Влияние температурных зависимостей теплофизических характеристик материала на нестационарную теплопроводность в стенке барабана парового котла

Abstract

Рассматривается нестационарная теплопроводность в стенке барабана парового котла с учетом температурных зависимостей теплофизических характеристик материала. Показано, что для решения таких задач целесообразно применять математические формулировки задач теплопроводности в виде системы уравнений для температуры и компонент теплового потока. Установлено, что способ учета температурных зависимостей теплофизических характеристик материала заметно влияет на результаты расчетов нестационарной теплопроводности в стенке барабана парового котла.The purpose of this research was to estimate the error in the simulation data of the processes of nonstationary heat conductivity that occur in the drum wall of a steam boiler due to the linearization of heat conductivity equation as a result of the averaging of temperature dependences of thermophysical characteristics of the material. It was shown that in the general case when the temperature dependences of thermophysical characteristics of the material are represented by the approximations of tabulated prescribed functions it is reasonable to use the mathematical formulation of the heat conductivity problem in the form of complete equation system that includes the heat balance law and the Fourier law for the investigation of nonstationary heat conductivity in the drum wall of steam boiler. Using the method of semi-descritization we obtain the sought unknown values in the form of time functions of nodal temperature values and heat flow components and for them we obtain the differential equation system and nonlinear algebraic equation system that interrelate nodal temperature values and heat flow components. It was shown that the linearization of heat conductivity equation due to the averaging of temperature dependences of thermophysical characteristics of the material introduces no substantial errors to the obtained data only in a narrow temperature range of the averaging that is limited by extreme temperature values at body points. In the general case the linearization of heat conductivity equation due to the averaging of temperature dependences of thermophysical characteristics of the material can bring in noticeable errors in the research data of nonstationary temperature fields that are induced in the drum wall of steam boiler.