Keeping in mind the stress relaxation tendency of many viscoelastic multi-phase flows (e.g., polymer solution flows and transport phenomena of red cell suspensions within blood media), the present research investigation intends principally to develop a realistic model for revealing properly the aspects of reacting-radiating Maxwell nanofluids during their laminar boundary layer flows in the steady regime over a horizontal impermeable surface under a transversal magnetic influence. For this purpose, the principal leading differential formulation is derived theoretically by linking Wakif’s-Buongiorno approach with Maxwell’s model. By invoking fundamentally the general boundary layer assumptions and the passive control strategy for the nanoparticles, the governing PDEs’ formulation is simplified accordingly and then stated properly for the case of the convective heating condition at the impermeable bi-stretching surface. By executing a feasible non-dimensionalization technique, the monitoring ODEs’ system is achieved successfully, whose solutions are presented precisely in different illustrative scenarios using Richardson’s extrapolation method. After carrying out successfully several validating tests, it is demonstrated that the weakly viscoelastic feature has generally a slight delaying effect on the nanofluid motion. This dynamical weakening can be reinforced more with the generation of thermal energy by intensifying the external magnetic field source. Additionally, these physical factors show an intensifying influence on the surface drag forces. However, a dropping impression is seen for the local heat transfer at the contact surface. Contrary to the broadening impact of the radiative heat transfer as well as the convective heating and thermophoresis mechanisms on the thermal and mass boundary layer regions, it is witnessed that the first-order chemical reaction mechanism and Brownian’s motion exhibit a shrinking impact on the mass boundary layer region.
