Numerical modeling of the thermoelectric cooler with a complementary equation for heat circulation in air gaps

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1 Open Phys. 17; 15:7 34 Researh Artile Open Aess En Fang*, Xiaojie Wu, Yuesen Yu, and Junrui Xiu Numerial modeling of the thermoeletri ooler with a omplementary equation for heat irulation in air gaps DOI /phys-17-4 Reeived Ot 13, 16; aepted Nov 14, 16 Abstrat: In this paper, a numerial model is developed by ombining thermodynamis with heat transfer theory. Taking inner and external multi-irreversibility into aount, it is with a omplementary equation for heat irulation in air gaps of a steady ooling system with ommerial thermoeletri modules operating in refrigeration mode. With two modes onerned, the equation presents the heat flowing through air gaps whih forms heat irulations between both sides of thermoeletri oolers (TECs). In numerial modelling, a TEC is separated as two temperature ontrolled onstant heat flux reservoirs in a thermal resistane network. In order to obtain the parameter values, an experimental apparatus with a ommerial thermoeletri ooler was built to haraterize the performane of a TEC with heat soure and sink assembly. At onstant power dissipation, steady temperatures of heat soure and both sides of the thermoeletri ooler were ompared with those in a standard numerial model. The method displayed that the relationship between Φ f and the ratio Φ /Φ was linear as expeted. Then, for verifying the auray of proposed numerial model, the data in another system were reorded. It is evident that the experimental results are in good agreement with simulation(proposed model) data at different heat transfer rates. The error is small and mainly results from the instabilities of thermal resistanes with temperature hange and heat flux, heat loss of the devie vertial surfaes and measurements. Keywords: Thermoeletri oolers; Thermoeletri generators; Peltier effet; Refrigeration performane PACS: e 1 Introdution The diret energy onversion between heat and eletriity based on thermoeletri effets is attrative for many appliations as an alternative to traditional methods in power generation and heat transmission [1, ]. Thermoeletri modules (TEMs) have outstanding advantages suh as solid-state, ompat, light-weight, ontaining neither moving parts nor refrigerants, maintenane free, highly reliable and quiet operation, environmental friendly performane, and so on [3, 4]. The use of TEMs for ooling, heating and power generation in a simple and reliable way has been omprehensively disussed in many industrial fields [5]. TEMs an be divided into two types, namely thermoeletri oolers (TECs) and thermoeletri generators (TEGs) [6 8]. Sine onventional air ooling tehniques for high power eletroni pakages are reahing the limits in term of ooling apaity, various efforts have been devoted to enhane the ooling design and performane [9]. Among them, the use of TECs, in ombination with air ooling or liquid ooling approahes, is gaining more and more attention. The major thermal benefit of this development trend lies in the fat that a negative temperature gradient and thus redued thermal resistane ould be generated from the use of TECs [1, 11]. Bell [1] points out two important pathways that will lead to additional appliations of thermoeletri devies. One is to promote the intrinsi effiienies of TE materials. The other is to improve the way that existing TEMs are urrently used by modeling and analyzing of thermoeletri systems [13, 14]. For TECs, the primary mission should be to keep the heat resoure working in a ertain temperature range. Thermoeletri devies ould not be used independently. Heat soures and exhangers should be onneted *Corresponding Author: En Fang: Shool of Information and Eletrial Engineering, China University of Mining and Tehnology, Xuzhou 18, Jiangsu Provine, China Xiaojie Wu, Yuesen Yu, Junrui Xiu: Shool of Information and Eletrial Engineering, China University of Mining and Tehnology, Xuzhou 18, Jiangsu Provine, China 17 E. Fang et al., published by De Gruyter Open. This work is liensed under the Creative Commons Attribution-NonCommerial-NoDerivs 3. Liense.

