The present work reports a study two-dimensional (2D) Blasius and Sakiadis an unsteady magnetohydrodynamic (MHD) radiated Williamson flow with variable conductivity of a chemically reacting fluid is considered. An approximate transformation was developed to transform PDEs into nonlinear ODEs. To current numerical calculation shooting technique is implemented. The computational results of the Blasius and Sakiadis flow on concentration, temperature and velocity distributions for some physical quantities are presented graphically and in tabular form. © 2021, Springer Nature Singapore Pte Ltd.