Heat Conduction or Diffusion With Change of Phase

TLDR: In this paper, the authors studied the diffusion equation subject to a phase change at one boundary, provided simple boundary conditions of the first, second, or third kind are specified, and provided exact solutions regarding relative motion between the phases, ablating slabs, and growth of a vapor film.

Abstract: Publisher Summary The study of the diffusion equation subject to a phase change at one boundary is in a relatively satisfactory state, provided simple boundary conditions of the first, second, or third kind are specified. Mathematically interpreted, the interesting features of the problem arise from the nonlinearity, exhibited for all but a few particular boundary motions. This chapter illustrates solution of the equation for diffusion of heat, mass, or some other scalar quantity, subject to the existence of a free boundary. The chapter aims to find exact solutions regarding relative motion between the phases, ablating slabs, and growth of a vapor film. Analytic approximation methods and analog and digital computer solutions are discussed in details. Integral equation methods, variation methods, and boundary layer methods along with active and passive analog solutions and application of numerical schemes are appropriate for bringing clarity to heat conduction or diffusion with phase change. In the search of growth of small particles of a condensed phase, the quasi-steady-state theory is applied particularly where a condensed phase exists whose volume changes slowly with time. This is true, for example, in the sublimation of ice or the condensation of water vapor from air on liquid droplets. While focusing on active and passive analog solutions, freezing problems remain symmetric in one, two, and three dimensions, where the liquid is initially at the fusion temperature. The heat capacity of the solidified phase is taken into account. Thermal properties are considered to be temperature independent.