ESTIMATION OF THE CONTRIBUTION OF HEAT RADIATION AND CONVECTIVE HEAT EXCHANGE FOR ALUMINUM OF VARIOUS DEGREES OF PURITY WITH NATURAL AIR HEAT DISCHARGE Текст научной статьи по специальности «Физика»

UDK 536.2

ESTIMATION OF THE CONTRIBUTION OF HEAT RADIATION AND CONVECTIVE HEAT EXCHANGE FOR ALUMINUM OF VARIOUS DEGREES OF PURITY WITH NATURAL AIR

HEAT DISCHARGE

NIZOMOV ZIYOVUDDIN

Chief researcher, S.U. Umarov Physical-Technical Institute of the National Academy of Sciences of

Tajikistan, Dushanbe

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

AVEZOV ZUBAYDULLO IMOMOVICH

Candidate of Technical Sciences, senior lecturer of the department of physics, Tajik Technical University named after academician M.S. Osimi, Dushanbe, Tajikistan

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

The cooling method was used to study the time dependence of the temperature of aluminum of different purity in the temperature range from 300 to 873 K. It is shown that the process of cooling the samples in all cases is carried out according to the convective and radiative mechanisms of heat exchange with the environment, which have characteristic relaxation times. A numerical estimate of the relaxation times of convective heat transfer and thermal radiation for the studied samples is carried out. For the first time, the coefficients of convective heat transfer and thermal radiation for metals are determined; the contributions of thermal radiation and convective heat transfer in the process of cooling aluminum of different purity are estimated. It is shown that with increasing temperature the fraction of thermal radiation in the cooling coefficient of metals increases. It was revealed that the values of the thermophysical parameters of aluminum of different degrees of purity are significantly influenced, mainly by the amount of iron and silicon present in them.

Key words: cooling, thermal radiation, convective heat transfer, temperature dependence, aluminum, impurities.

INTRODUCTION

The thermophysical properties of aluminum and its alloys, as a strategic material, represent the most important branch of solid state physics, on the solution of urgent problems of which many fundamental problems of the thermodynamics of condensed media, unresolved until now, depend, especially if we take into account their exceptional importance from a scientific and technical point of view [1 -6]. Research in this direction is necessary to create many new composite materials based on aluminum with better and fundamentally new physical and technological properties [7-11].

However, unfortunately, until now there is no unified theory that satisfactorily describes the dependence of the thermophysical characteristics of metals on their chemical composition [12-14]. In such a situation, it is the experimental study of the thermophysical properties of metals, in particular aluminum of various degrees of purity, that comes to the fore. Such studies will undoubtedly contribute to a broader practical application of precisely domestic aluminum for the needs of the national economy of Tajikistan, and not only. At the start of this work, there was no information in the literature on systematic experimental studies of the dependences of the thermophysical parameters of aluminum on the degree of its purity and types of impurities, which once again confirms the relevance of this study.

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Research objects and research methods

As an object of research, we selected samples of technical purity aluminum produced by the State Unitary Enterprise "Tajik Aluminum Company (SUE TALCo). The choice of objects is due to the wide prospect of using domestic aluminum in various fields of engineering and technology.

In work [15] it was found that the main components of the heat transfer coefficient with natural air heat removal of aluminum, copper and zinc are convective heat transfer and thermal radiation. In this paper, an assessment of these contributions is given in the cooling regime of aluminum of different purity degrees.

All samples were obtained from the physical laboratory of the State Unitary Enterprise TALCo. The chemical composition of the samples was determined using a Spectrolab spectrometer [16]. For greater reliability, the samples were additionally subjected to X-ray spectral analysis using a TERMO ARL-9900 X-ray apparatus (Kazakhstan). The elemental composition of the samples is shown in Table 1.

