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Suspending particles of tiny solid in a fluid used to transport energy can enhance its thermal conductivity and heat transport properties. Our main goal of this examination is to study the radiative unsteady two-dimensional (2D) flow on a continuously diminishing, horizontal sheet. with suction for the hybrid water-based nanofluid and an aligned field of magnetic, including the combined suction, magnetic, and velocity slip conditions effect. The Tiwari & Das model of nanofluid equations is used, which takes into consideration the solid volume percentage. Equations of similarity are derived by employing the transformations of similarity, and the associated equations have been simplified numerically by employing the bvp4c method in MATLAB software for a variety of values of the nanoparticle volume fraction, the unsteadiness, and the wall mass suction in water. It is discovered that, within the given the unsteadiness parameter range, two solutions exist. Moreover, it is found that the fluid velocity slows down in 1st solution as volume fraction of copper nanoparticles rises but speeds up in the second solution at first before slowing down again. Using a temporal stability analysis, it is found that only one of the dual branches is stable over the long run, while the other is unstable.