The present study deals with the computational analysis on an electrically conducting magneto viscoelastic fluid over a circular cylinder. Prescribed partial slip effects are also taken into account. The governing physical problem is tackled numerically highly efficient and reliable Keller box algorithm. Impact of sundry physical parameters on physical quantities of interest are evaluated. 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.