Performance Prediction of Commercial Thermoelectric Cooler. Modules using the Effective Material Properties

Transcription

1 Performance Prediction of Commercial ermoelectric Cooler Modules using te Effective Material Properties HoSung Lee, Alaa M. Attar, Sean L. Weera Mecanical and Aerospace Engineering, Western Micigan University, 93 W. Micigan Ave, Kalamazoo, Micigan , USA Office (69) Fax (69) Abstract is work examines te validity of formulating te effective termoelectric material properties as a way to predict termoelectric module performance. e tree imum parameters (temperature difference, current, and cooling power) of a termoelectric cooler were formulated on te basis of te ot junction temperature. en, te effective material properties (Seebeck coefficient, electrical resistance, and termal conductivity) were defined in terms of te tree imum parameters tat were taken from eiter a commercial termoelectric cooler module or te measurements. t is demonstrated tat te simple standard equation wit te effective material properties predicts well te performance curves of te four selected commercial products. Normalized parameters over te imum parameters were also formulated to present te caracteristics of te

2 termoelectric coolers along wit te normalized carts. e normalized carts would be universal for a given termoelectric material. Keywords: ermoelectric cooler, termoelectric module, effective material properties, imum parameters, normalized parameters, and normalized carts. Nomenclature A cross-sectional area of termoelement (m ) COP te coefficient of performance, dimensionless electric current (A) imum current (A) j electric current density vector (A/m ) K L k n termal conductance (W/K) lengt of termoelement (m) termal conductivity (W/mK) te number of termocouples q eat flux vector (W/m ) Q c Q cooling power, eat absorbed at cold junction (W) eat liberated at ot junction (W) Q c imum cooling power (W) R c electrical resistance () temperature ( C) low junction temperature ( C)

3 3 ig junction temperature ( C) average temperature c ( C) V Voltage of a module (V) V imum voltage (V) W work per unit time W R (W) x distance of termoelement leg (m) Z te figure of merit (K - ), Z k temperature difference c ( C), imum temperature difference ( C) Greek symbols Seebeck coefficient (V/K) electrical resistivity (cm) gradient operator vector Subscript p n p-type element n-type element Superscript * effective quantity

4 4. ntroduction ermoelectric coolers ave compreensive applications [-5] in electronic devices, medical instruments, automotive air conditioners, and refrigerators. ermoelectric penomena are often described by a simple standard equation, wic as been widely used in te literature [-5], sometimes in good agreement wit experiment [6,9,]. e simple standard equation is erein called te ideal equation, wic is virtually formulated under tree assumptions tat te electrical and termal contact resistances, te omson effect (temperature-dependent Seebeck coefficient), and te radiation and convection eat transfer are negligible [,]. e radiation and convection eat transfer is small for te moderate temperature differences between te ot and cold junction temperatures and te surrounding temperature in typical commercial cooler modules. e omson effect rater sligtly improves te performance [6,7]. e major errors between te measurements and te ideal equation lie on te electrical and termal contact resistances [,3]. Commercial termoelectric cooler modules consist of a number of termoelement couples (or termocouples), electrically connected in series and termally sandwiced in parallel between two ceramic plates. e manufacturers usually provide te performance curves along wit te imum parameters suc as te temperature difference, te current, te cooling power Q, and te voltage V. However, te material properties of te modules suc as te Seebeck coefficient, te electrical resistivity, and te termal conductivity k are not usually provided as manufacturers proprietary information. erefore, system designers find it difficult to obtain te material properties.

5 5 Huang et al. [4] measured te material properties of a commercial module for te optimum design using an evacuated and insulated test apparatus. ey confirmed tat te measurements were in good agreement wit te performance curves provided by te manufacturer. Neverteless, tey were not able to fit te measured data to te ideal equation, wic was deemed mainly due to te electrical and termal contact resistances not counted for witin te ideal equation. Lineykin and Ben-Yaakov [5] formulated te teoretical imum parameters from te ideal equation using te definitions used by manufacturers and ten expressed te pysical module properties (m, Rm, and Km) in terms of te tree parameters (,, and V) out of te four teoretical imum parameters (,, Q, and V). n tis way, te module properties contain information of te number of termoelement couples and geometric ratio. Lineykin and Ben-Yaakov extracted te pysical module properties by substituting te manufacturers imum parameters for te teoretical imum parameters. Luo [6] used two metods to determine te pysical module properties: not only te combination (,, and V) used by Lineykin and Ben-Yaakov, but also te different combination (,, and Q) out of te four imum parameters. Wen te two metods were compared to eac oter over four selected commercial modules, te pysical module properties over te four modules varied witin a 5% discrepancy range. Zang [7] obtained te pysical module properties of a commercial module using te tree parameters (,, and V) for application to an electronic cooling system and performed evaluation and optimization onto te system design, including te eat sinks.

