Improvement of transient supercooling of thermoelectric coolers through variable semiconductor cross-section
Introduction
Thermoelectric devices can convert heat into electricity by Seebeck effect or electricity into heat by Peltier effect. With the development of a new generation of nanostructured thermoelectric materials, figure of merit of materials is improved significantly, which promotes rapid growth of studies on thermoelectric devices [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. Thermoelectric coolers (TECs) have been widely employed in various cooling and refrigeration applications [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. Compared with conventional cooling technologies, TECs have many advantages such as high reliability, compact volume, layout flexibility, large operating temperature range, and rapid temperature response, because the coolers do not use any moving parts and environmentally harmful fluids [12], [13].
When a TEC operates at steady state with a constant hot end temperature, the lowest cold end temperature achievable is determined by the figure of merit of semiconductor materials, TEC structure, and input current [14], [15]. However, when a current pulse with magnitude several times larger than the optimal steady-state one is applied to the TEC, an instantaneously lower cold end temperature than that reachable at steady-state can be achieved. This phenomenon is referred to as transient supercooling, which can be applied in many fields where extra cooling for a short time is needed [16], [17].
At least five indicators can be used to evaluate the transient supercooling characteristics [16]: maximum cold end temperature drop ΔTc,max1 = Tc,s − Tc,min, maximum temperature overshoot ΔTc,max2 = Tc,max − Tc,s, time to reach the minimum cold end temperature tmin, holding time of the supercooling state Δthold, and recovery time to the next new steady state Δtrec, where Tc,s is the cold end temperature reachable at steady-state, Tc,min and Tc,max are respectively the minimum and maximum cold end temperatures reachable when a pulse current is applied to the TEC. In recent years, many efforts have been devoted to investigating the transient supercooling [16], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30]. These investigations found that for a specific pulse shape, pulse amplitude and width have significant effects on the transient supercooling. Various pulse shapes were also compared in Refs. [16], [31], [32], [33], [34], [35]. The results showed that there exists an optimal pulse shape to achieve the maximum cold end temperature drop, however, the optimal shape obtained in Refs. [16], [31], [32], [33], [34], [35] are different. Recently, our group has developed a multiphysics transient TEC model to investigate the effect of pulse shape [36]. The results showed that the optimal shape is only determined by the time to reach the minimum cold end temperature and the pulse width (τ). For the pulses with tmin < τ, a higher power pulse provides a lower cold end temperature, for the pulses with tmin = τ, however, the trend is reversed. The results reasonably explained the divergence for the optimal pulse shape reported by the previous studies [16], [31], [32], [33], [34], [35].
In the above studies [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], the p-type and n-type semiconductors were specified as regular cuboids or cylinders with constant cross-sectional areas. Hoyos et al. [37] proposed for the first time that it is possible to achieve a lower cold end temperature when variable semiconductor cross-sections are adopted. They fabricated a TEC with conical semiconductor legs and experimentally tested its transient supercooling characteristics. Their tests showed that with narrow pulse width and large amplitudes, additional cooling of the order of 45° below the steady-state maximum with recovery times in the range of 1–3 s was obtained. Following Hoyos et al.’s work, Yang et al. [16] developed a one-dimensional heat conduction model to investigate the transient supercooling performance of a axisymmetric TEC element with variable semiconductor cross-sectional area. Their results showed that a lower minimum transient temperature but a shorter holding time are observed for the tapered axisymmetric semiconductor legs with smaller cross-sectional area at the cold end. Thus, they concluded that the increase of holding time for TEC legs with a larger cross-sectional area at the cold end can be potentially useful for the device to be operated for a longer time.
It should be noted that in Yang et al.’s work, a freestanding TEC element was modeled with constant semiconductor properties, and only Joule heat was assumed as the internal heat source. Our previous study [36] has demonstrated that although the multiphysics model with constant and variable properties predict almost the same minimum cold end temperature, the model with constant properties underestimates the temperature overshoot by about 90 K. Accurate prediction of the temperature overshoot is very important for transient supercooling applications, because a larger temperature overshoot means that the TEC needs a longer time to return to the previous steady state. In additon, the larger temperature overshoot also could lead to burn-out of the electronic device that needs to be cooled. Thus, considering of variable properties is necessary for the accurate prediction of TEC transient supercooling performance. Furthermore, as expected, when the variable semiconductor cross-sectional areas are adopted, three-dimensional current and temperature distributions may occur in p–n junction and hence the one-dimensional model may be improper. In addition, an actual TEC element is composed of a p–n junction, three metallic connectors, and two electrically insulating ceramic plates. The ceramic plates have large heat capacity, hence, the transient response characteristics for the actual TEC element differs significantly from those for the freestanding TEC element.
