Estimation of Systematic Errors of the Multimodel Method for Nondestructive Determination of the Thermophysical Properties of Solid Materials

Abstract

We have considered the results of the analysis and estimation of systematic errors involved in the multimodel method for determining the thermophysical properties of solid materials. We have analytically obtained the condition that determines the upper limit of the reliably determinable thermal conductivity of the materials under study.Introduction. The multimodel method of nondestructive determination of the thermophysical properties (TPP) of materials relates to indirect measurement methods because not the very thermophysical quantity is measured directly in the course of an experiment, but rather thermograms (time dependences of temperature) are recorded [1][2][3]. The method is based on analytical solutions of the mathematical models of heat transfer processes occurring in a body under study exposed to the action of a constant strength round heat source (with the use of data for various portions of a thermogram [4,5]).Multimodel Method for Nondestructive Determining the Thermophysical Properties of Materials. The method is based on the following assumptions: 1) on a thermogram there are portions for which a highly accurate coincidence with the results of computational experiments by analytical models is ensured. Moreover, corresponding to these portions (Fig. 1, portions II and IV) there are the thermal regimes of the experiments that came up to the regularization stage (in what follows these portions will be called working);2) for the working portions there exist expedient computational relations allowing one to unambiguously determine the values of thermophysical properties depending on the parameters of the analytical function that describes the thermogram within the given interval.According to the method of [1, 2, 5], portion II of the thermogram (Fig. 1) is described by the equation of the form

Identity of Temperature Fields Produced by Flat and Spherical Heaters in the Method of Non-Destructive Thermal Testing

“…Участки термограммы II, IV и VII -рабочие, так как возможно однозначно определить значения ТФС в зависимости от параметров аналитических моделей, описывающих термограмму на данных температурно-временных интервалах, используя регулярные тепловые режимы на моделях плоского и сферического полупространств [1,2]. Оценка случайных и систематических погрешностей определения ТФС твердых материалов на ста-дии нагрева при реализации данного метода контроля приведена в работах [3,4].…”