2 8 E. Fang et al. with to dissipate and absorb heat [15]. The ommonly used approah is the iterative method as given in [11]. A numerial optimization of a TEC was presented by Xuan [16]. The results indiated that the onstrution ost of a TEC was losely related to the ooling power density; whereas the running ost was inversely proportional to COP. High effiieny was obtained when the length of the thermo elements was large [17]. In addition, the power generated delined with the ross-setional area of the thermo elements, whereas effiieny showed the opposite trend [6]. For ondution and onvetion, the heat only flows from the end at high temperature to low. In eletroni devies, the reliability and lifetime of eletroni omponents derease greatly with temperature rise due to power dissipation. Although a variety of ooling means have been used, suh as natural onvetion, fored air onvetion and liquid exhangers, heat pipe exhangers, and so on, the eletroni omponents are still often the parts with the highest temperature in eletroni devies. The TECs work as heat pumps onverting heat flux from the old end to hot ontinuously at the expense of eletri energy. They an be onveniently ontrolled by DC power suppliers. In this paper, a numerial model with the omplementary equation is established aording to various equations onerning with ooling system and thermoeletri oolers. Numerial model on a ooling system with TECs A TEC is a solid-state heat pump plaed between heat soures and heat sinks. It normally onsists of an array of N pellets from dissimilar semiondutor materials (p and n type) that make up N thermoeletri ouples whih are eletrially by onduting strips in series and thermally in parallel [18, 19]. The p and n legs are joined by metal interonnets with ohmi ontat. The onduting strips of the thermoeletri elements are fixed at a thermal onduting and eletrial insulating erami plate []. The module is pakaging by thermally insulating epoxy resin. The thermoeletri elements in most ommerial thermoeletri modules are not losely arranged, that is, air gaps exist in the module whih lead to heat miroirulations. The heat onvetion (or ondution) and radiative heat transfer our between two erami plates in the area that the thermoeletri elements do not oupy..1 Assumptions To simplify the ooling system with TECs, the following assumptions are made: (1) The numerial model is for a steady-state system; () The TEC is single-stage onstruted from N thermoeletri ouples whih are idential and joined eletrially in series and thermally in parallel [6]; (3) All the ooling means suh as onvetion, ondution and radiation are inluded in the omputational domain as a one-dimension thermal resistane varying with heat flux and temperatures in simplifiation; (4) Heat transfer at a finite rate, and eletrial resistive losses, are neessarily irreversible proesses and unavoidable in a thermoeletri devie [5]; (5) The erami plates work as favorable heat ondutors and eletrial insulators.. Standard Model One-dimensional thermal resistane network of the whole ooling system with a single-stage TEC is shown in Figure 1. The TEC is separated as two temperature ontrolled onstant heat flux reservoirs in thermal resistane network. The positive diretions of heat flow expeted in the senario are shown in Figure 1. Presenting the problems in eletroni iruit terms helps to understand its funtionality, and failitates the solving of ooling problems without the need for expertise in thermal engineering [1]. ' R Tj Ploss R T TECs Φ Th Φh Figure 1: One-dimension thermal resistane network of a ooling system with a single-stage TEC Aording to the non-equilibrium thermodynamis, the inner effets of the thermoeletri elements inlude Seebek effet, Fourier effet, Joule effet and Thomson effet. The inrement rate of inner energy of the infinitesimal is zero at steady-state, so one an obtain the energy onser- Rh Ta

