Parameter determination and experimental verification of thermoelectric cooling for a low-temperature chemical reactor

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1 Article Engineering hermophyic May 011 Vol.56 No.15: doi: / SPECIAL OPICS: Parameter determination and experimental verification of thermoelectric cooling for a lo-temperature chemical reactor WANG XiaoQun * ZHAO ZhenLu LIAO FangPing WEI DiSheng & DU ShanYi School of Material Science and Engineering Beihang Univerity Beijing China Received November 5 010; accepted December 0 010; publihed online April hermoelectric cooler (EC) ere ued to cool a lo-temperature chemical reactor (LR). A combined theoretical/ experimental tudy of the heat tranfer in LR ith EC a undertaken. Firt to model of a EC ith a LR junction ere developed to evaluate the equilibrium and tranient temperature of the reactor inner all. Next to method ere ued to determine the parameter of thee model. Finally the relationhip beteen the tranient temperature of the reactor inner all and cooling time a etablihed. he reult ho that the calculated reult of tranient temperature are in good agreement ith the correponding experimental data. thermoelectric cooling lo temperature reactor model parameter Citation: Wang X Q Zhao Z L Liao F P et al. Parameter determination and experimental verification of thermoelectric cooling for a lo-temperature chemical reactor. Chinee Sci Bull : doi: / A thermoelectric cooler (EC) alo knon a a Peltier cooler i a emiconductor-baed electronic component that function a a mall heat pump. When DC poer i applied to a E module heat move through the module from one ide to the other proportional to the applied voltage. Notably the thermoelectric module i only one element in the overall cooling ytem. hermoelectric module are olid tate device ell-knon to be reliable energy converter that are virtually maintenance-free. hey are alo noie-le and vibration-free a there are no mechanical moving part. hey are alo maller and lighter than comparable mechanical cooling ytem. heir olid-tate contruction enure high reliability hich i an advantage hen ued in ytem that are not eaily acceible after intallation. For example EC ued in air-conditioner offer ignificant advantage over more conventional cooling device becaue they ho better performance in active cooling precie controllability and reliability a ell a being environmental friendly depite high cot becaue of lo COP (Coefficient Of Performance) and production initialization *Correponding author ( angxiaoqun@buaa.edu.cn) [1]. Phelan et al. [3] invetigated a variety of refrigeration technologie including thermoelectric vapor compreion pule tube orption and revere Brayton and found that only EC are commercially available in mall ize. EC are idely ued to cool electronic device [4 8] becaue of the plurality of advantage mentioned above. Comparative reearch on EC ha alo been conducted. For intance Xu and coorker [10] have examined the heating proce occurring in EC and obtained an empirical equation decribing heat conduction ith a heat ource hen the current denity i evenly ditributed along the direction of the x-axi. In recent year EC have been applied in chemical indutrie or laboratorie to cool mall-volume part [10 1]. For example a EC-baed pre-concentrator [1011] a developed for the laboratory to overcome the limitation of lo-volume cryogenic device employed in an automated rapid vapor concentrator. he operation of the thermoelectric trap have been examined and optimized ith a ytem that utilized to independent ga chromatograph. EC are alo beginning to be ued to cool high-temperature gacooled tet reactor [1]. Hoever EC are eldom ued he Author() 011. hi article i publihed ith open acce at Springerlink.com cb.cichina.com.pringer.com/cp

