In this article, the combined theoretical and computational study of the magneto hydrodynamic heat transfer in an electro-conductive polymer on the external surface of a vertical truncated cone under radial magnetic field is presented. Thermal and velocity (hydrodynamic) slip are considered at the vertical truncated cone surface via modified boundary conditions. The Williamson viscoelastic model is employed which is representative of certain industrial polymers. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum and energy equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. Validation of the numerical solutions is achieved via benchmarking with earlier published results. The influence of Williamson viscoelastic fluid parameter, magnetic body force parameter, Thermal and velocity (hydrodynamic) slip parameters, stream wise variable and Prandtl number on thermos-fluid characteristics are studied graphically. The model is relevant to the simulation of magnetic polymer materials processing. © 2017, Global Digital Central. All rights reserved.