The melting of polymer caused by friction before the solid plug is formed is an important phenomenon in the plastic injection process. To analyze the melting process caused by solid particles sliding against the bellow, a method that can simulate behavior of each particle during the calculation should be used. Particle element numerical method is hence adopted in the analysis for this research to take into consideration the behavior of each particle, where the melting of pellets caused by friction against flight and screw are assumed as friction against adiabatic walls. In this paper, analytical expressions of the transient melting process for spherical polymer pellets sliding against adiabatic wall are derived, which is essential for the numerical simulation of melting process in solid conveying section by particle element method.