CC BY
7
23. Nevljudov, I. Sh. Tehnologicheskoe obespechenie tochnosti razmerov pri formoobrazovanii plastmassovyh izdelij [Text] / I. Sh. Nev-ljudov, S. V. Sotnik // Jelektronnaja komponentnaja baza. Sostojanie i perspektivy razvitija. - 2009. - P. 183-186.
24. Nevljudov, I. Sh. Metod rascheta oformljajushhih detalej formoobrazujushhejosnastki dlja tehnologicheskogo obespechenija zhiznennogo cikla plastmassovyh izdelij RJeA [Text] / I. Sh. Nevljudov, A. A. Andrusevich, S. V. Sotnik // Radiotehnika. - 2009. -Issue 156. - P. 240-243.
25. Shah, V. Spravochnoe rukovodstvo po ispytanijam plastmass i analizu prichin ih razrushenija [Text] / V. Shah. - Sankt-Peterburg: Nauchnye osnovy i tehnologii, 2009. - 746 p.
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28. Gol'dberg, I. E. Puti optimizacii lit'evoj osnastki. Ee velichestvo lit'evaja forma [Text] / I. E. Gol'dberg. - Sankt-Peterburg: Nauchnye osnovy i tehnologii, 2011. - 360 p.
Розглянуто вплив геометри гшок тер-моелементiв на основн параметри i показ-ники надiйностi однокаскадного термое-лектричного охолоджуючого пристрою для рiзних перепадiв температури при тепловому навантаженн 2,0 Вт для характерних режимiв (^/1)тах i {^/12)тах. Показано, що для рiзних перепадiв температури при зменшенш видношення висоти гшки термо-елемента до площини и поперечного зрiзу ттенсивтсть вiдмов зменшуеться
Ключевi слова: термоелектричний охо-лоджуючш пристрш, показники надшнос-тi, перепад температури, геометрiя тер-моелементiв
Рассмотрено влияние ветвей термоэлементов на основные параметры и показатели надежности однокаскадного термоэлектрического охлаждающего устройства для различных перепадов температуры при тепловой нагрузке 2,0 Вт для характерных режимов (^/1)тах и (&/Р)тах. Показано, что для различных перепадов температуры при уменьшении отношения высоты ветви термоэлемента к площади ее поперечного сечения интенсивность отказов уменьшается
Ключевые слова: термоэлектрические охлаждающее устройство, показатели надежности, перепад температуры, геометрия термоэлементов -□ □-
UDC 621.362.192
[DOI: 10.15587/1729-4061.2017.85322|
ANALYSIS OF THE MODEL OF INTERDEPENDENCE OF THERMOELEMENT BRANCH GEOMETRY AND RELIABILITY INDICATORS OF THE SINGLE-STAGE COOLER
V. Zaykov
PhD, Senior Researcher, Head of Sector Research Institute «STORM» Tereshkova str., 27, Odesa, Ukraine, 65076 E-mail: gradan@i.ua V. Mescheryakov Doctor of Technical Sciences, Professor, Head of Department
Department of Informatics Odessa State Environmental University Lvivska str., 15, Odesa, Ukraine, 65016 E-mail: gradan@ua.fm Yu. Zhuravlov PhD, Senior Lecturer Department of technology of materials and ship repair National university «Odessa maritime academy» Didrikhsona str., 8, Odesa, Ukraine, 65029 E-mail: zhuravlov.y@ya.ru
1. Introduction
The problem of improving reliability of thermoelectric coolers used in electronics thermal condition control systems remains the pressing problem because of permanently toughening requirements to the present-day land-based and on-board equipment. Improvement of reliability indicators of thermoelectric coolers is realized according to various principles at various steps:
- in design engineering: according to parametric and design approaches;
- in production: by technology development;
- in operation: by selection of operation conditions.
