Due to effective thermal conductivity, better stability and entropy optimization, greater energy efficiency, hybrid nanofluids are desirable in many industrial applications such as heat exchangers, electronic cooling, biomedicine, water treatment of plants, industrial thermal management, and material processing. The present model explores the transient magnetohydrodynamic (MHD) gravity driven flow of a water-based hybrid nanofluid \(Cu-Al_2O_3\) past an exponentially accelerated vertical porous plate with entropy generation. Moreover, the viscous dissipation, Joule heating, cross-diffusion and porous dissipation effects in the energy equation are incorporated for detailed analysis of the model. The developed coupled nonlinear PDEs are converted into dimensionless form by using some appropriate transformations and then resolved numerically via Finite Difference Method (FDM) with MATLAB solver fsolve. Graphical representations are used to study the impact of key parameters on hybrid nanofluid flow. The engineering quantities are discussed via tabular representations. A comparative analysis of hybrid nanofluid and nanofluid is performed for the profiles of velocity, temperature, species concentration, entropy generation, Bejan number and various engineering quantities via graphical and tabular representations. Code validation was performed by comparing the present results with the earlier findings by Rath and Nayak (in Heat Transf 52(1):467–494, 2023; https://doi.org/10.1002/htj.22703), exhibiting an excellent agreement. The analysis shows that the mass transport rate is depressed by Sr, whereas it is enhanced with Du. An increased volume fraction of copper nanoparticles ( \(\varphi _{2}\) ) in base fluid (water) enhances the thermal conductivity and viscous drag force of the fluid, enabling efficient utilization of cooling of electronic devices, industrial processes, and biomedical systems. Br and t accelerate the entropy generation rate which indicates more irreversibility and greater energy dissipation within the flow domain. The heat and mass transport rates for \(\varphi _{2}\) and Sr are amplified in an average of 4.45% and 12.08%, respectively, from nanofluid to hybrid nanofluid. The current analysis reveals higher heat, mass transfer, and entropy generation rates of hybrid nanofluid than nanofluid.
