•The nanoliquid flow over a wedge is modeled using the modified buongiorno model.•The heat transfer rate is optimized using response surface methodology (RSM).•Sensitivity of the heat transfer rate towards pertinent parameters is evaluated.•Exponential and thermal-based heat sources are scrutinized in the model.•The thermo-migration and haphazard motion of nanoparticles is examined. Sensitivity analysis of the heat transfer rate in the flow of the hybrid nanoliquid C2H6O2−H2O (base liquid) +MoS2−Ag (nanoparticles) over a wedge using the Response Surface Methodology (RSM) is carried out. The nanomaterial is modeled using the modified Buongiorno nanofluid model (MBNM) that considers the major slip mechanisms and the effective properties of the hybrid nanoliquid. Two distinct heat sources- linear thermal heat source and an exponential space-dependent heat source are taken into account. The governing nonlinear two-point boundary-layer flow problem is treated numerically. The effects of pertinent parameters on the flow fields in the boundary layer region are represented graphically with suitable physical interpretations. The exponential heat source and slip mechanisms are used to study the sensitivities of the heat transfer rate. Both heat source mechanisms lead to an improvement in the temperature profile, in which the effect of the exponential space-related heat source is predominant. The Brownian motion parameter was found to be the most sensitive to the heat transfer rate.