2. Literature review and problem statement
Considerable attention to analysis of the problems of reliability of thermoelectric coolers [1, 2] is paid because viability of the entire system is directly determined by the working capacity of critical heat-loaded elements. The parametric approach is based on choosing thermoelectric materials [3, 4]
©
with parameters connected with the thermoelectric device (TED) reliability indicators [5, 6]. Current mode choice determines energy-related operation conditions [7] which are directly related with the cooler reliability indicators [8]. When the design approach is analyzed, the qualitative aspect of ensuring specified levels of reliability of thermoelectric coolers is only considered [9, 10]. At the same time, the model of interrelation between the basic parameters and the reliability indicators was established and developed [11]. This enables a comprehensive estimation of thermoelement branch geometry effect on the single-stage TED reliability for various operation conditions. Potentially, this approach enables choice of optimal thermoelement branch geometry. At the same time, failure rate must decrease and probability of failure-free operation of the cooler must increase taking into account restrictive requirements to size, weight and power consumption. Obtaining of a quantitative relation between thermoelement geometry and reliability indicators of thermoelectric coolers involves studies for various temperature gradients and operation conditions.
tance of the thermoelement branch, Ohm; e, o are averaged values of coefficient of thermal electromotive force, B/K and electrical conductivity, Cm/cm of thermoelement branch respectively; T0 is temperature of the heat-absorbing junction, K; B=I/Imax is the relative operating current, relative units; I is the value of operation current, A;
Q= AT = T - T0
ATmax ATmax
is relative temperature gradient, relative units; T is the temperature of the heat-generating junction, K;
aTmax = 0,5zT02
is the maximum temperature gradient K; Z is the averaged thermoelectric efficiency of thermoelement branch, 1/K;
g = ILR = e2 0T2|
3. The aim and tasks of the study
The aim of this work is to find design approaches to the improvement of reliability indicators through selection of an optimal geometry of thermocouple branches for different operation conditions.
To achieve this objective, solution of the following tasks is necessary:
- develop a reliability-oriented model linking reliability indicators with the geometry of thermoelement branches for various temperature gradients and the fixed thermal load for operation modes (Q0/I)max and (Q0/I2)max;
- determine the possibility of improvement of reliability indicators of the single- stage TEU in modes (Q0/I)max and (Q0/I2)max by selecting thermocouple branch geometry.
4. Development and analysis of the model of interrelation between reliability indicators and design and energy parameters in modes (Qo/I)max and (Qo/I2)max
4. 1. The model of interrelation between reliability indicators of the single-stage TED and thermoelement branch geometry
The ratio of thermoelement branch height l to cross-sectional area S called as thermoelement geometry is directly connected with the cooler reliability indicators. By varying operation current value, it is possible to ensure the cooler operation in all operation modes from the maximum cooling power Q0max to the minimum failure rate Xmin. Consider the effect of geometry in the most frequently used modes (Q0/I)max and (Q0/I2)max for various temperature gradients AT=0-60 K for a given heat load Q0=2,0 W.
To solve this problem, use the earlier developed relationships [11].
The cooling power of the thermoelectric cooling unit (TEU) can be represented as:
Q0 = nlLR (2B - B2-01 = ng(2B - B2-0),
(1)
where n is the number of thermocouples; Imax=eT0/R is the
maximum operating current, A; R = is electrical resis-
oS
is the maximum thermoelectric cooling power, W. The TEU power consumption can be expressed as:
W = 2ngB
B + ATax 0 T
(2)
The TEU refrigeration coefficient can be written down as: .Qo _ 2B-B2-0
E = -
W
2B
B + ATax 0 T
J-n
(3)
Relative failure rate can be expressed as: nB2 (0 + C1)
A i
where
b + at- 0
1+
at
2
-KT,
(4)
0
C = Q0 = Q0. 1 nlLR ng
is the relative heat load, relative units; KT is the significance coefficient depending on the temperature [11].
The probability of failure-free operation of TEU can be determined by the formula:
P=exp(-Xt), where t is the assigned resource, hr.
(5)
4. 2. Analysis of the simulation results
Calculation of the basic parameters and reliability indicators of the single-stage TEU for different ratios l/S = var in modes (Q0/I)max and (Q0/I2)max was conducted with the following starting data:
- heat load Q0=2 W;
- temperature of the heat-generating junction T=300 K;
- temperature gradient AT=10-60 K;
- Xo=340-8 1/hr, t=104 hr.
