Engine oil has a vast application sector as it is the most essential working lubricant for industrial machineries, engines of vehicles, and aircraft combustion processing. In order to find out more effective engine oil-based hybrid nanofluid in terms of heat transfer capabilities and to minimize the production cost, the novelty of our present study focused on three different combinations of nanoparticles (TiO2+CuO, MOS2+ZnO, and Al2O3+Cu) that are dispersed in Engine oil (EO). The fundamental aim is to examine the thermal and flow fluctuation of a convective dissipative engine oil-based hybrid nano liquid to understand the physical quantities and thermal properties over a vertically moving plate by employing the Galerkin Method (GM). Similarity variables are initiated to permute the set of governing equations into the nonlinear coupled ordinary differential equations along with Bc’s, which are solved using both numerical (Maple) and analytical method (GM). This MAPLE software uses the fourth-fifth-order Runge-Kutta-Fehlberg (RFK45) technique as a default function to solve numerically boundary value problems. Validation for this study has been conducted by comparison with previously published results. The results of the present study are given for both opposing and assisting flow with the distribution of fluid motion and temperature profiles, wall shear stress, and rate of heat transfer. The assisting flow has great significance on the flow velocity and temperature with increasing mixed convection parameters. The Brinkmann number and Prandtl number have a larger flow near the wall in temperature distribution and then increase and decrease respectively satisfying the asymptotic boundary conditions. Our results also reveal that the TiO2+CuO/Engine oil has a significant augment in terms of heat transfer than that of MoS2+ZnO/Engine oil and Al2O3+Cu/Engine oil.