A multidimensional method of nondestructive determination of the thermophysical properties of solid materials subjected to thermal action from a circular plane heat source of constant power is considered.Introduction. In the present work, we consider a method of nondestructive determination of the thermophysical properties (TPP) of solid materials, a bounded portion of whose surface is subjected to thermal action from a circular plane heat source of constant power [1][2][3][4].An analysis of the well-known methods of measuring the thermophysical properties of solid materials and of the errors they incur shows that within the time interval of measurement of a thermal system the latter undergoes profound changes not allowing one to describe the entire process of heat transfer by a single analytical model with invariable restrictions and conditions. Neglect of this fact leads to a marked increase of errors in determining the thermophysical properties of a solid material.The methods of determining the thermophysical properties of solid materials based on the assumption of the existence of a regular thermal regime allow one to most accurately take into account systematic and random errors of such determination. It was proved by Academician A. V. Luikov that regular thermal regimes of the first and second kind have a common property characterized by the fact that the ratio of the heat flux at any point of a body to the heat flux on the body surface is independent of time. In the given case, most often the thermogram is described by a mathematical model linear with respect to parameters or easily linearized [5]. Many of the indicated methods are intended for investigation of bodies of finite dimensions (plates, cylinders, spheres); however, a major portion is based on models of half-spaces (flat, cylindrical, spherical).In relation to such models, one should refer not to a regular thermal regime for the entire body (since it is considered infinite), but rather to regularization of the thermal process only for a definite region. Consequently, if the thermophysical properties of a solid material are determined only from the thermogram portions corresponding to the thermal regime regularization in the region of heaters and thermal detectors, then, first, the computational relations will be simpler and in many cases linear with respect to parameters and, second, systematic error components will be either much smaller than random ones or constant, i.e., independent of time. In such a case, the major part of such characteristic portions can be found and described analytically, and more possibilities will be afforded by an informationmeasurement system that implements the method of exercising self-control, i.e., it becomes possible to determine the complex of thermophysical properties of a studied object in one experiment using various mathematical models that adequately reflect actual heat transfer processes at certain time intervals.Experimental Implementation of the Method. The measuring and thermal schemes of the multimode...

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Consideration is given to the theoretical foundations of the method of nondestructive testing of the thermophysical properties of solid materials subjected to thermal action from a plane heat source of constant strength on a bounded portion of the surface. It has been established that the evolution of the thermal process from a bounded plane heater will be analogous to the evolution of the thermal process in a plane half-space and to the processes in a spherical half-space at high values of time.There are many methods for determination of the thermophysical properties of materials [1][2][3]. Investigations in this field remain topical at present, however, primarily because of the fact that the thermophysical properties of a material are found based on indirect experiments and are calculated from certain mathematical models. The accuracy and reliability of determination of the thermophysical properties largely depend on how correctly the mathematical model describes the thermal processes occurring in measurement.In this work, consideration is given to the theoretical foundations of the method [3, 4] of nondestructive testing of the thermophysical properties of solid materials subjected to thermal action from a plane heat source of constant strength on a bounded portion of the surface.Let us consider a model of nonstationary heat transfer from a circular plane heat source of constant strength. We obtain an expression determining the evolution of a temperature field from a bounded circular plane heater in a half-space ( Fig.

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

The nondestructive method developed by the author with the use of a linear pulsed heat source makes it possible to determine the thermophysical characteristics of solid materials on the basis of the portions of thermograms that correspond to the regularization of the thermal regime in the region of the heater and temperature detectors. Consideration has been given to the influence of the outflows of heat to a probe on the error in determining the thermophysical characteristics of materials in the case where two semiinfinite bodies are in ideal contact. A mathematical expression upon the fulfillment of which one may disregard the heat loss to the material of the probe substrate has been obtained. In the work, consideration has also been given to the problem of heat loss to the probe material in the case where it occurs only in the region of the heater. It has been shown that the temperatures of the first and second bodies in the contact area will become closer with time.The determination of thermophysical characteristics is based on the physical model presented in Fig. 1. Thermal action on the body under study with a uniform initial temperature distribution is carried out using a linear pulsed heater. In the experiment, the temperature is recorded at a prescribed distance from the heater [1].The theoretical foundations of the method of nondestructive testing of the thermophysical characteristics of materials, which uses the model of a nonstationary process of heat transfer from a linear pulsed heat source, have been presented in [1]. The method allows for different states of operation of a measuring system. The analytical solution of the mathematical model of the process of heat transfer in the body under study from the action of a linear pulsed source for the second ("operating") portion of the thermogram has the form [2]