Calculation results are given in Tables 1, 2. At an equal heat load Q0 and temperature gradient AT:
ng=const (6)
for various thermoelement branch geometries l/S. 1) Mode (Q0/I) max
Analysis of the calculated basic parameters and reliability indicators has shown that with reduction in the ratio l/S
at a given temperature gradient AT and heat load Q0 in the mode (Q0/I) max
- maximum cooling power y increases (Fig. 1);
- operating current I increases (Fig. 1);
- the number n of thermoelements decreases (Fig 2);
- the voltage U drop decreases (Fig 2);
- the failure rate X decreases (Fig. 3);
- the failure-free operation probability P increases (Fig. 3) at constant values of power consumption W and refrigeration coefficient E.
Тable 1
Calculation data for basic parameters and reliability indicators of the single-stage TEU for various temperature gradients AT
at Т=300 K, heat load Q0=2.0 W in (Q0/I)max mode
l/S g, W n, pcs. Rx103, Ohm Imax, A I, A U, V I/I0 1x108, 1/hr P S=axb, mm
AT=10 K B=0.316; ©=0.1; KT=1.007; ATmax=101 K; ATmax/T0=0.35; W=1.03 W; E=1,94 e=1.99 V/K; c=920 Cm/cm; £=15.2 W/(cm-K) z=2.440-3 1/K
40.0 0.077 60.2 43.5 1.33 0.42 2.45 0.37 1.11 0.999889 1.0x1,0
20.0 0.154 30.2 21.7 2.66 0.84 1.23 0.185 0.555 0.999944 1.4x1,4
10.0 0.308 15.1 10.9 5.32 1.68 0.61 0.093 0.28 0,99997 2,0x2,0
4.5 0.577 6.8 4.89 11.8 3.73 0.28 0.042 0.125 0.999987 3.0x3,0
3.25 0.938 4.94 3.53 16.3 5.17 0,20 0.031 0.0915 0.9999909 3.5x3,5
2.0 1.54 3.02 2.17 26.6 8.4 0.123 0.019 0.057 0.9999943 4.5x4,5
AT=20 K B=0.463; ©=0.214; KT=1.011; ATmax=93.3 K; ATmax/T0=0.33; W=2.0 W; E=1.0; e=1.97 B/K; c=940 Cm/cm; £=15.3 W/(cm-K) z=2.3840-3 1/K
40.0 0.0715 55.8 42.6 1.30 0.60 3.33 1.35 4.0 0.99960 1.0x1,0
20.0 0.143 28.2 2.,3 2.60 1.2 1.67 1.08 3.2 0.99968 1.4x1,4
10.0 0.286 14.1 1.,64 5.2 2.4 0.83 0.54 1.62 0.99984 2.0x2,0
4.5 0.676 5.96 4.79 11.5 5.3 0.38 0.23 0.684 0.999932 3.0x3,0
3.25 0.880 4.57 3.46 15.9 7.4 0.27 0.175 0.525 0.999948 3.5x3,5
2.0 1.43 2.82 2.13 25.9 12.0 0.17 0.11 0.32 0.999968 4.5x4,5
1.0 2.86 1.41 1.06 52.0 24.1 0.083 0.055 0.165 0.999984 6.3x6,3
AT=40 K B=0.71; ©=0.5; KT=1.022; ATmax=79.8 K; ATmax/T0=0.31; W=5.9 W; E=0.34; e=1,94 B/K; c=980 Cm/cm; £=15,6 W/(cmK z=2,3740-3 1/K
40.0 0.0625 76.7 40.8 1.24 0.88 6.70 20.4 61.2 0.9939 1.0x1,0
20.0 0.125 38.5 20.4 2.47 1.75 3.4 10.2 30.6 0.99694 1.4x1,4
10.0 0.250 19.3 10.2 4.95 3.50 1.7 5.1 15.4 0.9985 2.0x2,0
4.5 0.577 8.7 4.6 11.0 7.80 0.76 2.3 6.9 0.99931 3.0x3,0
3.25 0.767 6.3 3.3 15.2 10.8 0.55 1.66 5.0 0.99950 3.5x3,5
2.0 1.220 3.9 2.0 24.7 17.5 0.34 1.02 3.0 0.99969 4.5x4,5
