Three-dimensional (3D) flow of non-Newtonian liquid is studied in this analysis. Also, this paper is mainly focused on an incompressible magnetic liquid with low Curie temperature and moderate saturation magnetization. An extremely long, straight wire delivering an electric current generates a magnetic field that affects the fluid. Thermal radiation and chemical reaction impacts are considered to study heat and mass transport characteristics. Appropriate transformations are used to reduce pertinent flow expressions into ordinary differential equations (ODEs). The obtained ODEs are solved by means of a numerical method (Runge–Kutta–Fehlberg's fourth–fifth order method (RKF-45) algorithm with shooting technique). The effect of pertinent parameters like chemical reaction rate parameter (between 0.1 and 1.5), ferromagnetic interaction parameter (between 0.01 and 1.0), viscous dissipation parameter (between 0.1 and 1.0), radiation parameter (between 0.1 and 1.0), Deborah number (between 0.1 and 1.0) and Schmidt number (between 1.0 and 2.0) on Maxwell liquid flow, heat and mass transport is illustrated via graphs. Furthermore, from the analysis, the heat transfer rate increases about 30%–40% for the increasing values of the ferromagnetic interaction parameter. Also, the mass transfer rate increases about 4%–6% for the increasing values of the chemical reaction rate parameter.