Based on the above analysis, a rigorous and comprehensive study on TEC shape effect on transient supercooling characteristics is quite lacking up to now. Therefore, the objective of this work is to investigate how variable semiconductor cross-sectional area influences the transient supercooling characteristics. To achieve this objective, a complete, three-dimensional, and multiphysics TEC model is firstly used to predict the steady-state TEC performance. The optimal steady-state currents are respectively obtained for the TEC with constant and variable cross-sectional semiconductor areas. Then, a pulse current with an amplitude several times larger than the optimal steady-state current is applied to the TECs to investigate and compare their transient supercooling characteristics. Finally, the effects of pulse amplitude and area ratio of hot end to cold end on the transient supercooling characteristics are investigated.
Section snippets
TEC with variable semiconductor cross-sectional area
Generally, a TEC is composed of several tens or hundreds thermoelectric elements. These thermoelectric elements are connected thermally in parallel and electrically in series, and hence a thermoelectric element can be extracted as the computational domain (Fig. 1). The element consists of a p-type semiconductor leg, an n-type semiconductor leg, three metallic connectors, and two ceramic plates. Fig. 1(a) shows the schematic of a conventional TEC element, in which the thicknesses of ceramic
Simulation cases
In this paper, the transient supercooling characteristics of the TEC element with variable semiconductor cross-sectional areas are firstly compared with that of the conventional TEC element. As shown in Fig. 2, design 1# is the convectional TEC element with H2 = 1.0 mm and Asemi = 0.5 × 0.5 mm2 with γ = 1, design 2# has Asemi,c = 0.5 × 0.5 mm2 and Asemi,h = 0.5Asemi,c with γ = 0.5, design 3# has Asemi,c = 0.5 × 0.5 mm2 and Asemi,h = 2Asemi,c with γ = 2, design 4# has Asemi,c = 2Asemi,h and Asemi,h = 0.5 × 0.5 mm2 with γ = 0.5, and
Numerical model
The three-dimensional, multiphysics, and transient TEC model includes energy equations and electric potential equations. These two sets of coupled equations need to be solved simultaneously to obtain the temperature and electric potential distributions within the TEC element. The model is described briefly in the following and more details can be found in our previous works [36], [38]where T is the temperature, t is the time,
Model validation
The experimental curve of Tc–t tested by Snyder et al. [18] is used to validate the present model. They used n-type Bi2Te2.85Se0.15 and p-type Bi0.4Sb1.6Te3 to fabricate 5.8 mm tall thermoelectric elements with 1 mm2 cross-sectional areas. The cold end was soldered to a 35 μm thick copper foil to which was soldered a 25 μm diameter Chromel-Constantin thermocouple for measurement of the temperature. The hot end was soldered to an electrically isolated heat sink where the heat sink temperature could
Determination of the optimal steady-state current
In order to study the transient supercooling characteristics, the optimal steady-state current, Iopt, needs to be determined first. Fig. 6 shows the I–Tc curves of the TEC elements with constant and variable semiconductor cross-sectional areas. The minimum cold end temperatures, Tc,min, for the five designs are 204.62, 204.79, 204.21, 204.84, and 204.17 K, respectively, indicating that Tc,min is almost independent of the TEC shape. This phenomenon is also observed for the TEC elements with
Comparison between various semiconductor shapes
The transient supercooling characteristics of the TEC elements with constant and variable semiconductor cross-sectional areas are shown in Fig. 8. The step pulse with pulse amplitude of P = 5 and pulse width of τ = 0.05 s is used here. As shown in Fig. 8, the changes of all Tc–t curves exhibit the similar trend: Tc fist keeps its steady-state value of Tc,s at t < 0.005 s; it starts to decline after the step current is applied to the TEC element; when Tc reaches Tc,min it starts to rise; after maximum
Conclusions
In this study, transient supercooling of the TEC with variable semiconductor cross-sectional area is investigated by a three-dimensional, transient, and multiphysics model. The transient supercooling characteristics can be evaluated by the minimum cold end temperature, maximum temperature overshoot, and several time constants, such as the holding time of supercooling state and the recovery time ready for next steady-state. These evaluation indicators for the proposed designs with variable
Acknowledgments
This study was partially supported by the National Natural Science Foundation of China (No. 51276060), the 111 Project (No. B12034), and the Fundamental Research Funds for the Central Universities (No. 13ZX13).
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