Table 1. Elemental composition of samples

№ Sample Si Fe Cu Mn Mg Zn Ga Ti Al

213 0,15 0,22 0,002 0,006 0,0074 0,01 0,016 0,009 99,61

218 0,17 0,24 0,002 0,007 0,0076 0,01 0,014 0,008 99,57

127 0,18 0,18 0,002 0,008 0,0068 0,01 0,012 0,006 99,62

26 0,21 0,26 0,002 0,009 0,0077 0,01 0,013 0,007 99,51

216 0,14 0,14 0,002 0,006 0,0068 0,01 0,012 0,006 99,70

128 0,15 0,14 0,002 0,006 0,0069 0,01 0,012 0,006 99,69

121 0,14 0,13 0,002 0,007 0,0066 0,01 0,012 0,006 99,71

21 0,27 0,32 0,003 0,008 0,0078 0,01 0,014 0,007 99,39

22 0,22 0,47 0,003 0,009 0,0076 0,02 0,013 0,008 99,28

27 0,20 0,56 0,003 0,009 0,0074 0,02 0,012 0,009 99,21

29 0,19 0,54 0,004 0,009 0,0075 0,02 0,012 0,009 99,24

118 0,21 0,68 0,004 0,01 0,0074 0,02 0,013 0,009 99,07

400 0,276 0,414 0,0035 0,0065 0,006 0,0123 0,0099 0,0113 99,27

800 0,109 0,129 0,0022 0,0045 0,0058 0,012 0,0095 0,0095 99,73

79 0,155 0,176 0,0032 0,0049 0,006 0,0126 0,0098 0,0098 99,63

30300 0,328 1,905 0,0057 0,013 0,0063 0,013 0,0096 0,0105 97,72

0,33 0,096 0,079 0,003 0,0042 0,0067 0,0132 0,0098 0,0094 99,79

407 0,109 0,16 0,003 0,0041 0,0077 0,0137 0,0096 0,0096 99,69

65 0,175 0,254 0,003 0,0056 0,0076 0,0137 0,0098 0,0099 99,53

The cooling method [19] was used to study the time dependence of the temperature of the samples in the temperature range from 300 to 873 K. The samples under study had a cylindrical shape with a diameter of 16 mm and a height of 30 mm. The relative error of temperature measurement in the range from 40 °C to 400 °C was ± 1%, and in the range from 400 °C to 1000 °C ± 2.5%. All processing of the measurement results was carried out using a special program in MS Excel. The graphs were built and processed using the Sigma Plot program.

To calculate the heat capacity of aluminum of various purities according to the Neumann-Kopp rule, data on the temperature dependence of its components are required. Therefore, using the Sigma Plot 10 program, processing the available literature data on the heat capacity of aluminum, iron, silicon, zinc, copper, magnesium, manganese and titanium at various temperatures [4], we obtained an equation for the temperature dependence of the specific and molar heat capacities, enthalpy, entropy and Gibbs energy [20].

For the convenience of using the obtained regularities in engineering calculations, the dependences of the thermodynamic function on the variable x = ((T-300)) /100 were used. Then, a graph of C (T) versus x is plotted. After statistical processing of the graph, the following formula was obtained

C(T) = a'1 + b[ x + c[x2 + d'xx3, (1)

where: a[ = C(300) b[ = b0 • 102, = c0 • 104, d[ = d'0 • 106.

3 О

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The coefficients of equation (1) are shown in Table 2. The last column shows the value of the regression coefficient.

Table 2. Values of coefficients of equation (1)

Metal a' bi ci d' R

Si 727,73 71,55 -11,00 0,724 1,0000

Fe 448,41 54,10 -7,000 1,300 1,0000

Cu 388,47 17,94 -2,000 0,220 1,0000

Mn 474,33 39,21 -3,000 0,121 1,0000

Mg 1028,69 50,10 -0,370 0,070 1,0000

Zn 393,96 15,52 -0,160 0,760 1,0000

Ti 531,29 21,68 2,000 -0,419 1,0000

In the future, we used the obtained graphs and equations for the heat capacity to calculate the heat capacity according to the Neumann-Kopp rule and to explain the regularities of the effect of impurities on the thermophysical properties of aluminum.

