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The nonlinear, steady state boundary layer flow, heat and mass transfer of an incompressible non-Newtonian Jeffrey’s fluid past a semi-infinite vertical plate is examined in this article. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit finite-difference Keller box technique. The influence of a number of emerging non-dimensional parameters, namely Deborah number (De), ratio of relaxation to retardation times (λ), Buoyancy ratio parameter (N), suction/injection parameter (fw), Radiation parameter (F), Prandtl number (Pr), Schmidt number (Sc), heat generation/absorption parameter (Δ) and dimensionless tangential coordinate (ξ) on velocity, temperature and concentration evolution in the boundary layer regime is examined in detail. Also, the effects of these parameters on surface heat transfer rate, mass transfer rate and local skin friction are investigated. This model finds applications in metallurgical materials processing, chemical engineering flow control, etc.