Computational analysis of nanoparticles and waste discharge concentration past a rotating sphere with Lorentz forces

As industries rely more and more on magnetohydrodynamic (MHD) systems for different uses in power, production, and management of the environment, it becomes essential to optimize these operations. The study seeks to improve the effectiveness and productivity of cooling structures, chemical reaction reactors, and contaminant control methods by investigating these intricate interconnections. Because of this, the work scrutinizes the endothermic/exothermic (EN/EX) chemical processes, convective boundary conditions, and pollutant concentration impacts on MHD nanofluid circulation around a rotating sphere. The governing equations based on the above assumptions are reduced into a system of ordinary differential equations and solved numerically with Runge–Kutta Fehlberg’s fourth- and fifth- order schemes. The obtained numerical outcomes from the numerical scheme are presented with the aid of graphs, and the results show that the rate of mass transfer decreases with an increase in the external pollutant local source and solid volume percentage. For changes in the values of the activation energy parameter and solid fraction, the rate of thermal dispersion drops for the EN case and upsurges for the EX case. The concentration profile shows increment with the addition of the external pollutant source variation parameter and local pollutant external source parameter. The outcomes of the present work can be helpful in cooling equipment, developing advanced methods for controlling pollution, environmental management, MHD generators, and various industrial contexts.