RESULTS AND DISCUSSION

The experimentally obtained time dependences of the temperature of the samples are described with a fairly good accuracy by an equation of the form:

T T

Г = Го+ДГо1е" + ДГо2е" , (2)

where: To is the ambient temperature, AT01 , AT02 are the amplitudes of the temperature change of the first and second processes, n and 12 are the characteristic cooling times of the samples.

The exponential dependence T (т) in formula (2) shows that heat is transferred simultaneously in two ways and the amount of heat transferred is proportional to the surface area of the sample, the difference in body and ambient temperatures, as well as the corresponding heat transfer coefficient for any mechanism of heat transfer (thermal conductivity, convection, or radiation). The transfer of heat from a warmer body to a less heated body is a relaxation process. In our case, the heated body transfers its heat to the body with infinite heat capacity - the environment. Therefore, the ambient temperature can be considered constant To. Then, the equation CmdT = -aS (T-To) dT can be written in the form

d(T — T0) aS

-=--dr,

T — T0 Cm

where: m and S are respectively the mass and surface area of the sample, is its temperature, C is the specific heat and a is the heat transfer coefficient.

Cm

Considering — = r1 = const, we obtain the law of body temperature change from time т of the form:

T = T0 + AT01e-T/ri или ДТ = AT01e-x/xi, (3) where: ДТ is the difference between the temperatures of the heated sample and the environment, ДТ01 is the difference between these temperatures at the start of measurements (at т = 0), ti is a constant numerically equal to the time during which the temperature difference decreases by a factor of . The n is proportional to the product of the mass m and the heat capacity C of the body and is inversely proportional to the heat transfer coefficient and the total surface area of the body S. If we assume that cooling occurs due to convective heat transfer and thermal radiation, we obtain equation (2). Differentiating (2), for the cooling rate we obtain

dT = -(A7oie-T/Tl +A7o2e-T/T2), (4) dr V Ti T2 /

where: ÀToi/t! h AT02 /t2 are, respectively, the contributions of convective heat transfer and thermal radiation to the cooling rate at the initial moment.

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Further, knowing the composition of the samples, the heat capacity values were calculated according to the Neumann-Kopp rule. Using these values and the values of the cooling rate, the heat transfer coefficients a (T) were calculated by the formula:

Table 3 shows the values of AT01, ti, AT02, T2, AT01 / ti, ЛТ02/ T2 of equations (2) and (4) for the studied aluminum samples.

Table 3. Experimental values AT01, ti, AT02, T2, AT01 / ti, AT02/ T2

№ Sample AT01, K Ti,S AT02, K T2S AT01 / T1,K/s At02/t2,K/S То, К

213 383,13 625,00 222,31 227,27 0,613 0,978 298,9

218 381,37 625,00 228,03 222,22 0,610 1,026 299,2

127 383,11 588,24 227,58 212,77 0,651 1,069 299,4

26 353,83 666,67 256,48 238,09 0,531 1,077 298,1

216 375,22 625,00 235,73 227,27 0,600 1,037 298,4

128 388,78 588,24 223,02 204,08 0,661 1,093 299,2

121 384,12 625,00 225,42 227,27 0,615 0,992 299,1

21 388,64 588,24 220,09 208,33 0,661 1,060 299,7

22 378,63 588,24 234,45 208,33 0,644 1,125 298,5

27 391,66 588,24 215,33 200,00 0,666 1,077 300,1

29 386,28 588,24 226,41 208,33 0,657 1,087 299,3

118 375,98 625,00 231,05 238,09 0,602 0,970 298,5

400 388,47 588,24 225,43 204,08 0,660 1,105 288,7

0,33 345,50 666,67 262,20 270,27 0,518 0,970 294,1

79 407,38 588,24 201,64 208,33 0,692 0,968 296,8

407 420,31 588,24 195,24 212,77 0,714 0,918 288,8

800 374,32 625,00 230,72 238,10 0,599 0,969 293,4

30300 353,40 666,67 244,04 238,10 0,530 1,025 292,5

Figures 1 and 2 show the time dependences of A^ (a^ = AT01exp- -(t/tt)), a T2 (aT2 = AT02exp~(T/r2)) and sample cooling rate 0.33 for convective heat transfer and thermal radiation.