AT=60 K B=0.949; ©=0.9; KT=1.035; ATmax=66.8 K; ATmax/T0=0.28; W=47 W; E=0.0426; e=1.89 V/K; c=1030 Cm/cm; £=15.9 BT/(cmK z=2.32-10-3 1/K
40.0 0.053 389 38.8 1.17 1.10 42.7 332.6 997.8 0.9050 1.0x1,0
20.0 0.106 194.5 19.4 2.34 2.2 21.2 166.3 500.0 0.9512 1.4x1,4
10.0 0.212 97.3 9.7 4.67 4.4 10.6 83.2 250.0 0.9753 2.0x2,0
4.5 0.471 43.8 4.4 10.4 9.9 4.8 37.5 112.4 0.9888 3.0x3,0
3.25 0.652 31.6 3.2 14.4 13.7 3.4 27.0 81.0 0.9919 3.5x3,5
2.0 1.06 19.5 1.9 23.4 22.2 2.1 16.6 50. 0.9950 4.5x4,5
Fig. 1. Dependence of the single-stage TEU parameters y, I on the value of relation l/s at T=300 K, AT=40 K and Q0=2.0 W in the mode (Q0/I)max)
, pes 35 30 25 20 15 10 5 0
11
!
U, B
10 12 / S
14 16 18 20
Fig. 2. Dependence of parameters n, U of the single-stage TEU оn the value of relation l/s at T=300 K, AT=40 K and Q0=2.0 W in the mode (Qq/IW
Fig. 3. Dependence of the failure rate 1 (solid lines) and the probability Р of failure-free operation (dotted lines) of the single-stage TEU on the value of relation l/s at T=300 K, Q0=2.0 W and various values of AT in the mode (Q0/I)max
Fig. 4. Dependence of the operation current I of the single-stage TEU on the temperature variation AT at T=300 K, Q0=2.0 W and various values of relation l/s in the mode (Qq/IW
With the growth of the temperature gradient AT at a given heat load Q0 for different values of l/S:
- the maximum thermoelectric cooling power y decreases;
- the value of the operation current I increases (Fig. 4);
- functional dependence of thermoelement number n in the TEU on AT is minimal (Fig. 5);
- failure rate 1 increases (Fig. 6);
- probability P of failure-free operation decreases (Fig. 7). Operation current I increases with reduction of ratio l/S
(Fig. 8).
Fig. 5. Dependence of the number n of thermoelements in the single-stage TEU on the temperature variation AT at T=300 K, Q0=2.0 W and various values of relation l/s in the mode (Qq/IW
Fig. 6. Dependence of failure rate 1 of the single-stage TEU on temperature variation AT at T=300 K, Q0=2.0 W and various relations l/s in the mode (Q0/I)max
Fig. 7. Dependence of the probability Р of failure-free operation of the single-stage TEU on the temperature variation AT at T=300 K, Q0=2.0 W and various values of ratio l/s in the mode (Q0/I)max
Note that the reduction in ratio l/S from 20 to 10 for the mode (Qo/I)max at AT=40 K and Qo=2.0 W makes it possible to reduce failure ratio 1 by 50 % and therefore increase the probability P of failure-free operation. Besides, the value of the oper-
ation current I increases from 1.75 to 3.5 A, power consumption W and refrigeration coefficient E remain constant (W=5.9 W and E=0.34) and the number of thermoelements halves.
