CALCULATION OF CHARACTERISTICS OF THERMOELECTRIC COOLING SYSTEM OF HEAT-LOADED ELEMENTS OF RADIO ELECTRONIC EQUIPMENT

全文:

Introduction. The resource, operational stability and operating characteristics of the heat-loaded elements (HLE) of radio-electronic equipment significantly depend on their temperature condition, so in case of increase in working temperatures from 20 to 60 °C equipment failure rates increase more than twice [1]. The perspective direction for cooling and temperature control of HLE is the use of thermoelectric modules (TEMs). Thermoelectric system of cooling and temperature control (TESCTC) possess a list of advantages in comparison with other cooling sys- tems, namely: possibility of smooth temperature control in rather broad range by changing of value and direction of supply current TEM; minor thermal inertness; high reliability; absence of moving parts; compactness and small weight; quietness of operation. TESCTC are effec- tively used for cooling of both miniature objects and large volume refrigerators [2-6]. Construction and characteristics of the cooling sys- tem. HLE 1 is considered to be a TESCTC widespread type applied to cooling, construction with heat distribut- ing plate (HDP) 2, TEM 3 and a cooler 4 (fig. 1). HDP is necessary for alignment of thermal power distribution arriving from HLE on TEM surface. At the same time TEM performs the function of a thermal pump transfer- ring heat from the cold side to the hot. The cooler re- moves the total thermal power produced by both HLE and TEM to the external environment. These elements of the system have thermal contacts on the boundaries. On the areas of contact surface A the cooler removes heat to the external environment having temperature Т0. The bound- ary of B corresponds to the contact surface of the cooler with the hot side of HLE which temperature is described by average value of Т2. The cold side of HLE (B surface) has average temperature of Т1. HLE seat (D surface) is characterized by average value of temperature Тe. In case tions influence of own heat release of HLE can on the contrary lead to its additional heating (line 3), not cooling. When analyzing efficiency of HLE cooling, basic operat- ing characteristics of HLE are used; they can be calcu- lated [7] or received from the vendor. In the present re- search the influence of HDP thermal resistance, cooler and thermal contacts on characteristics of thermoelectric cooling and HLE temperature are studied. HLE tempera- ture is determined by the ambient temperature and the sum of temperature drops of all construction elements. During calculations temperature drops were calculated gradually at first in configuration “TEM-cooler”, then in HDP in terms of thermal influence of HLE and TEM. The analysis of TESCTC characteristics is carried out on the example of serial TEM of NPO “Kristall”. Temperature calculation of the heat-loaded element. Values and temperature drop ratio depend on operating characteristics and parameters of all TESCTC construc- tion elements and their cross impact [8-11]. In TESCTC in case of heat exchange of TEM with an external envi- ronment from its hot side, it is necessary to remove the total thermal power developed by HLE and TEM, which is, as a rule, considerably higher than HLE power due to rather low refrigerating coefficient of TEM. It causes the corresponding growth of temperature drop on thermal contacts and the cooler, which, as a result, leads to lower- ing of cooling efficiency. The difference of temperatures ΔT0 between the cold side of TEM and the environment is determined from expression [11] of HLE suspension from the considered construction, the DT = T - T = R (Q + W ) - DT = normal heat-eliminating system, which is widely applied 0 1 0 s TEM to HLE cooling, for example, in the computer equipment, is widely used. Typical options of temperature distributions which can be implemented in TESCTC are given in fig. 2. Ambient temperature Т0 is the original value directly influencing HLE seat temperature. For the normal heat-eliminating system temperature value Тe of HLE seat certainly ex- ceeds Т0 value, increase in temperature is assured due to the temperature fluctuations caused by thermal resistance of HLE and cooler (line 4). The negative temperature drop made by HLE allows to reduce temperature Тe, which in this case can either exceed value of Т0 (line 2), or be lower than this value (line 1). Under certain condi- Fig. 1. Thermoelectric cooling system Рис. 1. Схема термоэлектрической системы охлаждения = RsQ + RsU (I , Q)I - DTTEM (I , Q), here T1, T0 - temperature values of the hot side ТEМ and environment; Rs - total thermal resistance of the cooler and its thermal contact with ТEМ; Q, W - heat release capacities of HLE and natural energy consumption of ТEМ; ΔTTEM = T2 - T1 - temperature drop between the cold and hot sides of ТEМ; U, I - power and current in- tensity of power supply of ТEМ. Operating characteristics of ТEМ from the manufacturer Q(ΔTTEM) and U(ΔTTEM) are basic data for dependences determination U(I, Q) and ΔTTEM(I, Q) and further calculation ΔT. The method of dependences calculation is presented in [10; 11]. Fig. 2 Temperature distribution in the cooling system Рис. 2. Распределение температуры в системе охлаждения Dependences of the cold side temperature drops of ТEМ and the environment on the power consumption under Q = 40 W and Rs = 0.1, 0.3 and 0.5 К/W are pre- sented in fig. 3 for ТEМ “S-127-14-11” (solid lines) and “S-199-14-11” (broken lines), having