Experimental determination of the temperature in a small neighborhood of the gas infrared sources

The results of the experiments carried out are the logical justification for the development of the heat transfer models in the air-filled enclosed areas which are determined by the walls of finite thickness and under conditions of the gas infrared sources operation. It was found that the air convection processes play an important role in formation of the thermal regimes of the areas heated by the radioactive flux coming from the upper boundary of such areas despite the low thermal conductivity of the gas.


Introduction
Gas infrared sources (GIS) have become increasingly promising sources of energy in the local heating systems of production facilities [1].However, their broad utility is constrained by the fact that to date there has not been developed any model of heat transfer processes in the areas with heat supplied through the GIS operation.The latter is mainly caused by the lack of experimental data on the thermal fields in the location of exposure of such sources.Though, it still remains to be one of the core issues about the energy transfer mechanism inflight at the GIS operation.
On a provisional basis, the heat transfer area in the GIS neighborhood can be divided into three zones: the major (or working) one, in which maintaining of the air temperature is the purpose of the source operation; a zone of the GIS energy accumulation and subsequent air heating; a small neighborhood of the working sources, in which the ambient temperature may be higher than maximum allowable.So far no reliable experimental data have been published on the thermal fields of each of these zones.
The objective of the present paper is the experimental study of the regularities of the thermal temperature fields formation in a relatively small (with characteristic dimensions up to 1,5 m) neighborhood of the gas infrared source and justification of the physical heat transfer model in the GIS-heated area.
a Corresponding author: marisha@tpu.ruThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Results and discussion
Experimental studies were performed on the large-size (with characteristic dimensions over 10 m) models of the heat supply facilities with the vertical and horizontal walls of a finite thickness (external envelope) under low temperatures (from −10 • C to −30 • C) in the exogenous environment.The ambient temperature was measured at eight points in the length of 1, 5 m over the GIS radiating surface (Table 1).
To ensure the reliability of the measurement results, the experiments were 10 times repeated under identical conditions (Table 1).The measurements were done under a steady-state distribution of the temperatures in the measuring range.
The methods of linear regression analysis were applied to determine the type of function t(x).Correlation field (Fig. 1) proves that this function is almost to be linear: where b 1 -coefficient of regression.
To calculate the coefficients b 0 , b 1 there has been used the least squares method -the sum of squared deviations of the measured (empirical) values t 3 from their calculated (theoretical) values t p was minimal, i.e., n i=1 (t 3 − t p ) 2 → min, where t p -value, calculated by equation of regression.The regression analysis allowed the point estimations of the equation of regression coefficients.The equation of regression is as follows: t = 341, 21 − 0, 167x.
( 1 ) There was checked one of the Gauss-Markov clauses -an expectation value of deviation to be zero for all observations (Table 3), (on the average the random deviations have no effect on the dependent variables): Determination coefficient of the derived model is equal to R 2 = 0, 943.At the next stage of processing of the experimental results the possibility was tested to present the equation of regression as a nonlinear function (polynom of the 2 nd degree).The equation of nonlinear regression is specified as follows:

Thermophysical Basis of Energy Technologies
Upon its linearization the equation of multiple regression is derived as: where The coefficients of this equation were estimated by the least squares method.The result is a nonlinear expression as follows: t = 377, 89 − 0, 314.x + 0, 00009.x 2 .
( 2 ) The deviations were calculated between the experimental values t and the values t * , derived from the formula (1).It was determined that the cumulative error was small (Table 4): The determination coefficient (R 2 = 0, 9909) in this case proved to be higher than in the linear model.It is determined that all coefficients are statistically significant at the significance level of 0,05.
Both models have a small cumulative error of the deviations, but a nonlinear regression model is preferred.Based on the obtained results the conclusion can be made that the ambient temperature varies from a maximum value of 335 0 C (x = 0, 1 m) down to 110 0 C (x = 1, 5 m) in the relatively small range (about 1,5 m) in the neighborhood of the radiating surface of the gas infrared sources.Such high temperatures can be caused only by intensive air heating due to thermal conductivity.The experiments were conducted in the environment of dust-free air (which can absorb and dissipate the radiation energy).Therefore, the temperature increase in this area can not be due to the direct effect of radioactive flux.
The obtained experimental data are the rationale to conclude the necessity of allowance for the conductive heat transfer processes at the analysis of thermal fields in the area of heating by gas infrared sources.

Conclusions
The results of the performed experimental studies are the rationale for the development of the heat transfer models in the air-filled enclosed areas which are -defined by the walls of finite thickness, and under conditions of the gas infrared sources operation.It was determined that the air convection processes, despite the low thermal conductivity of the gas, play an important role in formation of the thermal regimes of the areas heated by the radioactive flux coming from the upper boundary of such areas. 01021-p.4

Figure 1 .
Figure 1.Temperature distribution in the coordinates x.

Figure 2 .
Figure 2. Temperature distribution in the coordinates x.

Table 1 .
Results of the temperature measurements.

Table 4 .
Temperature values calculated by the formula (1)