<p>The implications of this study are profoundly significant across an extensive array of technological and engineering applications, ranging from aerospace systems and jet propulsion mechanisms to space dynamics, automotive engines, and myriad advanced mechanical systems. The current study is related to the Arrhenius activation energy of the magnetohydrodynamic two-phase nanofluid model in the occurrence of non-uniform heat sink/source, heat dissipation, and radiative heat on a stretching exponentially permeable surface geometry. A partial derivative mathematical model is developed and changed into a set of ordinary derivative equations using similarity transformation quantities. This is solved semi-analytically utilizing a modified partitioning weighted residual scheme using the MAPLE package. The impact of substantial constraints on temperature, flow rate, and concentration is displayed in plots. It is noticed that boosting magnetic and porosity terms leads to a reduction in flow velocity, signifying a retarding tendency. Thermal profiles increase as the thermophoresis parameter boosts because thermophoretic forces move particles from regions hotter to cooler. On studying solutal profiles, one can observe the phenomenon of Brownian assisted in decreased particle concentration. Heat transfer rate significantly increases with an elevation of the radiation parameter. The mass transfer rate was observed to increase by improving the energy activation term. Furthermore, the skin friction coefficient was able to decline by improving porosity and reduction in heat transfer rate with elevation of radiation parameter and mass transfer rates with elevation of energy activation term. The Buongiorno model of nanofluid has been effectively utilized to examine how nanoparticle concentration affects the diffusivity of nanofluids.</p>