This research aims to establish the MHD radiating convective nanofluid flow properties with the viscous dissipation across an exponentially accelerating vertical plate. As the plate accelerates, its temperature progressively increases. There are two separate types of water-based nanofluids that include copper ([Formula: see text]) and titanium dioxide ([Formula: see text]) nanoparticles, respectively. The most crucial aspect of this investigation is finding a closed-form solution to a nonlinear coupled partial differential equations scheme. Galerkin finite element method (G-FEM) is used to figure out the initial managing equations. Utilizing graphs, the effect of the flow phenomenon's contributing variables as well as the influence of other factors is determined and depicted. In the part dedicated to the findings and discussion, the properties of these emergent parameters are described in more depth. Nonetheless, the thermal radiation and heat sink factors increase the thermal profile. In addition, the greater density of the copper nanoparticles cause the nanoparticle volume fraction to lessen the velocity delineation.