Developing a method of accounting for the existence of local surface heat exchange in rods of variable cross-section

Abstract

The load-bearing elements of a number of strategic equipment are of limited length and variable cross-section. Most of them are exposed to certain types of heat sources. In order to ensure the reliable operation of this equipment, it is necessary to know the temperature field along the length of the variable cross-section rod. In this paper, a computational algorithm and a method for determining the temperature field along the length of a rod with a limited length and variable cross-section are proposed. They are based on the fundamental laws of conservation of energy. The nonlinearity of the process is due to nonlinear dependencies of the areas of the variable cross-section on the coordinate. The radius of the cross-section of the rod decreases linearly along the entire length, starting from the left end. The side surface of the first and third discrete elements of the rod is heat-insulated. Convective heat exchange with the environment takes place on the side surface of the second discrete element of the rod. The cross-sectional area of the left end of the rod is under the heat flow with a constant intensity, and a heat flow with different intensities is supplied to the right end, wherein the heat transfer coefficient is considered constant. For this task, you must first determine the law of temperature distribution along the length of the rod. In addition, if one end is rigidly fixed and the other end is free, the elongation must be calculated depending on the available heat sources, the physical and geometric characteristics of the rod, taking into account the presence of insulation. In case of pinching of both ends of the investigated rod, the value of axial compressive force is calculated taking into account the addition of real factors. The distribution of all components of the strain, stress, and displacement field is also defined