Mathematical modeling and computational investigation of the dependence of the thermal stressed state of the rod on the heat transfer coefficient in the presence of a temperature of constant intensity

Abstract

In the article on the basis of energy principles, a mathematical model of thermal stressed - deformed state of a rod from a heat - resistant alloy. The energy principle is focused on minimizing the potential energy of elastic deformations in combination, the application of the method of a quadratic finite element with three nodes. Rod of limited length and rigidly pinched by two ends. The lateral surface of the rod sections (0 ≤ x ≤ L/3) and (2L/3 ≤ x ≤ L) is thermally insulated. Through the cross - sectional area of both ends of the rod, heat exchange takes place with their environment. The temperature of T = const = 800^◦C constant intensity is given on the middle section of rod (L/3 ≤ x ≤ 2L/3). Investigated effects of heat transfer coefficient on the thermally stressed state of the core of the high - temperature alloy ANV-300 in the presence of a temperature of constant intensity and numerical research results are represented. Research were conducted for different values of the heat transfer coefficient. As a result, it was found that with an increase in the value of the h₀ - coefficient of heat transfer the amplitude of displacements increases against the direction of the axis Ox; coordinate of section, displacement amplitude, which will be the largest, increases; the amplitude of the interchange of the axis Ox direction is reduced; the maximum and average values of the thermoelastic stress decrease.