2 161 Wang X Q et al. Chinee Sci Bull May (011) Vol.56 No.15 in lo-temperature gla or metal reactor (a orking temperature are loer than room temperature) becaue their cooling capacity i limited. hee type of lo-temperature reactor are uually cooled by mechanical cooling ytem. Cooling agent uually ued are Freon liquid nitrogen liquid carbon dioxide circulating oil or ater. Hoever uch mechanical cooling ytem have everal diadvantage. For example thee are incapable of controlling accurately the temperature of reactor and their tructure are complex and bulky epecially for cooling minireactor. In thi paper e decribe the ue of EC in the cooling of a mini-reactor (actual volume can range from a fe to fifty milliliter) and tudy the temperature control of the reactor inner all. o model are developed to imulate the variation in temperature ith cooling time and equilibrium temperature of the reactor all cooled by a EC. o method to determine parameter of thee model are compared. he influence of electric current on the performance of EC ytem i analyzed uing thee model. Finally the reult from imulation are compared ith experimental data. 1 Sytem decription In an exothermic chemical reaction it i very important to keep the temperature of the reaction mixture at appropriate level. he more accurately the temperature i controlled the better experimental meaurement can be repeated. For thi reaon e conider here a typical ituation here a commercial EC i ued to cool a mini-reactor deigned by u in the laboratory to control the reaction temperature accurately. In addition compared ith conventional mechanical cooling ytem a EC i ilent clean and imple to operate in itu. A heat ink ith circulating ater i ued to diipate heat from the hotter ide of the EC. A chematic diagram of thi ytem i depicted in Figure 1. he cooling ytem include an alloy plate (of the ame material a the chemical mini-reactor all) a heating film (ued to imulate the exothermal capacity of the chemical reaction expected) a EC and a heat ink. he bonding of the EC ith the alloy all on one ide and the heat ink on the other i achieved by mechanical clamping ith thermally-conductive greae beteen the contact urface. Mot of the cooling ytem (including the alloy plate the heating film and the EC) i inulated to reduce heat loe. In fact in accordance ith the inner volume of the mini-reactor and the expected exothermal capacity of the chemical reaction the practical mini-reactor hould need more than one of thee cooling ytem. One commercially-available EC EC 1709 from Beijing Huimao Cooling Equipment Co i 40 mm in idth 40 mm in length and 3.4 mm in thickne. When a direct current i applied the EC extract heat from the all of the mini-reactor to the heat ink. he heat ink diipate the heat extracted by the EC via the circulating ater in the heat ink. he performance of the ytem a teted in a laboratory environment ith tap ater ued a a coolant. emperature of the alloy all and heat ink ere meaured ith platinum reitance thermometer. hermoelectric cooling ytem modeling.1 Steady tate heat tranfer model he operation of a thermoelectric module i baed on the Peltier effect hich a dicovered in When direct current pae through a pair of P- and N-type emiconductor material one ide of the junction i cooled and the other ide i heated. herefore if the colder ide of a EC i attached to the outer ide of a reactor alloy all and the hotter ide i connected to a heat ink a hon in Figure heat from the teel all can be tranferred through the EC to the heat ink by connecting the device to a DC ource. he heat ink pae heat to the circulating ater. It i aumed that all interface are in perfect thermal contact. In general the thermal problem ill be three dimenional. Hoever if the effective area of the EC i nearly equal to the area of the alloy plate ued a the reactor all it i reaonable to aume that the temperature varie only along a ingle dimenion the thickne of the EC a hon in Figure. hi greatly implifie to a 1D-thermoelectric problem. he energy balance equation at the alloy all and the heat ink are a follo [13]: Figure 1 Schematic diagram of the cooling ytem ued in the LR. Figure Steady-tate model of a teel all cooled by a EC ith heat ink. (a) Inner urface of teel all; (b) joint beteen outer urface of teel all and cold ide of EC; (c) hot ide of EC; (d) heat ink.