6 6 Simons [] sowed a capability of te module properties (m, Rm, and Km) wit a different set of te imum parameters (,, and Q) to predict te performance of an electronic module. an and Fok [] evaluated te module properties for commercial modules using te tree imum parameters (,, and V) and compared te predicted results wit te manufacturers performance curves. e comparisons sowed fair agreement and te errors increased wit increasing current or temperature difference. Recently, Aiska and Aiska [8] developed a new economic metod of measurement for termoelectric outputs and properties providing formulas based on te ideal equation by measuring te imum parameters (,, and V) and experimentally proved to be reasonably accurate. Most of te above mentioned works tried to extract te pysical module properties (m, Rm, and Km) from eiter te tree parameters (,, and V) or te oter set of parameters (,, and Q), wic imposes te uncertainties on te cooling power prediction. On te oter and, te present work extracts te effective material properties (and k) from te manufacturers imum parameters (,, and Q), wic imposes te uncertainties on te voltage prediction, particularly being good at module design for specific systems. Note tat, altoug te differences between te module properties and te effective material properties appear minuscule, te results and applications are of great consequence: te module properties are constrained to ave a validity for use of te module, but te effective material properties are not, wic is te uniqueness of te present paper. e optimal design [8] using te ideal equation wit te effective material properties will now be simple and robust. e present work studies to verify in detail te effective material properties comparing wit te performance curves

7 7 of four major manufacturers products. Hence, te usually intractable temperature dependence of te material properties and te subtle termal and electrical contact resistances can be examined wit te effective material properties tat are constant. e normalized carts wit te imum parameters were presented by Buist [9] and later Uemura [] for te purpose of te design of termoelectric devices. However, teoretical formulas for te normalized carts were not found to te autors knowledge. erefore, te present work studies te normalized formulas over te imum parameters providing te two normalized carts, wic coerently reveal te elusive general caracteristics of termoelectric coolers. Heat Absorbed p n n-type Semiconductor p-type Semiconcuctor p n p p n p n Positive (+) Electrical nsulator (Ceramic) Heat Rejected Negative (-) Electrical Conductor (copper) Figure. Cutaway of a typical termoelectric module. deal Equation

8 8 A typical termoelectric module is sown in Figure. Suppose tat te upper junction temperature (upper electrical conductor) is at c and te lower junction temperature is at. e cooling power at te junction of temperature c is given by Q c nc R K () were n is te number of termocouples, a te Seebeck coefficient, te current, R te electrical resistance, K te termal conductance, and = ( - c). From now on, Equation () is called te ideal equation. e current for te optimum COP can be obtained by differentiating COP and setting it to zero. COP R Z () were Z Z k and is te average temperature of c and. On te basis of, is expressed by Z Z (3). Maximum Parameters Let us consider a termoelectric module sown in Figure for te teoretical imum parameters wit te ideal equation. e module consists of a number of termoelement couples as sown. As mentioned before, te ideal equation assumes tat tere are no te electrical and termal contact resistances, no omson effect, and no radiation or convection. t is noted tat te teoretical imum parameters migt differ wit te manufacturers imum parameters tat are usually obtained by measurement.

9 9 e imum current is te current tat produces te imum possible temperature difference, wic always occurs wen te cooling power is at zero. is is obtained by setting Q c = in Equation (), replacing c wit ( ) and taking derivative of wit respect to and setting it to zero. e imum current is finally expressed by R Z Z (4) Or, equivalently in terms of, R (5) e imum temperature difference always occurs wen te cooling power is at zero and te current is at imum. is is obtained by setting Q c = in Equation (), substituting bot and c by and, respectively, and solving for. e imum temperature difference is obtained as (6) Z Z e imum cooling power Q c is te imum termal load wic occurs at = and =. is can be obtained by substituting bot and c in Equation () by and (since c = ), respectively, and solving for power for a termoelectric module wit n termoelement couples is Q c. e imum cooling

10 R n Q c (7) e imum voltage is te DC voltage wic delivers te imum possible temperature difference wen =. e imum voltage is given by n V (8) 3. Normalized Parameters f we divide te actual values by te imum values, we can normalize te caracteristics of te termoelectric cooler. e normalized cooling power can be obtained by dividing Equation () by Equation (7), wic is R n K R n Q Q c c (9) wic, in terms of te normalized current and normalized temperature difference, reduces to c c Z Q Q () were

11 Z Z () e coefficient of performance in terms of te normalized values is Z COP () e normalized voltage is V V (3) e normalized current for te optimum COP is obtained from Equation (). Z COP (4) were Z is expressed using Equation (3) by

