Inhomogeneous Stefan problems and underwater discharge

Abstract

Two-phase physical systems with sources and mobile interfaces are modeled by inhomogeneous parabolic problems which are considered as extensions of the classical problem of Stefan. The solutions in linear, cylindrical and spherical geometrical setups are found as a series in orthogonal (Hermite or Laguerre) polynomials. The deviation of the expansion law of the phase with sources from the classical similarity √t is determined. Underwater discharge is considered and explosion rates are plotted.

Keywords

• Stefan problem
• heat equation
• mobile interface condition
• underwater discharge.