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EFFECT OF THE SIZE OF AV 98 ALUMINUM CYLINDRICAL SPECIMENS ON THE
COOLING KINETICS
TURAKHASANOV ISFANDIYOR TURAKHASANOVICH
Senior lecturer of the department theoretical foundations of radio and electrical engineering, Tajik Technical University named after academician M.S. Osimi, Dushanbe, Tajikistan
NIZOMOV ZIYOVUDDIN
Chief researcher, S.U. Umarov Physical-Technical Institute of the National Academy of Sciences
of Tajikistan, Dushanbe
SODATDINOV SHAHNAVOZ SADRIDINOVICH
Competitor of the Department of Condensed Matter Physics named after Professor Narzullaev B.N., Research Institute of the Tajik National University, Dushanbe, Tajikistan
MIRZOEV FAYZALI MULLOJONOVICH
Candidate of Physical and Mathematical Sciences, senior lecturer of the department theoretical
foundations of radio and electrical engineering
Tajik Technical University named after academician M.S. Osimi, Dushanbe, Tajikistan
Annotation. The results of the study of the influence of the size of cylindrical samples of AV grade aluminum on the time and rate of their cooling are presented. It has been found out that during natural air cooling, the main mechanisms are convection heat transfer and radiation. The characteristic cooling time due to radiation is less than due to convection. The contribution of thermal radiation to the cooling process is noticeable at high temperatures. It was found that the characteristic times of cooling due to radiation and convection increase with increasing volume-to-area ratio of the sample.
Key words: aluminum grade AV 98, cooling, convection, thermal radiation, influence of size, temperature dependence.
Due to its low density and high specific strength, aluminum is widely used in various industries [1-3]. In our laboratory, the thermophysical properties of pure metals alloyed with REM and AEM aluminum alloys were previously experimentally studied [4-8]. In all these works, the cylindrical specimens had a constant size (diameter d=1.6 cm and height h=3.0 cm). The study of the mechanical properties of metals and alloys in [9-13] shows that the use of the results of laboratory studies of samples of small sizes and those used in technology in most cases do not coincide. There is practically no data in the literature on the influence of the sample size on its thermal characteristics.
At present, the theory of the dependence of the cooling time on the size of the samples has not been developed. Therefore, the accumulation of experimental data on the effect of sample size on the process of heat transfer with natural heat removal is relevant and timely. The purpose of this work is to study the influence of the size of cylindrical samples of aluminum grade AV 98 on the kinetics of their cooling and to elucidate the mechanism of heat removal.
Object of study. Aluminum grade AV 98. The samples had a cylindrical shape with a height of 3.368 cm and a diameter of 1.5 cm; 2.0 cm; 2.5 cm; 3.0 cm; 3.5 cm and 4.0 cm.
EXPERIMENTAL TECHNIQUE
The cooling method was chosen to study the kinetics. This method is based on the Newton-Kirchhoff external heat conduction law.
The measurement of the sample temperature from the cooling time was carried out on the installation, the principle of operation of which is described in detail in [5, 14]. The relative temperature measurement error in the range from 400 C to 4000 C was ± 1%, and in the range from 4000 C to 10000 C, ± 2.5%. Subtract the ambient temperature AT=T-To from the measured sample temperature. Next, we plot the dependence of the temperature difference between the sample and the environment on time: AT=f(x). All processing of the measurement results was carried out on a computer using the Microsoft Office Excel program, and the graphs were built and processed using the Sigma Plot 10 program.
RESULTS AND ITS DISCUSSION
The cooling method was used to study the dependence of the temperature of cylindrical samples of aluminum grade AV 98 of various diameters on the cooling time in a wide temperature range. The experimentally obtained time dependences of the temperature of the samples are described with a fairly good accuracy by an equation of the form [5]:
AT = A7\ e-T/Ti + A72 e-VT2 (1)
where A7\, AT2 - are the temperature difference between the heated sample and the environment at the start of measurements, t1 u t2 - are the cooling constant for the first and second heat transfer processes.