/, A 24
22 20
16 14 12 10
\T = 60 K
1 I
II
40 k
20 K.
\ OK
OK
0 2 4 6 8 10 12 14 16 18 20 22 (i/S)opt
Fig. 8. Dependence of the operation current I and the optimum value (l/s^pt of the single-stage TEU on the temperature gradient AT at T=300 K, Q0=2.0 W and various values of AT in the mode (Q0/I)max
2) Mode (Qo/I2) max-
Analysis of the calculated values of the basic parameters and reliability indicators has shown that with reduction in the ratio l/S at a given temperature variation AT and heat load Qo in the mode (Qo/I2)max:
- the maximum cooling power y increases (Fig. 9);
- the value of the operation current I increases (Fig. 9);
- the number of thermoelements n decreases (Fig. 10);
- the voltage drop U decreases (Fig. 10);
- the failure rate X decreases (Fig. 11);
- the probability P of failure-free operation increases (Fig. 11)at constant values of power consumption W and refrigeration factor E.
With the growth of temperature gradient AT at a given heat load Q0 for various values of l/S:
- the maximum thermoelectric cooling power y decreases;
- the value of the operation current I increases
(Fig. 12).
- the functional dependence of the number of thermoelements n in the TEU on AT has a pronounced minimum (Fig. 13) which can be explained by the growth of the cooling power per one thermoelement (Q0/n) for ATopt at the point of minimum;
- failure rate X increases (Fig. 14);
- probability P of failure-free operation decreases (Fig. 15).
Таble 2
Calculation data of the basic parameters and reliability indicators of the single-stage TEU for various temperature gradients
AT at Т=300 K, heat load Q0=2.0 W in the mode (Q0/I2)max
l/S g, W n, pcs. Rx103, Ohm Imax, A I, A U, V I/I0 1x108, 1/hr P S=axb, mm
1 2 3 4 5 6 7 8 9 10 11
AT=10 K B=0.1; ©=0.1; KT=1.007; ATmax=101 K; ATmax/T0=0.35; W=0.6 W; E=3.33; e=1.99 B/K; â=920 Cm/cm; œ=15.2 W/(cm-K) z=2.440-3 1/K
40.0 0.077 289.0 43.5 1.33 0.133 4.51 0.0094 0.028 0.9999972 1.0x1.0
20.0 0.154 144.7 21.7 2.66 0.266 2.26 0.0047 0.0141 0.9999986 1.4x1.4
10.0 0.308 72.2 10.9 5.32 0.532 1.13 0.00235 0.0070 0.99999997 2.0x2.0
4.5 0.682 32.6 4.9 11.8 1.18 0.51 0.00106 0.0032 0.99999987 3.0x3.0
2.0 1.54 14.5 2.17 26.6 2.66 0.23 0.00047 0.00141 0.99999986 4.5x4.5
AT=20 K B=0.214; ©=0.214; KT=1.011; ATmax=93.3 K; ATmax/T0=0.33; W=1.45 W; E=1.38; e=1.97 B/K; â=940 Cm/cm; œ=15.3 W/(cm-K) z=2.3840-3 1/K
40.0 0.0715 166.4 42.6 1.30 0.28 5.3 0.21 0.63 0.999937 1.0x1.0
20.0 0.143 83.2 21.3 2.60 0.56 2.64 0.104 0.31 0.99997 1.4x1.4
10.0 0.286 41.6 10.64 5.2 1.11 1.31 0.052 0.156 0.999984 2.0x2.0
