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Numerical investigation of the three-dimensional flow and heat transfer of 36 nm Al 2 O 3 –H 2 O nanoliquid over a wedge surface is carried out by utilizing the modified Buongiorno model (MBM). The boundary layer approximation is assumed to be valid. The thermophysical properties of Al 2 O 3 –H 2 O nanoliquid are deliberated in the study by modeling them through the use of correlations based on experimental data. The thermal boundary layer equation comprises the Brownian motion and thermo-migration effects caused by nanoparticles. Zero mass flux boundary condition is also accounted. Optimization of the heat transfer rate of nanoliquid is made using the Response surface methodology (RSM). Two stream functions are used to derive the similarity transformations and they are employed to arrive nonlinear ordinary differential system from the governing partial differential system, and then the subsequent nonlinear problem is treated numerically using the Finite Element Method (FEM). The heat flow features are scrutinized using two-dimensional, surface, and streamline plots. The results of flow due to a moving wedge in the same direction of free stream velocity are compared with those of a moving wedge in the opposite direction of free stream velocity. The thermal layer and nanoparticles volume fraction layers are enlarged due to the chaotic movement of nanoparticles. The thermophoresis mechanism improves the thermal layer at the wedge surface. The high level of pressure gradient factor, high level of shear-to-strain rate and low level of Lewis number, were found to be the optimal operating condition that would maximize the heat transfer rate. [ABSTRACT FROM AUTHOR]