12 Z Z (5) Note tat te above normalized values in Equations (), (), () and (3) are functions only of tree parameters, wic are, and Z. 4. Effective Material Properties e effective material properties are defined ere as te material properties tat are extracted from te imum parameters provided by te manufacturers or from measurements. e effective figure of merit is obtained from Equation (6), wic is Z (6) e effective Seebeck coefficient is obtained using Equations (5) and (7), wic is c (7) n Q e effective electrical resistivity can be obtained using Equation (5), wic is A L (8)

13 3 e effective termal conductivity is now obtained, wic is k (9) Z e effective material properties include all te losses suc as te contact resistances. Hence, te effective figure of merit appears sligtly less tan te intrinsic figure of merit as sown in able. Since te material properties were obtained for a p-type and n-type termoelement couple, te material properties of a termoelement sould be obtained by dividing by. 5. Results and Discussion n te previous reports [5-7], te pysical module properties (m, Rm, and Km) were extracted from a combination (,, and V) among te four manufacturer s imum parameters (,, Q c, and V). n te present work, te effective material properties (,, and k*) were extracted from a different combination (,, and Q c ) among te manufacturers imum parameters. erefore, te pysical module properties old information of te number of termoelement couples and te geometric ratio (A/L), wile te effective material properties do not. n order to examine te status of te ideal equation wit te effective material properties, several major manufacturers were cosen as sown in able. e effective material properties were first calculated using te manufacturer s imum parameters using Equations (6) - (9). e geometry of A and L were actually measured. Only one

14 4 set of te intrinsic material properties was provided by te manufacturer, wic is sown in able. n te column of Module CP-7-5, te effective material properties obtained appear very close to te intrinsic material properties. t sould be noted tat te dimensionless intrinsic figure of merit of.83 exibits sligtly larger tan te dimensionless effective figure of merit of.744, wic is reasonable because te contact resistances are conceptually imposed on te effective material properties. No appreciable improvement was found even toug te intrinsic material properties were used in calculation because te contact resistances exist anyway. t is noted tat te imum temperature differences provided by different manufactures may not be consistent wit one anoter. e manufacturability and contact resistances may be responsible for te inconsistency. able Comparison of te properties and dimensions for te commercial products of termoelectric modules Description EC Module (Bismut elluride) Symbols CP-7-5 ( =98 K) RC-4 ( =98 K) B ( =98 K) C-3-53 ( =98 K) # of termocouples n ntrinsic material properties (provided by manufacturers) Effective material properties (calculated using commercial,, and Q c) Measured geometry of termoelement V/K cm. x k (W/cmK).5 x Z V/K cm.9 x -3.5 x -3. x -3. x -3 k (W/cmK).6 x -.7 x -.6 x -.7 x - Z A (mm ).... L (mm) G=A/L (cm) Dimension (W L H) mm Manufacturers imum parameters ( C) (63) (A) Q c (W)

15 5 V (V) R () module Figure depicts comparison between te calculations (solid lines) and te manufacturer s performance data (triangles) of Module CP-7-5. e cooling power in Figure (a) was calculated using Equation (7) by substituting c by ( ) and using te effective material properties. e dotted curve indicates te cooling power at te optimal COP for wic Equation (7) was used wit substituting by te current at te optimum COP in Equation (). t is seen in Figure (a) tat te calculated effective imum parameters ( = 67 C, = 3.9 A, and Q c = 34.3 W) are in good agreement wit te manufacturer s performance curves. On te oter and, Figure (b) depicts tat te errors on te voltage-vs-temperature-difference curves increase wit decreasing te temperature difference. e errors are associated wit te combination (,, and Q c ) and partially te inerent contact resistances. e analysis including te temperature dependence of te material properties and te termal and electrical contact resistances are very formidable especially for optimal system design wic requires many iterations of calculations, also not available in te literature to te autors knowledge. erefore, te errors are a nature of tis work. e present work presents a single module, but system design involves multiple modules. However, te multiple modules in a system may be effectively andled using a termal isolation tecnique []. e marked data of te COP in Figure (c) were not provided by te manufacturer but generated in tis work using te measured data in Figures (a) and (b), wic are in a fair agreement.

16 6 Cooling Power, Qc (W) = 3.9 A Prediction Commercial product 3. A Optimal COP.4 A.6 A.8 A (a) emperature Difference, ( C) Voltage (V) Prediction Commercial product = 3.9 A 3. A.4 A.6 A.8 A (b) emperature Difference ( C)

17 7 3 Prediction Commercial product.5 = C COP.5 C 3 C.5 4 C 5 C 3 4 Current (A) (c) Figure. (a) Cooling power versus, (b) Voltage versus, as a function of current, and (c) COP versus current as a function of. e original performance data (triangles) of te commercial module (Module CP-7-5) are compared to te prediction (solid lines). e dotted line in (a) indicates te cooling powers at te optimum COP. Figures 3 (a) and (b) depict comparison between te calculations and te performance data of Module RC-4. n general, te calculations are in good agreement wit te manufacturer s performance data. Figure 3 (c) sows only te calculations (solid lines) werein te COP data (dotted lines) were not able to be generated due to te lack of information from te manufacturer.

