<p>In the various manufacturing processes as well as field of engineering, the flow of non-Newtonian nanofluid has tremendous effect because of its physical significance. Particularly, in recent scenario, the implementation of carbon nanotubes (CNT) presents its greatest impact in energy storage, chemical sensors, and structural composite materials. The ongoing analysis delves into the movement of a methanol-based SWCNT/MWCNT Maxwell nanofluid over an expanding sheet with a permeable surface. This work assesses the outcomes of thermal radiation and a magnetic dipole, focusing on the interaction of Darcy-Forchheimer drag force and its impact on inertial drag behavior. The convective condition in thermal boundary condition serves as novel approach for the enhanced thermal performance attributes. The specific transformation rules are adopted for the proposed designed model to get its standard non-dimensional form. Further, a shooting-based Runge–Kutta technique is employed for the solution of the transformed system of equations using MATLAB software. The major conclusions of the research demonstrate that that fluid speed declines as the ferromagnetic parameter gradually rises, while temperature field gradually intensifies with increasing Biot number and thermal radiation parameter. Furthermore, when the Biot number and thermal radiation parameter rise, so does the rate of heat transmission. The surface drag force falls with the augmentation in the viscous dissipation parameter and rises with greater solid volume fraction values.</p>