3 Wang X Q et al. Chinee Sci Bull May (011) Vol.56 No Q c = Qc = (1) Rc Qc = α Ic I R K( h c) () Qh = α Ih + I R K( h c) (3) Q h = Qh =. (4) Rh All material propertie are aumed to be contant. When c and h are eliminated from eq. (1) (4) the repective heat balance equation at poition a and d in Figure can be expreed a here Q = αiω( 1 αirh) I Rω( 1+ KRh αirh) K ( ) ω (5) Q = αiω( 1+ αirc) + I Rω( 1+ KRc + αirc) K ( ) ω (6) ω = 1. IR KR IR IR KR ( α + 1+ )( 1 α ) + ( α + 1) c c h c h If R h 0 eq. (5) (7) reduce to here (7) Qc = α Icω I Rω K( h c) ω (8) Qh = αihω( 1+ αirc) + I Rω( 1+ KRc + αirc) K ( ) ω (9) h c ω 1 =. α IR + 1+ KR c c (10) When heat i tranferred from the reactor mixture to the teel all Q the temperature h of the hotter EC ide and the EC parameter including the Seebeck coefficient α electrical reitance R and thermal conductivity K are all given. he temperature of the inner urface (directly in contact ith the reaction mixture) of the alloy all attached to the colder EC ide can be etimated uing the folloing equation Q + I R+ Kh = ω α I + K Q( 1+ α IRc + KRc) + I R+ Kh =. (11) α I + K. ranient heat tranfer model In the tranient tate the problem i much more complex than for the teady tate jut preented. he cooling capacity of the EC i related to h although all EC parameter (viz. α R and K) are conidered here a a contant independent of time t. he phyical model for the tranient tate i hon in Figure 3. he energy balance of the ytem i then Q = Q + Δ H (1) input output ytem here Q input i the heat tranferred from the inide of the reactor to a EC via the teel all Q output i the heat tranferred to the EC from the alloy all and ΔH ytem i the increae in energy of the alloy all. At any time t ΔH ytem i given by d d Δ Hytem = ρcv = ρcsd (13) dt dt here c and ρ are the pecific thermal capacity and denity repectively of the alloy all and S the area of the alloy all or of the electric module. Becaue the alloy all i thin (D = 3 mm) and the thermal conductivity of the alloy all i high (λ = 169 W/m K) it can be aumed that there i a QD mall temperature difference ( Δ = = 0.09 K) beteen the inner urface and the outer urface of the alloy λ all although the heat flux i very large (Q = 5000 W/m ) through the alloy all. A a reult it can be aumed that the temperature of the alloy all along the thickne dimenion i contant independent of time t. hu eq. (1) can be expreed a Q d input = Q output + ρ csd. (14) d t It i alo aumed that the interface beteen the alloy all and the colder EC ide i in perfect thermal contact. A a reult the temperature of the colder EC ide i equal to that of the alloy all c =. he heat aborbed by the EC may be calculated uing eq. () thereby modifying eq. (14) to Figure 3 ranient model of heat being tranferred from the reactor to the heat ink.

4 1614 Wang X Q et al. Chinee Sci Bull May (011) Vol.56 No.15 1 d = α ( ) + ρ. (15) Q I input h I R K csd d t It i further aumed that for all time t the heat flux tranferred from the reactor i contant and the interface beteen the hotter EC ide and the heat ink i in perfect thermal contact ( h = ). hu eq. (15) i expreed a d Q [ αi I R K( )] = ρcsd. (16) d t he initial temperature of the alloy all i tipulated to be = o t=0. (17) he temperature of the teel all i calculated uing the folloing equation: α I+ K ( t + A ) I R+ K + Q ρcsd = e + α I + K (18) here A i a contant that can be determined according to the initial condition t = 0 = o..3 Parameter of the model o method are conidered to determine the parameter of the propoed model mentioned above. One i to calculate the parameter from average temperature m ; the other i to extract the parameter from the manufacturer data of EC [14]. Method I Currently commercial EC device are made from emiconducting material uch a Bi e 3. According to tet reult by Melcor Corp. the relationhip beteen the Seebeck coefficient (α) electrical reitance (R) thermal conductivity (K) and average temperature ( m ) can be decribed a α P = α N =( m m ) 10 9 V/K (19) r P =r N =( m m ) Ω/m (0) k P =k N =( m m ) 10 4 W/(m K) (1) here m i the average of temperature h and. Subcript P and N ignify P and N-type arm repectively. A EC conit of a number of P- and N-type emiconductor pair (couple) connected electrically in erie and andiched beteen to ceramic plate. We can then calculate the Seebeck coefficient α electrical