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 wh ich the inner or outer surface is heated with an axisymmetric ring heater m oving at a constant velocity. The body temperature is expressed in a produc t solution, which leads to the derivation of a Klein-Gordon equation. A met hod 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 Volterr a types. finally, a least-squares iteration method is developed to solve fo r the interface positions. The four examples presented in this paper cover the pahs change in cylinders and cylindrical shells. Comparisons are made b etween the temperatures for materials with and without phase change.