In the study of solid conveying process in plastics screw extrusion, a particle element numerical method enables its to simulate behavior of each solid particle during the process and takes into consideration the parameters of individual particle in the calculation. The melting of pellets in the solid conveying section is caused predominantly ky heat from both friction and conduction through close contact. Experiments showed, melting happened before the solid plug was formed. Hence, when a particle element numerical method is used to simulate the conveying and melting process in the injection bellow, the analysis of melting process caused by solid particles sliding against wall of bellow should be included. Searching through the recent literature, no valid analysis of the transient close-contact melting process caused by viscous dissipation was found. This paper attempts to present an analysis of the melting process and derive an expression for describing the transient melting caused by both friction and close-contact heating. The melting model of polymer pellets sliding against the barrel was achieved by assuming the friction against the barrel as friction against an isothermal wall given the high heat conductivity of the barrel. To keep the expression simple, a constant temperature boundary condition is utilized for the wall which concurs with reality.