During heat transport through the walls of a hollow sphere, the heat stream can achieve extreme values. The same processes occur in regular polyhedrons. We can calculate the maximum heat transfer rate, the so-called critical heat transfer rate. We must assume here identical conditions of heat exchange on all internal and external walls of a regular polyhedron. The transfer rate of heat penetrating through the regular polyhedron with different heat transfer coefficients on the walls is called the heat transfer rate with asymmetric boundary conditions. We show that the heat transfer rate in this case will grow up if we replace those coefficients with their average values.

The paper is of practical importance and describes the construction of a test rig and the measurement method for determining the relative emissivity coefficient of thermosensitive thin polymer coatings. Polymers are high-molecular chemical compounds that produce chains of repeating elements called ‘mers’. The polymers can be natural and artificial. The former ones form the building material for living organisms, the latter – for plastics. In this work, the words plastics and polymers are used as synonyms. Some plastics are thermosensitive materials with specific physical and chemical properties. The calorimetric method mentioned in the title consists of two steps. The first stage, described here, involves very accurately measuring the emissivity of black paint with the highest possible relative emissivity coefficient, which covers the surface of the heater and the inner surface of the chamber. In the second step, the thermosensitive polymer will be placed on the inner surface of the chamber, while black paint with a known emissivity coefficient will remain on the heater. Such a way of determining the properties of thermosensitive polymers will increase the error of the method itself, but at the same time will avoid melting of the polymer coating. During the tests, the results of which are presented in this work, the emissivity coefficient of the black paint was obtained in the range of 0.958–0.965.