Phase change in a cylinder and a cylindrical shell heated with an axisymmetric front moving in the axial direction

A quasi-steady phase-change problem is solved for a cylindrical shell of which the inner or outer surface is heated with an axisymmetric ring heater moving at a constant velocity. The body temperature is expressed in a product solution, which leads to the derivation of a Klein-Gordon equation. A method of undetermined parameters is developed to solve this equation, and the temperatures are derived in multiple regions in the shell. The results are expressed in integral equations, which are none of the Fredholm or Volterra types. Finally, a least-squares iteration method is developed to solve for the interface positions. The four examples presented in this paper cover the phase change in cylinders and cylindrical shells. Comparisons are made between the temperatures for materials with and without phase change.