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In this article, the investigation is made to shed a light on the influence of convective boundary conditions on the boundary layer flow over a linearly stretching flat surface. The equations (partial differential equations) describing the model are transformed into system of nonlinear ordinary differential equations using similarity transformations. Equations contain various non-dimensional flow characterizing numbers viz. Prandtl number Pr, Lewis number Le, Biot number Bi, Brownian motion parameter Nb and thermophoresis parameter Nt. The influence of these parameters on thermal boundary layer, concentration distribution and temperature are analyzed in detail, by solving the equations using novel Shifted Chebyshev collocation method. The computed results, reduced Nusselt number, reduced Sherwood number, surface temperature and concentration profiles as functions of dimensionless numbers are validated by comparing the predicted results with available earlier findings (using other methods). To assert the convergence and stability of the scheme used (for much larger, but moderate, parameters values), predicted results are presented in various tabular forms. For presenting finer details of the computed values some results are also given graphically. The innovative semi-numerical scheme is robust and efficient compared with other conventional methods, used in previous studies and enables the analysis of the complex problem adequately.