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12ФИЗИКО-МАТЕМАТИЧЕСКИЕ НАУКИ UDK 536.242
THERMAL ISOTROPY OF PARALLELEPIPED BRONZE SPECIMENS
SODATDINOV SHAHNAVOZ SADRIDINOVICH
Research fellow, Tajik National University Research Institute, Dushanbe, Tajikistan
NIZOMOV ZIYOVUDDIN
Leading Researcher, Research Institute, Tajik National University, Dushanbe, Tajikistan
GULOV BOBOMUROD NUROVICH
Associate Professor, Department of General Physics, Tajik National University,
Dushanbe, Tajikistan
TOSHKHODZHAEV KHAKIM AZIMOVICH
Professor, Department of Electronics, "Khujand State University named academician B. Gafurov", Khujand, Tajikistan
Annotation. This paper presents the results of an experimental study of the dependence of the cooling kinetics of bronze parallelephedron samples on the spatial axes. It is found that during natural air cooling the main mechanisms are convection heat transfer, heat conduction and radiant release. The characteristic cooling time due to radiant flow is shorter than that due to conduction and convection. It is shown that the coefficient of heat transfer during natural air cooling of metal samples in all directions is the same.
Key words: cooling method, cooling kinetics, bronze, heat transfer coefficient, spatial directions.
So far in the research laboratory "Physics of Condensed State" named after Professor Narzullaev B.N. Research Institute of TNU studied the kinetics of cooling of metal samples with a single thermocouple, that is, measured the temperature only on the cylinder axis [1-9]. It was of interest how the temperature of the parallelepiped will change in three directions with time. For this purpose we investigated the kinetics of cooling of a bronze sample in the shape of a parallelepiped relative to its x, y and z axes. The main alloying element in bronze is tin.
EXPERIMENTAL TECHNIQUE
The cooling method was chosen to study the kinetics. This method is based on Newton-Kirchhoffs law of external heat conduction.
Measurement of the sample temperature from the cooling time was performed on an apparatus, the principle of operation of which is described in detail in [10,11]. The relative error of temperature measurement in the range from 400С to 4000С was ± 1%, and in the range from 4000С to 1000°С ± 2.5%. Subtract the ambient temperature AT=T-T from the measured temperature of the sample. Then plot the temperature difference between the sample and the environment as a function of time: AT=f(x). All processing of measurement results was performed on computer using Microsoft Office Excel, and graphs were plotted and processed using Sigma Plot 10 software.
RESULTS AND DISCUSSION
The temperature dependence of parallelepiped bronze samples on cooling time in a wide temperature range was investigated by the cooling method.
As an example, in Figure 1 shows the cooling curves of a parallelepiped bronze specimen 2.4 cm wide, 4.2 cm long, and 0.9 cm thick relative to the z axis. Processing the graph using the Sigma Plot program showed that it is best described by an equation with 7 parameters:
t = t0+ AT1e-T/Ti + AT2e-T/T2 + A T3e-r/r3, (1) where t0 is the ambient temperature, AT1, AT2, AT3 is the temperature difference between the heated sample and the environment at the start of measurements for radiation, heat conduction and convection processes, T1, T2 and T3 is the cooling constant for these heat transfer processes.
Formula (1) shows that heat is transferred to the environment simultaneously in three ways and the amount of heat transferred is proportional to the surface area of the sample, the temperature difference between the body and the environment, and the corresponding heat transfer coefficient for any heat transfer mechanism.
Below the graphs are the regression coefficient, the value of the parameters included in this equation and the standard error.
