The present article aims to examine the thermal performance and the sensitivity analysis of a GO−TiO2" role="presentation"> GO−TiO2 G O − T i O 2 /water hybrid nanofluid in the presence of different nanoparticle shapes along with heat absorption and thermal radiation effects over a wedge geometry. Analyzing the effects of heat generation and radiation effects is one of the key studies conducted by researchers in various nanofluid flows over some required geometries. However, a combined study of these effects has yet to be studied over a moving wedge, and that combination defines the novelty of the work. Similarity transformations are implemented to the governing equations to obtain the final set of nondimensional equations, which are solved using the bvp4c code in MATLAB. The results obtained were in close agreement with the published results. The Nusselt number decreased with an increase in the heat source parameter Q" role="presentation"> (Q) Q , and it increased with an increasing Hartree pressure gradient β" role="presentation"> (β) β and thermal radiation parameter Rd" role="presentation"> (Rd) R d . The sensitivity is statistically analyzed for the variations in radiation effect, heat source, and pressure gradient parameters on the Nusselt number. The high values for R2=99.99%" role="presentation"> R2=99.99% R 2 = 99.99 % and Adj R2=99.96%" role="presentation"> Adj R2=99.96% A d j   R 2 = 99.96 % validate the ANOVA results obtained using a Box–Behnken design (BBD) model in the response surface methodology (RSM) with 14 degrees of freedom. The input parameters Rd" role="presentation"> Rd R d and β" role="presentation"> β β show positive sensitivity, while Q" role="presentation"> Q Q shows negative sensitivity toward the skin friction. The Nusselt number proves to be most sensitive toward the pressure gradient parameter. TiO2, graphene (Gr), and the derivative forms of graphene, are gaining much importance due to their wide applications in the oil and petroleum industries. Thus, this study contributes to lubrication purposes, emulsion stabilizers, oxalic acid removal, anti-corrosive properties, etc.