The present paper focuses on the examination of the effect of Brownian motion and thermophoresis phenomenon and Lewis number on MHD nanofluid flow along with the heat transfer between two parallel plates. Utilizing a suitable transformation for the velocity, temperature and concentration, the basic governing equations of the flow, heat and mass transfer were reduced to a set of ordinary differential equations. After the governing equation is derived; various analytical methods such as Homotopy Perturbation Method (HPM), Collocation Method (CM) and Finite Element Method (FEM) are applied to deal with the problem. The obtained Results revealed that Collocation Method (CM) has an excellent agreement with Finite Element numerical method, so it can be a proper analytical method for solving the problem. Then the influence of the following parameters is investigated: Brownian motion parameter (Nb), thermophoresis parameter (Nt), Squeeze number (S), Hartmann number (M) and Lewis number (Le) on non-dimensional temperature, velocity and nanoparticle concentration. The results indicated that increasing the Brownian motion parameter would cause an increase in temperature profile while the effect of increasing Brownian motion on concentration profile is vice versa, moreover, by increasing the Thermophoresis parameter we would have a decreases in temperature profile and an increase in concentration profile