Figure 1. Dependence of the temperature of a bronze sample on cooling time relative to the z axis
R Rsqr
1,0000 1,0000
Adj Rsqr Standard Error of Estimate
1,0000 0,6383
Coefficient
Std. Error t
P
T0 299,0 0,5339 559,9819 <0,0001
ÙT1 345,3 3,3005 104,6256 <0,0001
1/т10,0218 0,0003 75,2099 <0,0001
ДТ2 367,1 7,7710 47,2362 <0,0001
1/т20,0046 0,0001 39,4159 <0,0001
ДТ3 256,2 10,3697 24,7083 <0,0001
1/т30,0016 4,0383E-005 39,0269
<0,0001
Figure 2 shows the cooling curves due to thermal radiation, thermal conductivity and convective heat transfer.
Figure 2. Dependence of the temperature of a bronze sample on the cooling time relative to the z-axis due to thermal radiation (blue), thermal conduction (red) and convection (violet)
Figure 3 shows the cooling rate curves due to thermal radiation, thermal conductivity and convective heat transfer.
Figure 3. Time dependence of the cooling rate of a bronze sample relative to the z-axis due to thermal radiation (purple), thermal conduction (blue) and convection (red)
Figure 4. Dependence of the temperature of a bronze sample on cooling time relative to the x axis
Standard Error of Estimate
0,7079
P
<0,0001 <0,0001
R Rsqr Adj Rsqr
1,0000 1,0000 1,0000
Coefficient Std. Error t
T0 297,62 0,8313 358,0215 AT1 317,50 2,8839 110,0925
1/^0,0232 ДТ2 355,20 1/т20,0041 ДТ3 237,14
0,0003 14,9195 0,0001 17,0710
1/т3
0,0016 6,7663E-0
67,1406 23,8076 29,4097 13,8916 23,0209
<0,0001 <0,0001 <0,0001 <0,0001 <0,0001
Figure 5. Dependence of the temperature of the bronze sample on the cooling time about the x-axis due to thermal radiation (blue), thermal conduction (red) and convection (green)
Figure 6. Time dependence of the cooling rate of a bronze sample about the x-axis due to thermal radiation (blue), conduction (red) and convection (black)
Figure 7. Dependence of the temperature of a bronze sample on cooling time relative to the y axis
R Rsqr Adj Rsqr
1,0000 1,0000 1,0000
Standard Error of Estimate
0,5474
Coefficient Std. Error
1/тз
T0 296,1 AT 374,8 1/T10,0225 AT2 391,2 1/T20,0045 AT3 231,3
1,2816 3,2132 0,0003 14,6787 0,0002 17,1088
t
231,0213 116,6338 68,9676 26,6518 29,8030 13,5184
P
<0,0001 <0,0001 <0,0001 <0,0001 <0,0001 <0,0001
0,0016 8,3383E-005
18,8765
<0,0001
Figure 8. Dependence of the temperature of the bronze sample on the cooling time about the y-axis due to thermal radiation (blue), thermal conduction (red) and convection (green)
Figure 9. Dependence of the cooling rate of a bronze sample on time relative to the y-axis due to thermal radiation (blue), conduction (red) and convection (black)
The table shows the values of the parameters included in equation (1).
axis AT1, К т1, с ДТ2, К Т2,С ДТз, К Тз,С to, 0С
x 317,5 42,0 355,2 232,5 237,1 625 24,6
y 374,8 44,4 391,2 222,2 231,3 625 23,1
z 345,3 42,9 367,1 208,3 256,2 625 17,0
Figure 10 shows for comparison the cooling curves with respect to t
ie x, y, z axes.
Figure 10. Dependence of sample temperature on cooling time about the x, y and z axes
As can be seen from the figure, the cooling of the sample is isotropic - does not depend on the direction.
CONCLUSION
The influence of the direction of parallelepiped bronze specimens on the time and rate of spontaneous air cooling has been studied. It is assumed that the samples are cooled by thermal conduction, convective heat transfer and thermal radiation. The characteristic cooling time due to radiation is less than the characteristic cooling time due to thermal conduction and convection. The effect of thermal radiation on the cooling process is noticeable at high temperatures.
The results obtained show that the heat transfer coefficient for natural air cooling of metal samples is the same in all directions.
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