18 8 7 6 Prediction Commercial product Q c = W Q c = 5 W 5 Q c = W ( C) 4 3 Q c = 5 W Q c = W Q c = 5 W Q c = 3 W (A) Q c = 35 W (a) 3 5 Prediction, Qc = Prediction, = Comm. product, Qc = Comm. product, = Voltage (V) 5 5 Q c = (b) Current (A)

19 9 3.5 Prediction No commercial product = 3. C COP C C 5.8 C 3 4 Current (A) Figure 3. (a) versus current as a function of cooling powers, (b) Voltage versus current for Qc = and =, respectively, and (c) COP versus current. e original performance data (triangles and squares) in (a) and (b) of te commercial module (Module RC-4) are compared to te prediction (solid lines). Figures 4 (a), (b) and (c) depict comparison between te calculations and te performance data of Module B , wit an excellent agreement.

20 35 3 = 3.6 A Prediction Commercial product Optimal COP Cooling Power, Qc (W) A.8 A.9 A (a) emperature Difference, ( C) 6 4 = 69 C = 5.75 C = 34.5 C = 7.5 C Voltage (V) Prediction Commercial product 3 4 (b) Current (A)

21 Prediction Commercial product.6 = 7.5 C. COP C C 3 4 Current (A) (c) Figure 4 (a) Cooling power versus as a function of current, (b) Voltage versus current as a function of, and (c) COP versus current as a function of. e original performance data (triangles) of te commercial module (Module B ) compared to te prediction (solid lines). e dotted line in (a) indicates te cooling powers at te optimum COP. Figures 5 (a), (b) and (c) depicts comparison between te calculations and te performance data of Module C-3-53, wit a good agreement.

22 35 Cooling Power, Qc (W) = 3.5 A 3 A.5 A A.5 A A Prediction Commercial product Optimal COP emperature Difference, ( C) (a) Voltage (V) = 3.5 A 3 A.5 A A.5 A A (b) Prediction Commercial product emperature Difference ( C)

23 3 3.5 = C Prediction Commercial product COP.5 C 3 C.5 4 C 5 C 3 4 Current (A) (c) Figure 5. (a) Cooling power versus as a function of current, (b) voltage versus, as a function of current, and (c) COP versus current as a function of. e original performance data (triangles) of te commercial module (Module C-3-53) are compared to te prediction (solid lines). e dotted line in (a) indicates te cooling powers at te optimum COP.

24 4.9 / =. / = Q c /Q c.4 V/V / Figure 6. Normalized cart : cooling power and voltage versus as a function of current. e solid lines depict te data at Z =.75, wile te dotted lines depict te alternate current ratios at Z =.4. e dased line depicts te cooling power ratios at te optimum COP.

25 / = / = Q c /Q c.5.5 COP / Figure 7. Normalized cart : cooling power and COP versus current as a function of. e solid lines depict te data at Z =.7, wile te dotted lines depict te alternate temperature difference ratios at Z =.4. Figures 6 and 7 depict te normalized cooling power Q c Q c, COP, and voltage V V, wic were plotted using Equations (7), (9), and (3), respectively. e above tree dependent parameters are only functions of tree independent parameters: /, /, and Z as sown in te equations. From te previous discussion, we learned tat te ideal equation wit te effective material properties predicts well te real performance of a termoelectric cooler module. ese normalized carts sould also predict well te performance wit a given Z. e solid lines depict te predictions at Z =.75, wic is a typical dimensionless figure of merit used in te commercial

26 6 products. n order to see te effect of Z, te predictions at Z =.4 were plotted as te dotted lines for comparison. We find from te figures tat te normalized carts are not significantly influenced by Z. ese carts are ten considered being universal to approximately represent te performance of most termoelectric cooler modules in te present market. Wit inserting te imum parameters provided by te manufacturers into te carts, te reasonable cooling power, COP and voltage could be obtained as functions of current and temperature difference. 6. Conclusions e accuracy of te ideal equation in connection wit te effective material properties is demonstrated by comparing wit several manufacturers performance data (wic are usually obtained by te measurements), being in good agreement. Usually, te analysis of termoelectric devices, including te temperature-dependence of te material properties and te electrical and termal contact resistances, is very formidable. However, wen one uses te ideal equation wit te effective material properties for moderate temperature differences, te analysis becomes simple and robust and could be a platform for optimal system design. e imum temperature differences given by manufacturers may not be consistent. Normalized carts are constructed using te ideal equation and te imum parameters defined in tis work. e normalized carts and represent well te performance of any termoelectric modules at a given dimensionless figure of merit.

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