A study has been carried out to analyze the effects of variable electric conductivity, non-uniform heat source/sink and higher order chemical reaction on unsteady, free convective viscoelastic (Walters liquid model-B) fluid flow over a moving vertical cone and a flat plate saturated with porous medium. The constitutive equations for the boundary layer regime are solved by an efficient finite difference scheme of the Crank-Nicolson type. The features of the fluid flow, heat and mass transfer characteristics are analyzed by plotting graphs and the physical aspects are discussed in detail to interpret the effect of various significant parameters of the problem. It is observed that the impact of variable electric conductivity with magnetic field has significant effect on the viscoelastic fluid flow through porous medium. The effect of temperature dependent heat generation is much stronger than the effect of surface dependent heat generation. The mass transfer of the reactive species strongly depends on the chemical reaction parameter as well as the order of chemical reaction. It is stronger for the first-order reaction than that for the higher order reaction. (C) 2013 Elsevier Ltd. All rights reserved.