The purpose of current communication is to analyze the characteristics of static–moving wedge for unsteady 2D Falkner–Skan flow of cross fluid in the presence of nonlinear thermal radiation. Furthermore, revised Buongiorno’s relation of nanomaterials is implemented for mathematical modeling of Falkner–Skan flow of cross fluid. Nanofluid characteristics for Brownian movement and thermophoresis are deliberated in this communication. In the considered model, we have utilized the aspects of constructive–destructive phenomenon to elaborate the mechanism of mass transfer. The transformed nonlinear system of ODEs are computed numerically by implementing bvp4c scheme. Physics related to the assumed flow model is described graphically. Furthermore, the graphical analysis revealed that the considered physical model has a significant impact on the physical parameter involved in this problem. It is anticipated from graphical data that declining conduct is observed with the impact of chemical reaction parameter temperature profile for n = 0.5, for static–moving wedge.