The MHD (magnetohydrodynamic) fourth-grade nanofluid flow consisting of aluminum alloys (Ti6Al4V) nanoparticles over a Riga plate is studied. The study of fourth-grade fluids (FGFs) improves the capacity to design systems and procedures for a variety of industries, ultimately promoting performance and the durability of the product. Ti6Al4V nanoparticles (NPs) are dissolved in water to prepare the nanofluid. The FGF flow has been analyzed under the impacts of Arrhenius activation energy, heat source/sink, and chemical reaction. The modeled equations (momentum, energy, and fluid concentration equations) are reformed into dimension-free form through similarity conversion. The transform set of ordinary differential equations (ODEs) is numerically solved by using the parametric continuation method (PCM). For accuracy of the results, the outcomes are compared to the published work. The error between the present results and the published study is -0.00028% at M = 5.0 (magnetic parameter), which ensures that the proposed methodology and model are accurate and reliable. From the graphic results, it has been noticed that the velocity field improves with the influence of fourth-grade fluid parameter, cross-viscous coefficient, and third-grade fluid parameter. The thermal profile of NF boosts with the variation in heat source parameters and the rising number of Ti6Al4V-NPs.