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In this study, numerical treatment is performed to study the dynamical analysis of hydro-magnetic nanofluids problem for heat and mass transfer of an unsteady nanofluid flow between parallel plates by exploiting the strength of Adams and explicit Runge-Kutta method. Original PDEs of the model are transformed to equivalent system of ODEs by utilizing the similarity transformations. Numerical and graphical illustrations prove the validity of the proposed methods for number of scenarios of the system by considering different physical quantities such as the squeeze number, Nusselt number, Schmidt number, Hartmann number, thermophoretic parameter, Brownian motion parameter, and Eckert number. Keywords: Fluid dynamics, Nanotechnology, Thermophoresis, Numerical computing, Magnetohydrodynamics