The major focus of this work is on the flow of a time-dependent biviscosity hybrid nanofluid boundary layer across a rotational permeable disk with the consideration of the applied external effects of magnetic field and thermal radiation. This study also investigates the transfer of heat flow both subjectively and quantitatively. In the classic Von Karman issue, nanofluids comprising nanoparticle volume fractions of Ag-MgO/60% water and 40% ethylene glycol nanofluid are considered instead of Newtonian regular fluids. The governing equations are transformed into a system of nonlinear ordinary differential equations using Von Karman transformations. The equation for the generation of entropy is calculated as a function of velocity and temperature gradient. This equation has been made non-dimensional by adding geometric and physical flow field-dependent parameters. The velocity profiles in the radial, tangential, and axial directions, as well as the axial pressure gradient, nanoparticle temperature distribution, local skin friction, Nusselt number, and Bejan number, are calculated by using MATLAB bvp4c. The concept of multivariate analysis is executed in the numerical results of the Nusselt number, which is helpful to indemnify the behavior of the rate of heat transfer in the disk. Additionally, a rotation parameter is generated by the spinning phenomena, which regulates the disk's movement. Increasing the rotation of the disk causes fluid velocity to accelerate in both the radial and cross-radial directions, while contrasting phenomena can be noticed in the axial velocity of the flow. Entropy generation in a system is measured by the Bejan number. It has a significant infl