In this article, two-dimensional unsteady incompressible viscous nanofluids magneto-hydrodynamic (MHD) flow among two parallel plates extended infinitely is investigated. The equations that results from the use of similarity transformations for non-linear partial differential system are solved by the new algorithm. The important key to this construct is the derivatives that appear as coefficients in the power series. The effects of apparent physical parameters on velocity concentration and temperature distributions are described using a schematic diagram and interpreted physically. The effects of apparent physical parameters on concentration, temperature, and velocity distributions are described by graphs. For the flow of nanofluids, the results indicate that it is inversely proportional between the rate of mass and heat transfer with nanoparticle size fraction and magnetic parameter. Over time, squeeze number and schmidt number lead to increase the rate of mass transfer. This problem is dissolved numerically by using the Runge-Kutta scheme of fourth-order (RK4S) .