Melting around a shaft rotating in a phase-change material

In this paper we describe the thin-film melting of a block of solid phase-change material (the bearing) around a rotating cylinder (the shaft). We determine the relation between the force applied on the shaft and the speed with which the shaft migrates into the bearing, the relation between the applied force and the torque, and the angle between the applied force and the direction of migration into the bearing. The method is based on contact melting theory, which combines the Reynolds thin-film lubrication theory with an analysis of phase-change heat transfer in the melt. The paper addresses three limiting regimes of the contact melting phenomenon: (1) the long bearing with melting due to frictional heating in the melt layer; (2) the short bearing with melting due to frictional heating in the melt layer, and (3) the short bearing with melting due to a temperature difference imposed between the hot cylinder and the cold phase-change material.