The magnetohydrodynamic flow of a water‐based Al 2 O 3 − normalCu hybrid nanoliquid through a vertical microchannel has been investigated in the presence of collective effects, such as volume fraction of nanoparticle, suction/injection, magnetic field, temperature‐dependent heat source, hydrodynamic slip, and convective boundary conditions. The current mathematical formulations have been worked out numerically by using the fourth‐ and fifth‐order Runge–Kutta–Fehlberg scheme. The physical aspects of variation in velocity, temperature, entropy generation, and Bejan number with considered governing parameters have been discussed via corresponding graphs. The obtained numerical results demonstrated that radiation parameter and nanoparticle volume fraction reduce the thermal energy of the hybrid nanofluid. Moreover, entropy generation diminishes with the Hartmann number and permeability parameter, whereas it enhances with the Grashof number and Biot number.