Current paper focusses on the mathematical simulation of thermo-fluidic unsteady flow in a magnetohydrodynamic (MHD) Couette channel containing novel (ZnO–Al2 O3)-water hybrid nanofluid (HNF). The nanoparticles of zinc oxide(ZnO) and aluminium oxide(Al2O3) are supplemented to basefluid water in 1:1 ratio. The bottom wall of channel kept stationary and stretchable, while the top is set in uniform motion with convective cooling. A uniform magnetic field appealed normally to lower plate. The governed nonlinear partial differential equations(PDE) are integrated employing finite difference method (FDM). A comparison of effect of hybrid nanofluid versus nanofluid (NF) is performed. The effects of non-dimensional quantities namely, nanoparticle volume fraction(NVF), magnetic field, stretching parameter, Biot number and Eckert number are reported graphically. The results demonstrate that (ZnO+ Al2O3)-water HNF shows significant impact over ZnO–water NF on velocity and temperature in the Couette channel.