A numerical solution for the free convective, unsteady, incompressible, laminar convective heat and mass transfer in a viscoelastic fluid along an impulsively started vertical plate with variable temperature and concentration in considered. The rheology of the fluid is studied through the Walters' (model B) to simulate medical creams, biotechnology and chemical engineering. The governing boundary layer equations are reduced to non-dimensional form and the resulting non-linear system of partial differential equations are then solved by an efficient, accurate and unconditionally stable finite element method. The velocity, temperature concentration fields have been studied to include the effect of viscoelasticity parameter (Γ) and surface temperature power law exponent (m) and surface concentration power law (n). The effect of various parameters; the local skin-friction, the Nusselt number (Nu x ), thermal Prandtl …