3 Numerial modeling of the TECs 9 to that flows through the old side Φ. But in fat, due to the existenes of onstrition thermal resistane, they are not equal. Comparing the heat flow in TECs against the air flow in an unsealed dut with two exhaust fans, two modes are maintained in Figure. Thus, Φ = Φ + Φ f + Φ l () (a) Φ Φ + Φ l Where, Φ f is the heat flowing through air gaps whih forms heat irulations between both sides of TECs. It should be a pieewise funtion depending on the relationship of Φ and Φ. Φ l is the leakage heat through the thermal insulation material. The ondution properties and insulation harateristis of the materials should have signifiant effet on Φ f. It is also related to the thikness of erami plates and ondution trips, the area ratio of N(S n + S p )/S, and so on. As these parameters vary little in a ertain range, in view of the air flow in an unsealed dut with two exhaust fans, the pieewise funtion is proposed to be linear. And the positive diretions of heat flow are defined as in Figure (a). Φ δ 1 + Φ p1, Φ (Φ + Φ Φ f = Φ (3) δ + Φ p, Φ < (Φ + Φ (b) Φ < Φ + Φ l Figure : Two modes of heat flow in TECs vation equation as follows: Φ = NαIT 1 I R K(T h T ) Φ h = Φ + NαI(T h T ) + I R Φ h = T h T a Φ = P loss T j T a R T j T = Φ R.3 Proposed Model with omplementary equation (1) While Φ (Φ +, Φ f and vie versa. As mentioned before, with the omplementary equation for the heat flowing through air gaps, the model is proposed as, Φ δ 1 + Φ p1, Φ (Φ Φ Φ + Φ Φ l = Φ δ + Φ p, Φ < (Φ + Φ Φ = NαIT 1 I R K(T h T ) Φ h = Φ + NαI(T h T ) + I R Φ h = T h T a Φ = P loss T j T a R T j T = Φ R The proposed numerial model may be applied to the alulation of harateristi parameters, temperature predition and further optimization study for thermoeletri oolers. The simulation results an be used as feasibility and effetiveness referene by employing omponent pakage and devie ooling. (4) In standard models, the heat flux Φ absorbed by the semiondutor nodes is assumed to be of an equivalent amount

4 3 E. Fang et al. 3 Experimental setup 3.1 System haraterization with TEC in refrigeration In order to realize the output performane following ontrol of this ase study, a ooling proess with a TEC was onsidered where film resistor temperature sensors were loated at different plaes, as shown in Figure 3. grease. The sensors have an unertainty of ±.5 K. Two programmable DC power supplies (Chroma 61H-45) are employed for heater and TEC, respetively. The voltage aross and urrent through the path heater are measured to determine the heat dissipation in the ooling system. The unertainty in the measurements of voltage and urrent are ± 1 mv and ± 1 ma, respetively. Figure 3: Setup to measure the temperatures of heat soure and TEC A sandwihed struture (from top to bottom) of thermal insulation layer/path heater/thermal silione grease/opper plate/thermal silione grease/tec/thermal silione grease/heat sink was introdued. The CH-J44 is one of the path heater modules available from Company MCH, whih was attahed to a opper plate on the old side of the TEC. The TEC 176AJ (N = 17) is manufatured by Wanhao Tehnology. A water ooled exhanger was used to absorb the heat from the hot side of TEC. The oolant (water) was supplied from a waterirulating hiller. In order to redue thermal ontat resistane, a thermal interfae material, thermal silione grease (Aobaili ABL361) was smeared uniformly on every ontat surfae. Figure 4 shows the shemati diagram of the experimental ooling system. The assembly was insulated with heat-insulated foam to minimize the parasiti heat load from the ambient exept for the heat sink and is held under ompression between four aluminum lathes for proper ontat between surfaes at a onstant pressure. Temperatures on the heater (T j ), old side (T ) and hot side (T h ) of the TEC, as well as the ambient temperature (T a ), are measured using film resistor temperature sensors whih are held in plae with thermally ondutive silione 1-Thermal insulation layer -Path heater 3-Thermal silione grease 4-Temperature sensor 5-Copper plate 6-TEC 7-Heat sink 8-Water ooler 9-Water tank 1-Pump 11-Valve 1-Volumetri flowmeter Figure 4: Shemati diagram of the experimental setup of water ooling system The programmable DC supply for TEC worked as a onstant urrent power The programmable DC supply for TEC worked as a onstant urrent power supply, while the other one as a onstant voltage soure for path heater (U heater = V). All the temperatures at different urrents of the TEC with this water ooled exhanger were reorded. Then, the programmable DC supply for TEC worked as a onstant urrent power supply (I TEC =.5A), while the other one as a onstant voltage soure for path heater. By replaing the water ooled exhanger with aluminum radiator, the experimental temperatures at different heat transfer rate with aluminum heat sink were also reorded. 