Analytical solution for a cylinder glaciation model with variable latent heat and thermal diffusivity

Abstract

We consider a Stefan type problem that models the glaciation of the outer surface of a cylindrical gas pipeline in sea water. An equivalent integral formulation is obtained, considering that the latent heat and the thermal diffusivity depend on the radial distance. When the radial component of the heat flux vector from sea water to glaciation front is inversely proportional to the radial distance, local existence and uniqueness of solution is shown. In the general case, existence is ensured but uniqueness of solution is not guaranteed.