4.5 0.676 17.6 4.79 11.5 2.46 0.59 0.022 0.066 0.9999934 3.0x3.0
2.0 1.43 8.3 2.13 25.9 5.54 0.26 0.010 0.03 0.999997 4.5x4.5
AT=30 K B=0.346; ©=0.346; KT=1.016; ATmax=86.8 K; ATmax/T0=0.32; W=2.8 W; E=0.71; e=1.96 B/K; â=970 Cm/cm; œ=15.5 W/(cmK z=2.3840-3 1/K
40.0 0.0675 131.1 41.2 1.28 0.443 6.32 1.545 4.63 0.999537 1.0x1.0
20.0 0.136 65.6 20.6 2.57 0.89 3.15 0.77 2.31 0.99977 1.4x1.4
10.0 0.272 32.8 10.3 5.14 1.78 1.57 0.385 1.155 0.99988 2.0x2.0
4.5 0.603 14.7 4.64 11.4 3.94 0.71 0.173 0.518 0.999948 3.0x3.0
2.0 1.36 6.5 2.0 25.7 8.89 0.315 0.0765 0.229 0.9999774 4.5x4.5
Continuation o^ble 2
1 2 3 4 5 6 7 8 9 10 11
AT=40 K B=0.5; 0=0.5; KT 1.022; ATmax=79.8 K; ATmax/T0=0.31; W=5.24 W; E=0.38; e=1.94 B/K; ô=980 Cm/cm; œ=15.6 W/(cm-K) z=2.3740-3 1/K
40.0 0.0625 128.0 40.8 1.24 0.62 8.4 7.98 23.6 0.9976 1.0x1.0
20.0 0.125 64.0 20.4 2.47 1.24 4.22 3.94 11.8 0.9988 1.4x1.4
10.0 0.25 32.1 10.2 4.95 2.48 2.10 1.98 5.94 0.99941 2.0x2.0
4.5 0.557 14.4 4.6 11.0 5.50 0.95 0.89 2.67 0.999973 3.0x3.0
2.0 1.25 6.4 2.04 24.7 12.4 0.42 0.40 1.20 0.99988 4.5x4.5
AT=60 K B=0.9; 0=0.9; KT=1.035; ATmax=66.8 K; ATmax/T0=0.28; W=46.1 W; E=0.043; e=1.89 B/K; 0=1030 Cm/cm; ®=15.9 W/(cm-K) z=2.3240-3 1/K
40.0 0.053 420 38.8 1.17 1.05 39.0 294.6 883.8 0.9154 1.0x1.0
20.0 0.106 210 19.4 2.34 2.11 19.7 147.3 442.0 0.9568 1.4x1.4
10.0 0.212 105 9.7 4.67 4.20 11.0 73.7 221.1 0.9781 2.0x2.0
4.5 0.471 47.2 4.4 10.4 9.4 4.9 33.2 99.6 0.9901 3.0x3.0
2.0 1.06 21.0 1.9 23.4 21.1 2.2 14.8 44.4 0.9956 4.5x4.5
y, W 1,0 0,8 0,6 0,4 0,2 0,0
T, '
1 A 10 8
6 4
2 0
10
l/S
12 14 16 18 20
Fig. 9. Dependence of parameters y, I of the single-stage TEU on the value of ratio l/s at T=300 K. AT=40 K and Q0=2.0 W in the mode Q0/I2)max
/1, pes.
60 50 40 30 20 10 0
n
U
a, b 6 5 4 3 2 1 0
10
l/S
12 14 16 IS 20
Fig. 10. Dependence of parameters n. U of the single-stage TEU on the value of relation l/s at T=300 K. AT=40 K and Q0=2.0 W in the mode Q0/I2)max
With the reduction of ratio l/S, operation current I increases (Fig. 16), the refrigeration coefficient does not change (E=0.38) and the number of thermoelements decreases by 2 times.
Note that for the mode (Q0/I2)max at AT=40 K and Qo=2.0 W, reduction of the ratio l/S from 20 to 10 enables
reduction of the failure rate X by 50 %, and hence increase in the probability P of the failure-free operation. At the same time, the value of the operation current I increases from 1.24 to 2.48 A. and the power consumption W and refrigeration coefficient E remain constant (W=5.24 W and E=0.38) and the number of thermoelements is halved.
