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In this paper, we applied the successive linearization method (SLM) in solving highly system of nonlinear boundary value problem. The method is presented in detail by solving the problem of free convective heat and mass transfer of an incompressible fluid past a moving vertical plate in the presence of radiation effect. The governing partial differential equations are converted into system of non linear ordinary differential equations by a similarity transformation, which are converted into system of linear ordinary differential equations using SLM. The linear system is solved using the Chebyshev spectral method to find solutions that are accurate and converge rapidly to the full numerical solution. Comparison with previously published works are performed to test the validity of the obtained results with focus on the accuracy and convergence of the solution. The effects of selected fluid parameters on the velocity as well as the temperature and concentration distribution are determined and discussed.
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