RESEARCH OF INTEGRAL CHARACTERISTICS OF PROCESS OF HEATTRANSFER IN THE SENSITIVE ELEMENT OF RESISTIVE TEMPERATURE DETECTOR

Heattransfer models in a sensitive element of the resistive temperature detector taking into account temperature dependence of heatphysical characteristics of elements of the sensor are developed. The assessment of the relative deviation of results of numerical research of integral characteristics of process of heattransfer in a sensitive element of the sensor from the data obtained by means of the model which isn't considering influence of temperature on heatphysical properties of substances is executed. It is shown that the relative error of computation makes from 7,3% to 14,9% depending on type of the sensor and the taken temperature.


Introduction
Temperatureone of the key parameters characterizing a status of technology equipment and efficiency of course of technological processes [1,2].The share of systems of measurement and regulation of temperature makes to 50% (in some casesto 80%) from the total amount of monitoring systems of technological processes.For temperature measurement in the industry, mainly, thermoelectric converters (TEP) and resistive temperature detector (RTD) [3,4] are used.One of the main methods of increase of measuring accuracy is prognostic process modeling of heattransfer in a sensitive element of the sensor.Simulation by means of numerical methods was widely adopted [5].In this case, an important role is played by the heatphysical characteristics of materials used in researches.Often characteristics are accepted constant and independent of temperature that can lead to appearance of an additional error of computation.It is possible to minimize possible errors in this case by approximation of dependences of heatphysical properties of materials and use in numerical researches of the received approximating expressions [6][7][8].
The purpose of this work is modeling of process of heattransfer in RTD and comparison of results of numerical researches of the integrated characteristics of heattransfer received taking into account dependence of heatphysical properties of materials on temperature and at their constant values.In case of creation of model the task of heat conduction for the area representing the non-uniform system including a sensitive element of the resistive temperature detector, a protective cover (a metal jacket) and area in between, filled by powder of oxide of Al 2 O 3 aluminum (fig. 1) is considered.At numerical modeling it is accepted that the sensor has the correct cylindrical form.During research minimum necessary times of heating of the sensor, and also temperature fields in the RTD sensitive element were defined.The minimum duration of heating of the sensor corresponds to time necessary for this purpose, the deviation of temperature of a sensitive element 1 (fig.1) from the taken didn't exceed a tolerance (table 1).

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The boundary conditions which have been set on an axis of symmetry r=0: Boundary conditions on boundary x=L: .
Boundary conditions on boundaries on an axis y: At the internal borders of the area specified condition of fourth type: The area of the solution of the task (fig. 1) is broken into the uniform grid consisting of 200 nodes.The slot pitch on radial and axial coordinates is equal 2,5•10 -2 mm.The step on a temporal grid changed in the range from 10 -4 to 10 -2 sec for reduction of volume of computation and increase of accuracy of the decision.
System of equations 1-3 with the appropriate initial and boundary conditions decided using a method of finite differences [10].The solution of the difference analogs of the differential equations representing linear algebraic equations was carried out by a local and one-dimensional method [10].The pro-race method was applied to the decision of system of the difference equations on the basis of the implicit four-point diagram [10].
The conservatism verification of applied difference schemes was conducted to estimate the confidence of numerical simulation results similar to [11][12][13]) and the comparison with experiment results was accomplished.

Results and discussion
The constant values of heatphysical characteristics accepted at numerical research are given in table 2.  During research minimum necessary duration of execution of measurement with which the measurement error doesn't exceed the permissible deviations given in [10] was defined.The received results of necessary runtimes of measurements for the RTD different types are given in fig. 2. From a figure 2 it is visible that the heating up necessary for duration received when using of the characteristics approximated the teplofi-zicheskikh exceed the similar values received when using constant heatphysical characteristics.
The numerical assessment of a relative deviation of necessary times of heating of the sensors received with use of constants and the approximated heatphysical characteristics for the RTD different types is given in table 4. Deviations of the received results for the researched RTD types make: for copper RTDfrom 11,7% to 14,8%, for platinum RTDfrom 7,3 % to 14,3 %, for nickelfrom 10,5 % to 11,4 %.

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Distribution of temperatures on RTD thickness, received when using of the approximated and constant heatphysical characteristics is shown, respectively, in figures a and b.In the article integrated characteristics of process of heattransfer are provided in a sensitive element of thermoconverters of resistance: heatings of sensors minimum necessary for duration (for copper, nickel and platinum RTD), temperature fields in sensitive elements of sensors.The specified integrated characteristics are received with use of constants and the approximated heatphysical characteristics.It is established that relative deviations of results are in range from 7,3% to 14,8% and depend on the RTD type and the taken temperature.
This work was supported by the Russian Foundation for Basic Research (No. 14-08-00057).

Figure 1 .
Figure 1. the Diagram of area of the solution of the task: 1sensitive element; 2isolation powder (Al2O3); 3metal jacket (steel); Hheight of a section of the RTD sensitive element; Lradius of the RTD sensitive element

Figure .
Figure .Temperature fields in a sensitive element of platinum RTD at measurement of temperature 700 zs, received by means of constants (1) and the approximated (2) and heatphysical characteristics From fig. it is visible that distribution of temperatures on a layer of a sensitive element of the thermoconverter of resistance has nonlinear character.Taking into account that duration of heating is both cases (fig.a and b) it was limited and I made 2 seconds, it is possible to draw a conclusion that when using of the approximated heatphysical characteristics are received big heating duration.

Table 2 .
[14,15]sical characteristics of materials RTD[14,15]Approximation of dependences of heatphysical characteristics is executed by method of the smallest squares.The received approximating expressions in the considered range of temperatures are given in table 3.

Table 3 .
Approximating expressions of heatphysical properties of materials

Table 4 .
Relative error of calculation of necessary duration of heating of RTD