539.3

нелінійна задача теплопровідності
термочутливе тіло
скінчений циліндр
конвективний теплообмін
середовища змінної температури
метод лінеаризувальних параметрів
аналітично-числова методика
nonlinear heat conduction problem
thermothensitive body
finite cylinder
convective heat exchange
temperature variable environment
linearizing parameters method
analytic-numerical method

Розглянуто двовимірну нелінійну стаціонарну задачу теплопровідності для термочутливого циліндра скінченої довжини. Враховано теплообмін на усіх поверхнях циліндра із зовнішніми середовищами різних функційно-змінних температур. Розв’язок задачі побудовано з використанням методу лінеаризувальних параметрів щодо визначення температурних полів у термочутливих елементах конструкцій та скінчених інтегральних перетворень.
A lot of structural elements of modern technology take the form of a finite cylinder and in the manufacture and operation are often subjected to significant temperatures (high and low level temperatures). To ensure their reliable operation already at the design stage the detailed analysis of the temperature field and flow conditions of heat exchange processes should be carried out taking full account of heterogeneity (due to the fact that the physical and mechanical properties of materials depend on temperature changes) and actual operating condition also (taking into account heat exchange on all surfaces the surrounding temperatures of which are not constant). The method of construction the solutions to two-dimensional nonlinear stationary heat conduction problems on the example of thermosensitive cylinder with convective heat exchange is proposed. The convective heat exchange with varying (on the coordinates) surroundings temperature through all cylinder surfaces is considered. The two-step linearization (partial - by introducing the Kirchhoff variable and final - by using the linearizing parameters method) is realized for solving the corresponding nonlinear heat conduction problem. This method is effective for constructing analytical and numerical solutions of heat conduction problems for thermosensitive bodies, if they have convective heat transfer conditions at their surfaces. This method involves the construction of solution to the equation for Kirchhoff variable with a linear condition that includes certain "linearizing parameters". The resulting linear problem for the Kirchhoff variable is solved by finite integral transformation method. The distribution of temperature field of cylinder and also the influence of material temperature-sensitivity on it taking into account linear dependence of heat conduction factor is determined. The comparison of the obtained solutions with solutions of similar problems for the permanent characteristics of the material and the mid-integral characteristics values for a given temperature range is made.