Entropy generation and MHD flow characteristics of unsteady Williamson fluid toward a stagnation point over a vertical Riga plate

This study presents a mathematical model to explore two-dimensional, time-dependent fluid flow towards a stagnation point over a Riga plate, under the influence of magnetohydrodynamics (MHD), activation energy, and a higher-order chemical reaction. The surface of the Riga plate is lined with magnets and electrodes, arranged in a structured manner. The research investigates the effects of radiation and Joule heating on fluid motion and includes an entropy generation analysis based on the second law of thermodynamics. The partial differential equations (PDEs) that govern the physical system are reduced to ordinary differential equations (ODEs) via similarity variables, and solved using both the shooting method and the bvp4c algorithm. Results indicate that the unsteadiness parameter increases skin friction by 5.53 %, while the heat source parameter reduces heat transfer by up to 33.4 %. Entropy generation is found to rise with increasing Brinkman number and concentration difference, whereas higher temperature differences lower entropy production. The combined effects of Lorentz force, exponential chemical reaction, internal heat generation, and suction/injection within an unsteady Riga plate configuration have not been explored previously. Furthermore, the inclusion of irreversibility analysis enhances the novelty and provides deeper insight into energy dissipation mechanisms and system efficiency, offering valuable guidance for designing advanced MHD-based thermal control and energy systems. These numerical results are well aligned with existing literature, reinforcing the reliability of the analysis and highlighting its significance for energy-efficient thermal system design.