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Abstract: In this paper a specific measurement method for the determination of thermo-physical parameters of materials is described. All kinds of non-stationary thermal processes in a specimen can be used in this method. In practice, convenient thermal processes(taking into account parameters of dimension etc.) are chosen. The repeated measurement does not guarantee that identical non-stationary thermal processes are applied. In the measurement of the thermal conductivity of insulating materials, it is advantageous to use accumulated core. The time-dependence of the temperature in chosen points of the specimen is to be recorded continuously. The analysis of these records yields thermal parameters. In some cases, the variable thermal power of the laboratory oven is also continuously recorded. The method can be applied to the measurement of temperature dependences of thermo-physical parameters in a wide temperature interval.
Considering the measurement of thermo-physical parameters, one may state that there is a plethora of measuring methods and arrangements. Many of them were described in Refs. [1-6]. The methods used for measuring thermo-physical parameters of materials can be divided into steady-state and dynamic ones. Krempasky [2] estimated that there are approximately 500 measuring methods.
1.1 Measurement of Thermal Conductivity Coefficient by the Accumulation Core Method (ACM)
This paper is a follow up to an earlier one [5]:“Method of accumulation core and its use by measuring thermal parameters of porous materials”. This paper includes a proposal and theoretical analysis of a measuring method for thermo-physical parameters of materials using the so-called accumulation core. The accumulation core AC is a body with a very good thermal conductivity (Fig. 1). Heat penetrates into the accumulation core from an outer metal block (MB) through the measured specimen (sample) S. Thermal differences in the volume of the metal block are to be ignored. The work deduces some general relations applicable for the accumulation core method in the case of a permanent temperature increase. The accumulation core method is an integral method. It is suitable for measuring parameters of heat insulator within a wide temperature range from low up to high temperatures. Essentials of the accumulation core AC method are fully displayed in Fig. 1.
1.2 Steady Temperature Increase Conditions
Under these conditions, the temperature of the outer block increases linearly in time. Such increase of the border temperature is realized over the whole surface surrounding the specimen and the accumulation core steadily creates regular temperature conditions of the system characterized by linear temperature increase of
the specimen volume at each point, including the accumulation core.
After having reached the steady state, the created profile of the temperature field is “evenly” shifted towards higher temperatures, while the speed of the temperature shift at each point of the system equals the speed of the temperature increase at the outer isotherm. Under the condition of steady temperature increase it can be shown that the coefficient of the thermal conductivity λ of the specimen can be stated (written) as
Evaluating the “agreement” between T(t)-theor and T(t)-exp functions, we have to take into account that the functions are not continuous. The both compared functions consist of a set of discrete points, the density of which is different. That demands a non-standard procedure, the idea of which is shown in Fig. 3. A point on one curve does not have its pair on the other curve, because each of them corresponds with a high probability to different time data. A way out of this situation is the point grouping shown in Fig. 3. It is based on the fact that for a group of points detected at a time interval we assign one representative point on one curve and another point on the other. In this way we reach an acceptable number of paired points in chosen time intervals. Based on them, we can determine the differences of both functions and the corresponding value S. A similar sequence can be applied for measurements, at which a varying thermal power P(t) of the heating body is recorded.
The accumulation core method is an integral method. It uses the thermal capacity of a core inserted into the sample for the detection of heat transported through the sample. It does not require the source power measurement. The accumulation core has a high thermal conductivity, so it can be considered as an isothermal body. The sample with the accumulation core is inserted into an outer metal block, which creates another isothermal body. The measurement records the time-dependence of both temperatures, the core and the outer block temperature. At a general temperature regime, the temperature of the outer metal block varies freely, it increases or decreases. Thereby, an error related to the repeatability of the temperature regime at standard measurements is eliminated. The real outer block temperature course is “input” into the calculation, this regime need not to be repeated in another measurement. Errors in measurements of the accumulation core temperature are eliminated. However, speed temperature changes are inevitable from the point of view of the measurement accuracy. The thermal conductivity is calculated parametrically
The authors would like to thank Prof. Viktor Bezák from the Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava and Ing. Gabriela Pavlendová, Ph.D. from the FCE, Slovak University of Technology in Bratislava for valuable discussions on this topic.
Considering the measurement of thermo-physical parameters, one may state that there is a plethora of measuring methods and arrangements. Many of them were described in Refs. [1-6]. The methods used for measuring thermo-physical parameters of materials can be divided into steady-state and dynamic ones. Krempasky [2] estimated that there are approximately 500 measuring methods.
1.1 Measurement of Thermal Conductivity Coefficient by the Accumulation Core Method (ACM)
This paper is a follow up to an earlier one [5]:“Method of accumulation core and its use by measuring thermal parameters of porous materials”. This paper includes a proposal and theoretical analysis of a measuring method for thermo-physical parameters of materials using the so-called accumulation core. The accumulation core AC is a body with a very good thermal conductivity (Fig. 1). Heat penetrates into the accumulation core from an outer metal block (MB) through the measured specimen (sample) S. Thermal differences in the volume of the metal block are to be ignored. The work deduces some general relations applicable for the accumulation core method in the case of a permanent temperature increase. The accumulation core method is an integral method. It is suitable for measuring parameters of heat insulator within a wide temperature range from low up to high temperatures. Essentials of the accumulation core AC method are fully displayed in Fig. 1.
1.2 Steady Temperature Increase Conditions
Under these conditions, the temperature of the outer block increases linearly in time. Such increase of the border temperature is realized over the whole surface surrounding the specimen and the accumulation core steadily creates regular temperature conditions of the system characterized by linear temperature increase of
the specimen volume at each point, including the accumulation core.
After having reached the steady state, the created profile of the temperature field is “evenly” shifted towards higher temperatures, while the speed of the temperature shift at each point of the system equals the speed of the temperature increase at the outer isotherm. Under the condition of steady temperature increase it can be shown that the coefficient of the thermal conductivity λ of the specimen can be stated (written) as
Evaluating the “agreement” between T(t)-theor and T(t)-exp functions, we have to take into account that the functions are not continuous. The both compared functions consist of a set of discrete points, the density of which is different. That demands a non-standard procedure, the idea of which is shown in Fig. 3. A point on one curve does not have its pair on the other curve, because each of them corresponds with a high probability to different time data. A way out of this situation is the point grouping shown in Fig. 3. It is based on the fact that for a group of points detected at a time interval we assign one representative point on one curve and another point on the other. In this way we reach an acceptable number of paired points in chosen time intervals. Based on them, we can determine the differences of both functions and the corresponding value S. A similar sequence can be applied for measurements, at which a varying thermal power P(t) of the heating body is recorded.
The accumulation core method is an integral method. It uses the thermal capacity of a core inserted into the sample for the detection of heat transported through the sample. It does not require the source power measurement. The accumulation core has a high thermal conductivity, so it can be considered as an isothermal body. The sample with the accumulation core is inserted into an outer metal block, which creates another isothermal body. The measurement records the time-dependence of both temperatures, the core and the outer block temperature. At a general temperature regime, the temperature of the outer metal block varies freely, it increases or decreases. Thereby, an error related to the repeatability of the temperature regime at standard measurements is eliminated. The real outer block temperature course is “input” into the calculation, this regime need not to be repeated in another measurement. Errors in measurements of the accumulation core temperature are eliminated. However, speed temperature changes are inevitable from the point of view of the measurement accuracy. The thermal conductivity is calculated parametrically
The authors would like to thank Prof. Viktor Bezák from the Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava and Ing. Gabriela Pavlendová, Ph.D. from the FCE, Slovak University of Technology in Bratislava for valuable discussions on this topic.