SOLUTION OF THE STEFAN PROBLEM FOR QUASI-STATIONARY FLUCTUATIONS OF AMBIENT TEMPERATURE

A solution to the Stefan problem for a one-dimensional layer of thermal phase-changing material insulation of the walls of a room is proposed under the assumption that the temperature of the outer surface of the wall is equal to the ambient temperature and its fl uctuations are harmonic and quasi-stationary. The indicated problem was solved depending on the relative amplitude of fl uctuations of the ambient temperature Δϑ, the Biot number, which characterizes heat emission from the room, and a set of physical properties of the thermal insulation material. An analytical solution to the problem for relatively large amplitude of ambient temperature fl uctuations is observed — Δϑ ≥ 1. It is shown that in using a phase-change material with a phase transition temperature equal to the room temperature, there are no fl uctuations of the temperature of the inner surface of the room wall, the temperature of which is equal to the room temperature during the entire period of ambient temperature fl uctuations.
A solution to the Stefan problem for a one-dimensional layer of thermal phase-changing material insulation of the walls of a room is proposed under the assumption that the temperature of the outer surface of the wall is equal to the ambient temperature and its fl uctuations are harmonic and quasi-stationary. The indicated problem was solved depending on the relative amplitude of fl uctuations of the ambient temperature Δϑ, the Biot number, which characterizes heat emission from the room, and a set of physical properties of the thermal insulation material. An analytical solution to the problem for relatively large amplitude of ambient temperature fl uctuations is observed — Δϑ ≥ 1. It is shown that in using a phase-change material with a phase transition temperature equal to the room temperature, there are no fl uctuations of the temperature of the inner surface of the room wall, the temperature of which is equal to the room temperature during the entire period of ambient temperature fl uctuations.
Author:  E. P. Valueva, E. A. Morozov
Keywords:  Stefan problem, phase-change materials, quasi-stationary regime
Page:  100