Fig. 11. Dependence of the failure rate X (solid lines) and the probability Р of failure-free operation (dotted lines) of the single-stage TEU on the value of relation l/s at T=300 K. Q0=2.0 W and various values AT in the mode (Q0/I2)max
Fig. 12. Dependence of the operation current I of the singlestage TEU on the temperature variation AT at T=300 K, Q0=2.0 W and various values of relation l/s in the mode
(Q0/I2)max
Fig. 13. Dependence of the operation current I and the number n of thermoelements of the single-stage TEU on the temperature gradient aT at T=300 K. Q0=2.0 W and various values of relation l/s in the mode (Q0/I2)max
Fig. 14. Dependence of the failure rate x of the single-stage TEU on the temperature variation aT at T=300 K. Q0=2.0 W and various values of relation l/s in the mode (Q0/I2)max
Fig. 15. Dependence of the probability P of failure-free operation of the single-stage TEU on the temperature gradient aT at T=300 K, Q0=2.0 W and various values of relation l/s in the mode (Q0/I2)max
Fig. 16. Dependence of the operation current I on the optimum relation (l/s )Qpt of the single-stage ТEU on the temperature gradient aT at T=300 K, Q0=2.0 W and various values of aT in the mode (Q0/I2)max
6. Discussion of the results of analysis of the influence of the branche geometry on performance of the single-stage TEU
Analysis of the calculation data for the mode (Q0/I)max at aT=40 K and Q0=2.0 W has shown that reduction in the thermoelement branch ratio l/S of the single-stage TEU from 20 to 10 results in the following:
- 2-fold increase in the maximum cooling power y;
- 2.1-fold reduction in the required number n of thermoelements;
- 2-fold increase in the operating current I value;
- about a 2-fold reduction in the magnitude of the voltage U drop;
- 2-fold reduction in the failure rate x;
- the failure-free operation probability P increases.
Besides, refrigeration coefficient E=0.34, the relative
operation current B = 0.71, power consumption W=5.9 W.
For the mode (Q0/I)max, the following occurs at various fixed values of l/S and Q0=2.0 W with an increase in the temperature variation aT from 20 to 40 K:
- 14 % lower maximum cooling power y;
- functional dependence n=f(aT) has a pronounced minimum which can be explained by the maximum cooling power at an optimum aT;
- 47 % increase in operation current I;
- 2 times increase in the value of the voltage drop U;
- 9.4 times higher failure rate x at l/S=20;
- reduced probability P of the failure-free operation;
- 53 % increase in the relative operation current B;
- 3 times increase in the power consumption W;
- 2.9 times reduced refrigeration coefficient E;
- 2.3 times increase in relative temperature gradient ©.
Analysis of calculation data for the mode (Q0/I2)max at aT=40 K and Q0=2.0 W has shown that with reduction from 20 to 10 in the ratio l/S of the thermoelement branch of the single-stage TEU, the following occurs:
- 2 times increase in the maximum cooling capacity y;
- 2 times decrease in the required number n of thermoelements;
- 2 times increase in the value of the operation current I;
- 2 times reduced magnitude of voltage U drop;
- 2 times reduced failure rate x;
- probability P of the failure-free operation increases.
Besides, refrigeration coefficient E=0.38, relative operation current B=0.5, power consumption W=5.24 W.
For the mode (Q0/I2)max, the following occurs at various fixed values of l/S and Q0=2.0 W with an increase in the temperature gradient aT from 20 to 40 K:
- 14 % reduced maximum cooling power y;
- functional relation n/f(aT) has a pronounced minimum which can be explained by maximum cooling power at an optimal gradient aT;
- 2.2 times higher operation current I;
- 1.6 times higher voltage drop U;
- 38 times higher failure rate x;
- reduced probability P of failure-free operation;
- 2.3 times increase in the relative operation current B;
- 3.6 times increase in power consumption W;
- 3.6 times reduced refrigeration coefficient E;
- 2.3 times higher relative temperature gradient ©.
7. Conclusions
1. We proposed the model of interconnection of the reliability indicators and the basic parameters of the single-stage TEU during variation of the thermoelement branch geometry for various temperature gradients and a fixed heat load in modes (Q0/I)max and (Q0/I2)max. The model makes it possible to design TEU at l/S=var with consideration of restrictive re-
quirements to size, weight, power consumption and reliability with a possibility of choice of a compromise design.
2. The possibility is defined of a significant increase in the reliability indicators of the single-stage TEU both in (Q0/I)max and (Q0/I2)max modes by choosing thermoelement branch geometry with a smaller ratio l/S for the specified values of temperature gradient, heat load and power consumption.
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