<p>Two-phase Maxwell nanofluid flow focusing on the impact of Brownian and thermophoresis exhibits several practical applications due to their viscoelastic properties. More or less, these include enhancing heat transfer in electronic cooling systems, improving the efficiency of chemical reactors, optimizing thermal energy storage performance, etc. Focusing on the behavior mentioned above, the present study aims to investigate the magnetohydrodynamic radiative Maxwell nanofluid past an extending permeable surface in association with the role of activation energy. The property of the Maxwell nanofluid is characterized by its unique viscoelastic behavior. Further, the transport phenomena are enriching for the collective role of slip velocity and heat flux surface conditions. The cross-diffusion processes involving the Brownian and thermophoresis with the activation energy play a crucial role in chemical reactions and energy conversion processes. The advanced model equipped with dimensional quantities is transformed to dimensionless by supper-imposing similarity rules. Moreover, the combined effects of these factors are executed employing the Adomian decomposition method, a powerful semi-analytical technique. The physical characteristics of the proposed factors with their numerical results are obtained and depicted graphically with validation of the current and previous in particular cases. However, the important findings of the study are; enhanced elasticity for the appearance of the Deborah number attenuates the fluid velocity acting as a controlling parameter whereas the Brownian and thermophoresis both favor in enhancing the fluid temperature distribution.</p>