The time-dependent flow past an impulsively started vertical infinite isothermal plate in a viscous electrically conducting natural convective incompressible nano-fluid is considered in this article by taking into account the effects of heat absorption, heat generation, and radiation. An analytical study is performed to obtain exact solutions for water-based nanofluid TiO₂. The dimensionless governing equations for this investigation are solved analytically by using the small perturbation technique. The effects of various physical parameters on velocity and temperature fields are presented graphically. With the aid of these, the expression for the skin friction and Nusselt number profiles was done with the help of tables.