maximum refrig- erating values 79.3 and 124.2 W. Negative values ΔT0 correspond to the modes, in which cold side temperatures of ТEМ are lower than ambient temperature. Temperature drop values ΔT0 considerably depend on Rs, variation interval of values ΔT0 for the fixed W within the range of Rs = 0-0.5 K/W averages at about 55-60 °C. For the given dependencies presence of least values is typical. This least values correlate with the best values of energy consump- tion W, under which the maximum cooling of HLE can be achieved. When increasing Rs from 0.1 to 0.5 K/W these values W fall from 103 W to 38 W for ТEМ “S-127-14-11” and from 120 W to 37 W for ТEМ “S-199-14-11”. For temperature drop losses in HDP measurement mathematical model based on numerical solution of the three-dimensional equation of heat conduction is used with regard to the load characteristic of TEM: ¶T æ ¶2T ¶2T ¶2T ö the method of total approximation with splitting of the task into spatial coordinates [12] was applied. Based on calculations distributions of temperature HDP with different values of its thickness δ and HLE size a were obtained. The integral parameter characterizing heat-transmitting ability of HDP is the thermal resistance of R. Quantitative thermal resistance is calculated as the relation of average temperatures of HLE seat difference and the bottom surface of HDP to the transferred thermal power, where time value R depends both on heat conduc- tion of HDP material and HLE and HLE sizes. Depend- ences R on thickness of copper HDP are shown in fig. 4 for different values a, curves 1, 2, 3, 4 and 5 correspond to values 22.5, 17.5, 12.5, 7.5 and 2.5 of mm. Based on values of thermal resistance R and power of heat release of HLE, Q value of temperature drop on HDP is defined by the expression ΔTHDP = RQ. The figure shows that the range of best values δ makes approximately from 3 mm where a = 22.5 mm up to 5 mm where a = 2.5 mm. Opti- mization of HDP parameters allows to minimize tempera- ture drop and as a result to reduce HLE temperature. Besides, calculations proved that inhomogenuity of the ç ¶ 2 2 2 ÷x ¶y ¶z cvr ¶t = l + + , è ø temperature field of TEM cold side leads to essential increase in thermal resistance of HDP compared to the where c, ρ, λ - specific heat capacity, density and heat conduction coefficient of material; T - temperature; t - time; x, y, z - spatial coordinates. Values c, ρ and λ in all estimated area had constant values corresponding to copper. HDP sizes were equal in cross x and y direc- tions were equal to TEM 40×40 мм2 overall dimensions, in z direction its thickness δ varied. The HLE seat was set in the center of HDP’s upper surface in the form of a square with side a. On the upper and lower boundaries of HDP inhomogenuity of heat fluxes, caused by influence of HLE and TEM was considered. To solve this equation case of isothermal heat-eliminating surface [13; 14]. This increase R is explained by the increase in average length of heat transmission in HDP capacity, caused by lower values of temperature on TEM edges. Lowering thermal resistance value and losses of HDP temperature drop can be assured by applying materials with higher coefficient of heat conduction or hyper heat-conducting plates (plane thermal pipes) in which high effective heat conduction is reached due to phase transformations of the heat carrier in case of movement in the porous environment [15; 16]. Fig. 3. Dependences of the TEM cold side temperature drops and the environment on the power consumption under Q = 40 W and various values of Rs Рис. 3. Зависимости разности температур холодной стороны ТЭМ и окружающей среды от потребляемой мощности при Q = 40 W и различных значениях Rs Fig. 4. Dependencies R(δ) for the cooper HDP, curves 1, 2, 3, 4 and 5 correspond to a = 22.5, 17.5, 12.5, 7.5 and 2.5 mm Рис. 4. Зависимости R(δ) для медной ТРП, кривые 1, 2, 3, 4 и 5 соответствуют a = 22.5, 17.5, 12.5, 7.5 и 2.5 мм Thus, the considered two-step algorithm allows to calculate HLE temperature. At the first stage temperature of the TEM cold side is determined by calculation of total temperature drop in the “cooler - TEM” system with regard to the HLE thermal power, operating characteristics of TEM, cooler thermal resistance and thermal contacts, ambient temperature. Then temperature drop in HDP is calculated and based on HDP temperature distribution on the upper boundary of HDP with regard to the thermal resistance of heat contact on its seat, foundation temperature is determined. Final expression for average temperature of HLE seat calculation has the following appearance Te = T0 + DT0 + RQ. Under the known internal thermal resistance of HLE (information of the vendor) its influence is considered the same way, herewith the temperature of the semiconductor crystal, located in the HLE case, will be defined. Conclusion. In the present paper heat exchanging processes in TESCTC are considered; the algorithm allowing to carry out calculation of HLE temperature and TESCTC modes optimization to increase cooling efficiency of HLE and lowering of TEM energy consumption are provided. It is stated that the value of effective power consumption of TEM corresponding to the modes with maximum cooling efficiency depends on the thermal resistance of the cooler and power of HLE heat release.

作者简介

E. Vasil’ev

Krasnoyarsk Science Centre SB RAS, Institute of Computational Modelling SB RAS

Email: ven@icm.krasn.ru
50/44, Akademgorodok, Krasnoyarsk, 660036, Russian Federation

参考

补充文件