3. System haraterization with TEM for thermal ondution Before the system performane testing, a performane haraterization should be ahieved by means of testing the parameters, suh as the equivalent thermal resistane

5 Numerial modeling of the TECs 31 of ontat thermal resistane, onstrition thermal resistane and onvetion thermal resistane, and so on. Firstly, the path heater was enapsulated bilateral symmetry by thermal insulation layers. R = (T j T a ) P loss Temperatures of the path heater above ambient at different applied heat load are presented in Figure 5. The thermal resistane of insulation layer is K/W as slope. The value of R-square in Figure 5 is.9966 whih imply the auray of the fitting lines that explain our measurement results are more than 99%. Due to high insulation apability of the layer, the thermal resistane value hanges little with the heat flux and temperature. T j and T a (K) 33 T a T j ( Tj Ta ) Linear fitting urve Heat transfer rate P loss Y R X Figure 5: Temperatures of the path heater above ambient at different applied heat load Then, the test apparatus mentioned before were tested. The TEM was treated as a ondution module without being powered. As the assembly was insulated with heat-insulated foam, little heat dissipated from vertial sides to ambient, that is to say, Φ Φ h. Φ = Φ h = P loss T j T a R R = T j T Φ = T h T a Φ h Φ K = T T h The tested temperature differenes of (T j T ), (T T h ) and (T h T a ) are plotted against the applied heat load in Figure 6. The equivalent thermal resistane R and ould be obtained by urve fitting. Hene the slope of the = = ( T T ) (K) j a linear fit in Figure 6(a) provides the thermal interfae resistane and onstrition resistane. In Figure 6(b), the thermal ondutivity of the module is haraterized. Figure 6() and (d) represent the ombined heat sink and water ooled exhanger with parasiti resistane in parallel, respetively. 4 Results A total of 51 samples was olleted and then analyzed for modeling. Figure 7 shows the measured and simulated (standard model) urves of temperatures versus urrent of the TEC at the same power dissipation with water ooling system. Based on the standard model without the miroirulation heat Φ f and leakage heat Φ l, the theoretial results in Figure 7(a) and (b) are quite different from those in experiments. It shows the neessity of proposing an aurate model to predit the temperature behavior of TECs. In Figure 7(), the results of the experiment and simulation were highly onsistent due to the auray of and Φ h. Figure 8 shows the linear relationship between the temperature differenes and urrent of TEC with water ooled exhanger at onstant power dissipation. The temperature differenes derease from positive to negative with TEC urrent inreasing. While the urrent of TEC remains about 4.4A, the experimental juntion temperature is the same as the predited one. The maximum absolute value of temperature differene in test range is K. In view of the proposed model in formula (4), based on the measured temperatures, the heat flows in every thermal path are alulated. The fator (Φ f + is shown in Figure 9. In this ase, the method of least squares nonlinear regression and subsetion funtion are introdued to deal with data. As mentioned before, Φ f should be a pieewise funtion of Φ at onstant Φ, Φ f + Φ l = {.8879Φ , Φ (Φ Φ , Φ < (Φ + In the proposed model, there is a turning point from whih Φ f hanges from positive to negative with inreasing Φ. Compared to the segmental fitting equations, the intersetion point (19.98,.11) is the turning point of subsetion. Thus, at the turning point for this experimental system, Φ f = W, Φ = 19.98W, Φ l =.11W and Φ = (5)