reitance R and thermal conductivity K of a EC uing the folloing equation: α = Nα () p l R = Nρ p (3) K = Nkp (4) l here N i the number of couple l i the length of the P and N arm i the cro-ectional area of the P and N arm. Method II he parameter of the propoed model can be extracted from the manufacturer data of a EC [14] a Umax α = (5) R U Δ h max h max = (6) Imax h U I Δ K = Δ max max h max max h (7) here Δ max i the larget temperature differential that can be obtained beteen the hot and cold ceramic plate of a EC for a given level of h I max i the input current hich ill produce the maximum poible Δ acro a EC and U max i the DC voltage that deliver the maximum poible Δ at the upplied I max. 3 Reult of imulation and experiment A commercial thermoelectric cooler EC1709 i teted over a broad range of orking condition. All tet ere made under lo electrical current (I = 1 9 A) becaue performance i better at loer current. he tet ere alo performed ith heat tranfer Q c = Q = or 40 W. 3.1 Steady-tate analyi In accordance ith Method I e tart ith the number of couple N=17 and average temperature m =300 K. For a PN-pair the length of the P and N arm i l = 1 mm giving area = mm. Applying eq. (19) (4) one can calculate the model parameter to obtain value: α= V/K R=1.50 Ω K=0.785 K/W. Similarly for Method II e find from the manufacturer data heet: under h = 300K condition Δ max = 6 K I max = 9 A U max = 15. V and Q max = 89. W. Applying eq. (5) (7) one can calculate the model parameter: α= V/K R=1.34 Ω K=0.875 K/W. Equilibrium temperature of the reactor all can be calculated from eq. (10) and (11). Here h = 300 K the input current I range from 1 to 9 A R c =D/λS= K/W and Q = or 40 W. Figure 4 ho the reult of calculation uing the teadytate model for the EC ytem and the experimental data for Q c = W. In thi figure the dahed line i the calculation reult uing model parameter determined by Method I the olid line i the calculation reult ith model parameter

5 Wang X Q et al. Chinee Sci Bull May (011) Vol.56 No obtained by Method II and point repreent data from experimental meaurement. A one can ee reult from Method II are in good agreement ith the experimental data under different Q c. hu Method II i better in determining thee parameter than Method I. From Figure 4 it i alo clear that the equilibrium temperature i loet hen the input current I i et at 6 A given any et cooling capacity. 3. ranient analyi ranient temperature of the reactor all are calculated uing eq. (17) and (18). he temperature of the heat ink i meaured a = 300 K; the phyical propertie of alloy all are c=881 J/(kg K) ρ=700 kg/m 3 S=4 cm 4 cm and D=3 mm. In thi tudy different EC input current at a pre-determined cooling capacity of 10 W are conidered. he time- dependence of the temperature at the inner urface of the alloy all i preented in Figure 5. Here the dahed line i the calculated reult ith the model parameter determined by Method II hile the olid line correpond to the experimental reult. Clearly the calculated curve i in good agreement ith the experimental curve although the rate of decreae in the meaured temperature of the alloy all ith cooling time i lightly loer than the calculated reult. he difference eem to be more apparent at higher electrical current. he reaon may be due to the fact that thermal reitance are ignored beteen the EC and the alloy all and beteen the EC and the heat ink. 4 Concluion Figure 4 Calculational reult of the teady-tate model and tet data under different Q c condition. (a) Q c =10 W; (b) Q c =0 W; (c) Q c =30 W; (d) Q c =40 W. he equilibrium all temperature of an LR cooled by a EC and temperature change ith applied direct current ere ell-decribed by the teady-tate model. he tranient temperature and their change ith cooling time ere calculated uing the tranient model. In particular to method ere ued to determine the model parameter. It a found better to extract the parameter of the propoed model from the manufacturer data of the EC than from the average temperature m. he reult of calculation uing the teady-tate model ere in good agreement ith the experimental data at different value of Q c. he equilibrium temperature a loet hen the input current I a 6 A at any of the pre-et cooling capacitie. A good fit a alo achieved beteen the experimental and imulation reult of the tranient model although the