Definition and mathematical modeling of the thermostressed state of a two-component thermosensitive cylinder under convective-radial heating

Abstract

Визначено та досліджено розподіли температури й спричинених нею напружень у двоскладовому термочутливому циліндрі, на одній з обмежуючих поверхонь якого підтримується стала температура, а через іншу відбувається конвективно-променевий теплообмін із навколишнім середовищем.The thermosensitive body model is used in order to implement the requirements of modern engineering practice for the calculation of temperature fields and tensions in multilayer structures operating under high-temperature heating. The thermosensitive body model takes into account the dependence of the thermal and mechanical characteristics of the material components on the temperature. Such models describe their thermal and thermostressed state more accurately. However, these problems usually do not have exact analytical solutions, and therefore require the development of new methods for their solution. It is also important to take into account their actual heating conditions and interaction with the environment. In this article the nonlinear mathematical model of temperature distribution in a two-component thermosensitive cylinder based on the thermosensitive body model is defined. It occurs under conditions of complex heat transfer on flat limiting surfaces, in particular the constant temperature from one side cylinder and the convective-radial heat transfer with the environment of constant temperature from another. There are also evenly distributed heat sources on the adjacent surface of the cylinder components that produce thermal flow. The temperature tensions which were caused by defined temperature distribution have been found. In order to estimate the influence of the thermosensitivity of the material of cylinder components the same nonlinear mathematical model of temperature distribution was created, but for nonthermosensitive cylinder. The influence of the thermosensitivity of thermal and mechanical characteristics of the material components on the nature and extent of temperature and stresses distribution depending on the input parameters have been investigated. It was established, that it is of great importance to take into account the thermosensitivity of materials, as the maximal differences between the thermosensitive and non-thermosensitive cylinders with basic and average integral values can reach the large values. However, in order to make a rapid assessment of the temperature and stresses distribution under conditions of the above complex heating and composition of the materials, it is necessary to use the basic values of thermomechanical characteristics