6 3 E. Fang et al T j 37 T.8 T R Fitting urve between R and Φ T h K Fitting urve between K and Φ Φ K = Φ R = T j and T (K).8 (K/ W) R T and T h (K) K (W/ K) R = Φ R = Heat transfer rate Φ Heat transfer rate Φ (a) (b) 355 T h 15.3 T h.5 35 T a T a 345 Fitting urve between Rh and Φh 15. Fitting urve between Rh and Φh T h and T a (K) 35 Rh = R = Φh (K/ W) T h and T a (K) Rh =.69 R = Φh.3 (K/ W) Heat transfer rate Φh Heat transfer rate Φh () (d) Figure 6: Tested temperatures and orresponding thermal resistane/ondutivity against the applied heat load Φ + Φ l = 17.87W Φ , Φ (Φ + Φ Φ f = 8.13 Φ , Φ < (Φ + Φ Then the water ooled exhanger was replaed with aluminum radiator. The differenes between experimental and alulated (proposed model) temperatures at different heat transfer rate are shown in Figure 1. In Figure 1, the predition temperatures are very onsistent with that observed in test at onstant urrent of TEC (i TEC =.5A). There is a maximum differene between theoretial and experimental juntion temperatures up to 4K when experimental T j reahes K. (6) 5 Disussion and onlusion Eletriity is onsumed by thermoeletri effet with Φ to maintain system balane. But in fat, there are lots of air gaps between semiondutor legs whih lead to the appearane of heat miroirulations between both sides of TEMs. Due to the onstrition resistane, onduting strips and air gaps, there is a differene between thermal power absorbed by the semiondutor nodes and the heat fluxing through the erami plate on the old side, whih leads to the error between theoretial and experimental T j as in Figure 7. High preision of the model an be obtained by the introdution of a orret funtion Φ = Φ + Φ f + Φ l. And the heat flowing through air gaps Φ f an be treated as a linear pieewise funtion of Φ /Φ. The oeffiient δ is related to the thikness of erami plates and ondution trips, the area ratio of N(S n + S p )/S, the ondution properties and insulation harateristis of materials, and so on. The

7 ' Numerial modeling of the TECs Experimental T j Experimental T a Theoretial T j Temperature differenes between theoretial and experimental T j First-order polynomial fitting urve 5 Temperatures (K) Temperature differenes (K) Y = X R = Current of TEC itec (A) 4 6 Current of TEC itec (A) (a) Experimental T Figure 8: Temperature differenes between experimental and theoretial T j for different urrents of the TEC with the water ooled exhanger Experimental T a Theoretial T 1 CalulatedΦf + Φl Linear fitting urve Temperatures (K) CalulatedΦ f + Φ l Y =.8879 X R = Y = X R = Current of TEC itec (A) (b) 335 Experimental T h Experimental T a Φ Figure 9: Calulated Φ f + Φ l for different Φ Temperatures (K) () Theoretial T h 4 6 Current of TEC Figure 7: Temperatures for different urrents of the TEC with water ooled exhanger at U heater = V itec (A) linear relationship is approximate beause there are fators (suh as heat onvetions and radiative heat transfer) whih aused inauray in thermal resistane measurements. For the predition model of juntion temperature, it is very diffiult to obtain aurate thermal resistane values, whih varies with ambient temperature, heat flux, devie layout and other fators in the ooling system with TECs. The way to obtain the thermal resistane values by theoretial analysis an be ahieved in other papers. In order to verify the validity of the proposed model, thermal resistane values with experimental method are adopted. Figure 6 illustrates temperature distribution in heat flow path inluding TEC (T j, T h, T and T a ) related to applied heat load. The results show that R dereases with the inrease