Fig. 1. Dependence of the temperature of Fig. 2. Dependence of the cooling rate of aluminum sample 0.33 on time during cooling for aluminum sample 0.33 on time for the first the first and second processes. and second processes

As can be seen from Table 2 and Figure 1, the values of the relaxation times of these processes differ. Cooling due to convective heat transfer is slow, and with heat radiation - very fast.

It should be noted that using the experimental values of the cooling rate, it is possible to determine only the ratio of the heat transfer coefficient to the heat capacity of the sample:

a(T)/C(T) =

m(dT/dr) S(T-To) .

(7)

Figure 3 shows the dependence of a/C on temperature for samples aluminum of different purity. According to the Newton-Kirchhoff law CmdT = — aS(T — T0)dx, we get:

Cm — = —aS(T — T0), where a = a1 + a2 and — = ( —) + (—) . dr 0 12 dT \drJi \dr/2

The amount of heat leaving due to convective exchange is Cm (^f) = —a1S(T1 — T0), and due to thermal

\dr/1

radiation is Cm (—) = —a2S(T2 — T0).

\dT/2

Using the values of the cooling rate and specific heat capacity (Table 4), we calculate the heat transfer

coefficient ai(T) =

Cm

(Э Ст(^) and emissivity a2(T) =-—

S(T-To)

S(T-To) '

a/C, kg m-2 s"1

0,024 -, 0,022 -0,020 -0,018 0,016 0,014 -0,012 -0,010 -0,008

Т-300, К

0

Figure 3. Dependence of a/C on temperature for aluminum of different purity.

Coefficient values in the equation

Table 4

00

200

300

400

500

600

700

Ср(Г - 300) = a0 + Ь0(Г - 300) + с0(Г - 300)2 + d0(7 - 30C >)3

ao bo -co do, 10-7

0.33 902.5725 0.4737 0.0004 8.6394

30300 893.8240 0.4755 0.0004 8.7160

In fig. 1-4 show the temperature dependences of the coefficients of heat transfer ax and radiation a2 for aluminum of different purity.

The temperature dependence of the heat transfer coefficient for convective heat transfer ax and the emissivity a2 is described by the equation

a = a + b(T- 300) + c(T - 300)2 + d(T - 300)3 . (3)

Table 3 shows the values of a, b, c, and d in equation (3).

Figure: 4. Dependence of the heat transfer coefficient during convective exchange (1) and the emissivity

(2) on temperature for aluminum sample 0.33.

Processing results for Al-0.33. m = 16g, h = 31mm, d = 16mm, t = 19.5C.

a2 = 8.2305 + 0.0268(7 - 300) - 7.2046 10~Ь(Т - 300)2 - 2.7492 10~9(T - 300)

-9/

R Rsqr Adj Rsqr

1.0000 0.9999 0.9999

Coefficient Std. Error

a 8.2305 0.0104

b 0.0268 0.0003

с -7.2046E-006 2.5095E-006

d -2.7492E-009 5.5421E-009

a1 = 9.4191 - 0.0050 (T - 300) + 1.1327 10-5

Standard Error of Estimate

0.0173 t P

794.8778 <0.0001 84.7615 <0.0001 -2.8709 <0.0076 -0.4961 <0.6236

(T - 300)2 - 8.4979 10

-9

VIF

11.8499< 272.9261< 912.4721< 293.2695<

(Г - 300)3

R

0.9998

a b с d

Rsqr

0.9995

Coefficient

9.4191 -0.0050 1.1327E-005 -8.4979E-009

Adj Rsqr

0.9995

Std. Error

0.0030 9.2591E-005 7.3534E-007 1.6240E-009

Standard Error of Estimate

0.0051

t P VIF

3104.3878 <0.0001 11.8499<

-53.8915 <0,0001 272.927<

15.4032 <0.0001 912.474<

-5.2327 <0.0001 293.270<

3

Figure: 5. Dependence of the heat transfer coefficient during convective exchange (1) and the emissivity

(2) on temperature for aluminum sample 30300.

