticles offers a versatile platform for various industrial, technological, and biomedical applications. It provides enhanced properties and functionalities compared to conventional fluids or nanoparticle dispersions. Thus, we considered two nanoparticles \({\text{CuO}}\,\,{\text{and}}\,\,{\text{TiO}}_{2}\) $\text{CuO}\text{and}{\text{TiO}}_2$ with the base fluid ethylene glycol in nanofluid flow. Governing partial equations are renewed in ordinary differential form with apposite similarity renovation. The 4th-order R-K method with shooting approximation is adopted to get the approximate results of reduced ordinary equations. Plotting graphs discuss the consequences of entirely unknown parameters on fluid motion and temperature. Also, the skin drag force and Nusselt number are deliberated in tabular form for different physical numbers. For two different nanoparticles, it is seen that \({\text{CuO}}\) $\text{CuO}$ gives better temperature and rate of heat transfer compared to \({\text{TiO}}_{2}\) ${\text{TiO}}_2$ . The investigation reveals that the magnetic parameter has a normal behavior in the velocity profile due to the resistive Lorentz force. The findings indicate a direct connection between the nanoparticles' shape factor and the energy profile.