8 34 E. Fang et al. T, T, T and T (K) j h a Experimental T j Experimental T Experimental T h Experimental T a Theoretial T j Theoretial T Theoretial T h Heat transfer rate Ploss Figure 1: Temperatures for different heat transfer rate with aluminum heat sink at i TEC =.5A of heat flux aording to exponential deay. And the thermal ondutivity K inreases as the reiproal of aording thermal resistane. The model is derived basing on the struture of the TEMs, so it an be used also in TEGs. In TEGs, there are initiative heat absorptions to generate power. The orretion funtion Φ f works only in one mode Φ Φ, and remains linear to Φ as in TECs. It is worth mentioning that in most researh artiles on TEMs, the thermal ondutivity is only effeted by semiondutor materials, K = λa x /L = λ N A xn /L N + λ P A xp /L P ρ N L N /A xn. In this ase, the thermal ondutivity K, representing the heat transferring from the hot surfae to old through ondution element (not only semiondutor materials but also devies within the pakage) due to the temperature differene, should be onsidered. In fat, the thermal ondutivity with only semiondutor materials aused a signifiant error between theoretial and experimental data. The total thermal ondutivity tested by experiments is more than one hundred times than the theoretial value of semiondutor materials. Referenes [1] Simons R.E., Chu R.C., Appliation of thermoeletri ooling to eletroni equipment: a review and analysis, 16th Annu. IEEE Semiondutor Thermal Meas. Manag. Symp.,, 1-9. [] Hsu C.T., Huang G.Y., Chu H.S., Yu B., Yao D.J., Experiments and simulations on low-temperature waste heat harvesting system by thermoeletri power generators, Appl. Energy, 11, 88, [3] Kane A., Verma V., Singh B., Temperature Dependent Analysis of Thermoeletri Module using Matlab/SIMULINK, IEEE Int. Conf. 5.5 Power Energy, 1, [4] Zebarjadi M.,Esfarjani K., Dresselhaus M.S., Ren Z.F., Chen G., Perspetives on thermoeletris: from fundamentals to devie appliations, Energy & Environ. Si., 1, 5, [5] Meng F., Chen L., Sun F., A numerial model and omparative investigation of a thermoeletri generator with multiirreversibilities, Energy, 11, 36, [6] Wang C., Hung C., Chen W., Design of heat sink for improving the performane of thermoeletri generator using two-stage optimization, Energy, 1, 39, [7] Wen S., Zhang G., Dan Y., Wang D., Model output following ontrol for an aluminum plate ooling proess with a Peltier devie, Int. Conf. Adv. Mehatroni Syst., 1, [8] Wang D., Zhang L., Zhang G., Yang K., Cooling ontrol of aluminum plate with a Peltier devie thermal proess by using a robust right oprime fatorization approah, 1th World Congr. Intelligent Control Automation, 1, [9] Deng M., Yanou A., Tokuda Y., Wang A., Robust fault tolerant thermal ontrol system design of an aluminum plate with Peltier devie, Int. Conf. Adv. Mehatroni Syst., 1, 3-8. [1] Nandini K.K., Muralidhara, Peltier based abinet ooling system using heat pipe and liquid based heat sink, Nat. Conf. Challenges Res. & Tehnol. in the Coming Deades, 13, 1-5. [11] Zhang H.Y., Mui Y.C., Tarin M., Analysis of thermoeletri ooler performane for high power eletroni pakages, Appl. Thermal Eng., 1, 3, [1] Bell L.E., Cooling, heating, generating power, and reovering waste heat with thermoeletri systems, Si., 8, 31, [13] Gou X., Xiao H., Yang S., Modeling, experimental study and optimization on low-temperature waste heat thermoeletri generator system, Appl. Energy, 1, 87, [14] Takahashi K.,Wen S., Sanada M., Deng M., Nonlinear ooling ontrol for a Peltier atuated aluminum plate thermal system by onsidering radiation heat transfer, Int. Conf. Adv. Mehatroni Syst., 1, [15] Aranguren P., Astrain D., Perez M.G., Computational and experimental study of a omplete heat dissipation system using water as heat arrier plaed on a thermoeletri generator, Energy, 14, [16] Xuan X.C., Optimum design of a thermoeletri devie, Semiondutor Si. & Tehnol.,, 17, [17] Riffat S.B., Ma X., Improving the oeflient of performane of thermoeletri ooling systems: a review, Int. J. Energy Res., 4, 8, [18] Lineykin S., Ben-Yaakov S., Modeling and Analysis of Thermoeletri Modules, IEEE Trans. Ind. Appl., 7, 43, [19] Rabari R., Mahmud S., Dutta A., Biglarbegian M., Effet of onvetion heat transfer on performane of waste heat thermoeletri generator, Heat Transfer Eng., 15, 36, [] Hsiao Y.Y., Chang W.C., Chen S.L., A mathemati model of thermoeletri module with appliations on waste heat reovery from automobile engine, Energy, 1, 35, [1] Hodes M., On one-dimensional analysis of thermoeletri modules (TEMs), IEEE Trans. Compon. Pakag. Tehnol., 5, 8, 18-9.