Processing results for Al-30300. m=16g, h=31mm, d=16mm, t=19C.

a2 = 0.0210(7 - 300) + 4.9393 10-5(7 - 300)2 - 6.1534 10-8(7 - 300)3

R

0.9996

a b c d

Rsqr

0.9992 Coefficient

0.0000 0.0210 4.9393E-005 -6.1534E-008

Adj Rsqr

0.9992 Std. Error

0.0004 1.8608E-006 2.4854E-009

Standard Error of Estimate

0.1169 P VIF

t

59.6355 26.5444 -24.7580

<0.0001 <0.0001 <0.0001

65.4771< 292.8962< 115.8242<

a1 = 12.0685 - 0.0086 (7 - 300) + 1.2158 10-6 (7 - 300)2 + 8.1913 10-9 (7 - 300)3

R Rsqr Adj Rsqr Standard Error of Estimate

1.0000 1.0000 1.0000 2.5060E-014

Coefficient Std. Error t P VIF

a 12.0685

b -0.0086 c 1.2158E-006

d 8.1913E-009

Table 3

Values of a, b, c and d for the studied samples.

Sample a b c. 10-5 d. 10-8

Al-30300 12.0685 -0.0086 -0.1215 0.8191

«2 0.0000 0.0210 4.9393 6.1534

Al-0.33 9.4191 -0.0050 1.1327 -0.8498

«2 8.2305 0.0268 -0.7205 -0.2749

For comparison, Fig. 6-7 show the contribution of thermal radiation and convective exchange for some of the studied samples.

Fig. 6. Temperature dependence of the convective exchange coefficient for aluminum samples of

different purity.

Fig. 7. Dependence of the thermal radiation coefficient on temperature for aluminum samples of various

purity degrees.

Using the values of the cooling rate and heat capacity, the coefficients of convective heat transfer and thermal radiation are calculated.

Dependence of the heat transfer coefficient for convective heat transfer ai and emissivity a2 on temperature is described by the equation:

a = a + b(T- 300) + c(T - 300)2 + d(T - 300)3 . (11)

As can be seen from the figures, natural air cooling has a low coefficient of convective heat transfer - up to 9 - 13 BT/(m2K) and decreases with temperature and with an increase in aluminum purity and silicon concentration. Using the formula x = 100%, where a = ai + a2, the share of thermal radiation in the

total heat transfer was estimated. In fig. 8 shows the temperature dependence of the fraction of thermal radiation in cooling for aluminum of different purity.

технические науки

<х2/(а.-мх,),% 80-i

20 -

60 -

40 -

0

Т-300, к

о

100

200

300

400

500

600

700

Fig. 8. Temperature dependence of the fraction of thermal radiation in cooling for aluminum of different

purity.

As can be seen from the figures, with an increase in temperature during natural cooling, the proportion of thermal radiation increases.

Due to the lack of development of the theory describing possible changes in the thermophysical properties of substances, depending on its composition, quantitative estimates and qualitative explanations of the data obtained are still premature. The strongest effect on the thermodynamic functions is exerted by impurities, which differ significantly in mass and interaction potential from the atoms of the main substance.

The obtained reference data on the thermophysical parameters of aluminum can be used in calculating the thermophysical characteristics of composite materials and thermal modes of operation of metal structures and products at high temperatures;

The results obtained on the effect of impurities on the thermophysical characteristics of aluminum can become a good help in the development of the macroscopic theory of the thermal properties of metals, and the results on the dependence of the coefficients of convective heat transfer and thermal radiation on temperature can be a significant addition to the reference data bank on the thermophysical properties of metals.

CONCLUSIONS

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