Analytical analysis has been done for the unsteady, natural convective flow of an impulsive water-based nanofluid consisting of nanoparticles Cu, Al2O3, and TiO2 through a vertical plate under a uniform magnetic field when the magnetic field fixed to the plate (K=1) or to the fluid (K=0). For this model, we considered a radiative heat flux as well as pressure gradient defined by the Boussinesq’s approximation in the energy equation for a non-scattering medium. The Governing PDE’s are derived and transformed to dimensionless form and then obtained a closed-form solution using Laplace transform procedure without any limitation. The fluid properties have been discussed for a moving and the static plate through graphs for different water-based nanoparticles and also dimensionless parameters such as volume fraction parameter(Ø), radiation parameter(Nr), and magnetic parameter(M^2), Grashof number(Gr) etc. of the physical model.