rate of decreae in meaured temperature i a little loer than etimated reult. Overall e revealed that not only can EC be ued in the cooling of mini-reactor but the teady-tate and tranient model can alo be ued to aid the deign of practical LR. he author ould like to thank Dr. Huang Chen Xu Jun and Zhu Xiaoguang for their aitance in the reearch ork. Nomenclature Figure 5 Calculation reult of the tranient model and tet data at different current (Q c =10 W). (a) Current 3 A; (b) current 4 A; (c) current 5 A; (d) current 6 A. A contant determined by eq. (17) and (18); c thermal capacity ratio of the alloy all; D thickne of the alloy all; ΔH ytem energy increae for the alloy all ith increaing of the temperature; I current through the thermoelectric module; I max input current hich ill produce the maximum poible Δ acro a EC; k thermal conductivity of P and N-type arm; K total thermal conductivity of thermoelectric module; l length of P-type and N -type arm;

6 1616 Wang X Q et al. Chinee Sci Bull May (011) Vol.56 No.15 N number of PN emiconductor couple; Q c cooling capacity in the thermoelectric cooling ytem; Q h heat diipated from hot-ide of the thermoelectric module; Q input heat tranfer from the inide of the reactor to a EC through the alloy all; Q output heat tranfer to the EC from the alloy all; Q Q heat diipated by circulating ater in the heat ink; heat diipated by the reactor mixture into the alloy all; r electrical reitance of P-type and N-type arm; R total electrical reitance of thermoelectric module; R c total thermal reitance of the alloy all and the cold ide of a EC; R h total thermal reitance of the hot-ide of the thermoelectric module and the heat ink; area of the one P or N -type arm; S area of the alloy all or area of the electric module; t time; c cold ide temperature of thermoelectric module; h hot-ide temperature of the thermoelectric module; m average temperature beteen cold and hot ided of a EC; temperature of the heat ink; Δ max larget temperature differential beteen the hot and cold ceramic plate of a EC; temperature of the alloy reactor all; Δ temperature difference beteen the outide and inide of the alloy all; U max DC voltage that deliver the maximum poible Δ at the upplied I max ; V volume of the alloy all; Greek ymbol; α Seebeck coefficient of thermoelectric module; ρ denity of the alloy all; λ thermal conductivity of the alloy all; ω ω = 1. IR KR IR IR KR ( α + 1+ )( 1 α ) + ( α + 1) c c h c h 1 Riffat S B Qiu G Q. Comparative invetigation of thermoelectric air-conditioner veru vapour compreion and aborption airconditioner Appl hermal Eng 004 4: Gao M Roe D M. Experimental evaluation of prototype thermoelectric dometic-refrigerator Appl Energy : Patrick E P Victor A C Yu et al. Current and future miniature refrigeration cooling technologie for high poer microelectronic. IEEE ran Comp Pack ech 00 5: Simon R E Chu R C. Application of thermoelectric cooling to electronic equipment: A revie and analyi. In: Sixteenth IEEE SEMI- HERM Sympoium March DiSalvo Franci J. hermoelectric cooling and poer generation. Science : Fukutani K Shakouri A. Deign of bulk thermoelectric module for integrated circuit thermal management. IEEE ran Comp Packaging ech 006 9: Yamanahi M. A ne approach to optimum deign in thermoelectric cooling ytem. J Appl Phy : Zhu D S Lei J X Wang C H et al. Reearch progre in electronic comonent heat diipation uing thermoelectr ic cooling technology. Microelectronic : Xu S L Yu G L He D Derivation of ne formulae of thermoelectric cooling. Chinee Sci Bull : Gehrke M Kapila S Hambacker K et al. Deign of an automated rapid vapor concentrator and it application in nitroaromatic vapor ampling. Proceeding of SPIE SPIE Digital Library Hambacker K Kapila S Nam P et al. A rapid vapor concentrator and detection ytem for nitroaromatic. Proceeding of SPIE Ihiyama S Fukaya K Eto M. Synthei and fabrication technique of SiC/SiC thermo element. Key Eng Mater : Ioffe A F. Semiconductor thermoelement and thermoelectric cooling. Infoearch Simon L Sam B Y. Analyi of thermoelectric cooler by a picecompatible equivalent-circuit model. IEEE Poer Electro Lett 005 3: Open Acce hi article i ditributed under the term of the Creative Common Attribution Licene hich permit any ue ditribution and reproduction in any medium provided the original author() and ource are credited.