This work explores the two-dimensional time-dependent hydromagnetic flow of a hybrid nanofluid across a permeablestretching/shrinking sheet. Moreover, the current study includes the combined effect of heat generation, velocity slip, thermalradiations, and convective conditions. Using the similarity transformations, the governing nonlinear PDEs have been converted toordinary differential equations (ODEs). Finally, the MATLAB solver bvp4c has been used to get the numerical solutions. The variousgraphical results of temperature, heat transport, velocity, and friction drag have been plotted for the diverse values of parametersassociated with the current effects of the problem. These outcomes state that the higher values of nanoparticles concentration causeto reduce the velocity and enhance the fluid temperature. The rising values of nanoparticles concentration, slip parameter,unsteadiness parameter, and the inclination angle of magnetic field intensify the skin friction, however, it decreases with the growth ofHartmann and Darcy number. Additionally, the rate of heat transport intensifies with the rising values of concentration and alignedmagnetic field angle, although the growth of the Hartmann number and slip parameter reduces the rate of heat transport. Moreover,the skin friction and the local Nusselt number respectively decline and enhances for the increasing values of the stretching parameter.