The Riga plate is arrangement of electrodes and permanent magnets allows for efficient regulation of fluid flow. The Riga surface leverages Lorentz forces to control boundary layers (BL) and improve cooling purposes for effective electromagnetic flow control in nuclear and aeronautical engineering systems. Furthermore, by utilizing synergistic interactions of different nanoparticles, heat transfer rat can be optimized in industrial setup. The primary focus of this work is to investigate the unsteady BL flow of water-based tri-hybrid nanolfuid (tri-HNF) flow over a Riga plate senor under the influence of activation energy, cross-diffusion, and convective heating. Three different nanoparticles \(A{l}_{2}{O}_{3}\) , \(CuO\) and \(Ti{O}_{2}\) are dispersed in a pure water. The model equations are constructed using BL theory and transformed into ordinary differential equations using an appropriate similarity rule. The Runge–Kutta fourth-order (RK-4) method, along with shooting approach, is used to address the problem numerically. The skin friction and Nusselt and Sherwood numbers are assessed using optimized statistical Response Surface Methodology (RSM) technique. The Gharesim model viscosity and Hamilton-Crosser thermal conductivity models are deployed in the governing model. A mathematical model is designed and developed using RSM to obtain an optimal skin friction, heat and mass transfer rate. Sensitivity analysis (SA) is performed to investigate the response of input on these coefficients. SA shows that in narrow BL, the skin friction rises with nanoparticle concentration. Velocity of tri-HNF boost with the Hartman number and the electrode-magnet distance parameter. The Soret number, and activation energy increases the concentration profile. Higher Nusselt number indicates improved heat transfer with increased nanoparticle load. Activation energy uplift the mass transfer rates, but dwindle with nanoparticle concentration.
