<p>The steady non-Darcian magnetohydrodynamic flow of a hybrid copper–aluminum oxide–water nanofluid over a wedge and a cone with an irregular heat source/sink was investigated with taking into account the influence of the nonlinear radiation, the Joule heat, the viscous dissipation, the Arrhenius activation, and the Soret and Dufour effects on this flow. The modified governing equations were resolved with the use of the bvp4c tool. It was established that the boundary momentum, temperature, and concentration layers of the fluid flow over the wedge and the cone are nonuniform. It is shown that, when the volume fraction of nanoparticles in the base fluid increases, the velocity of the fluid flow decreases, while its temperature increases, and the skin frictions of the wedge and the cone increase by 6.21 and 5.72%, respectively, when copper and aluminum oxide nanoparticles are added in amount of 1% to the base fluid.</p>