Formula (1) shows that heat is transferred to the environment simultaneously in two 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.
Differentiating (1), we obtain a formula for calculating the cooling rate: — = -— e-7ri-AZk e-Tr2 . (2)
dr T1 T2
As an example, in fig.1 shows the dependence of the temperature of a sample of aluminum
grade AV 98 with a diameter of 1.5 cm on the cooling time.
Fig. 1. Dependence of the temperature difference of a cylindrical sample of aluminum grade AV 98 with a diameter of 1.5 cm and the environment on the cooling time.
Figures 2-3 show the dependences of the temperature difference between the samples and the environment AT, cooling due to radiation AT1 and convective heat transfer AT2 for cylindrical samples of diameters 1.5 and 3.5 made of aluminum grade AV 98.
Fig.2. The dependence of the sample temperature on the cooling time for aluminum grade AV 98
with a diameter of 1.5 cm.
Fig.3. The dependence of the sample temperature on the cooling time for aluminum grade AV
98 with a diameter of 3.5 cm.
As can be seen from the figures 2 and 3, the cooling process due to thermal radiation proceeds faster than in the case of convective heat transfer. The contribution of thermal radiation to heat exchange with the environment is noticeable at high temperatures.
As an example, Figure 4 shows the dependence of the cooling rate on time for a sample of AV 98 aluminum with a diameter of 4.0 cm.
Fig.4. The dependence of the cooling rate on time for a sample of aluminum grade AV 98
with a diameter of 4.0 cm.
Table 1 shows the found values of the constants in the equation for the dependence of the sample temperature (1) and the cooling rate (2) on time for samples of aluminum grade AV 98.
Table 1. Value of constants in equation (1) and (2)
Diameter, m Ti - То, K T1,S T2 - То, K T2,S T1-T0 К Ti , s T2-T0 К T2 , S
0,015 164,0 39,84 440,6 454,54 4,12 0,97
0,02 166,8 47,39 441,0 660,00 3,52 0,67
0,025 163,3 67,57 441,1 820,33 2,42 0,54
0,03 156,1 108,20 444,2 940,23 1,44 0,47
0,035 155,0 180,64 445,0 1028,00 0,85 0,45
0,04 155,0 333,33 445,5 1095,00 0,46 0,43
Figures 5 and 6 show the dependence of the characteristic cooling time due to thermal radiation and convective heat transfer on the ratio of the sample volume to its surface area V/S for
AV 98 grade aluminum.
Fig. 6. Dependence of the characteristic cooling time due to irradiation on V/S for AV 98
aluminum specimens.
Processing of the curved dependence of the characteristic cooling time due to irradiation on V/S for aluminum samples of different grades using the Sigma Plot 10 program showed that it is expressed by the equation:
r1 = r0 + aebx ,
where x=V/S, r0 =37,63 s; a=0,05 s; b=13,66 s/cm. Regression coefficient R=0,9997.
Fig.5. Dependence of the characteristic cooling time due to convective heat transfer on V/S
for AV 98 aluminum specimens.
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Processing the obtained results on the dependence of the characteristic cooling time due to convective heat transfer on V/S for samples made of AV 98 grade aluminum showed that it obeys a cubic equation of the type (x=V/S, cm): т2 = r0 + ax + bx2 + cx3,
где:т0 = -646,43 s; a = 4343,07 —, b = -2433,25 с = -113,06
cm cm2 cm3
CONCLUSION
The effect of the size of cylindrical specimens of AV 98 aluminum on the time and rate of spontaneous air cooling has been studied. It is assumed that the samples are cooled due to convective heat transfer and thermal radiation. The characteristic cooling time due to radiation is less than the characteristic cooling time due to convection. The effect of thermal radiation on the cooling process is noticeable at high temperatures. It has been established that the characteristic times of cooling due to thermal radiation and convective heat transfer increase nonlinearly with an increase in the volume to area ratio of the sample. The regularities found confirm the results obtained by us for samples made of aluminum grades A6 and A0 [15-17].
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