Peltier coefficient measurement in a thermoelectric module This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2013 Eur. J. Phys. 34 1255 (http://iopscience.iop.org/0143-0807/34/5/1255) Download details: IP Address: 128.119.168.112 The article was downloaded on 02/09/2013 at 17:11 Please note that terms and conditions apply. View the table of contents for this issue, or go to the journal homepage for more Home Search Collections Journals About Contact us My IOPscience
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Peltier coefficient measurement in a thermoelectric module
This article has been downloaded from IOPscience. Please scroll down to see the full text article.
2013 Eur. J. Phys. 34 1255
(http://iopscience.iop.org/0143-0807/34/5/1255)
Download details:
IP Address: 128.119.168.112
The article was downloaded on 02/09/2013 at 17:11
Please note that terms and conditions apply.
View the table of contents for this issue, or go to the journal homepage for more
Home Search Collections Journals About Contact us My IOPscience
Received 5 March 2013, in final form 24 May 2013Published 29 July 2013Online at stacks.iop.org/EJP/34/1255
AbstractA new method for measuring the Peltier coefficient in a thermocouple X/Ybased on the energy balance at the junction has been proposed recently. Thistechnique needs only the hot and cold temperatures of a thermoelectric modulewhen an electric current flows through it as the operational variables. Thetemperature evolutions of the two module sides provide an evident and accurateidea of the Peltier effect. From these temperatures, the heat transfer betweenthe module and the ambient is also evaluated. The thermoelectric phenomenaare described in the framework of an observable theory. Based on thisprocedure, an experiment is presented for a university teaching laboratoryat the undergraduate level.
(Some figures may appear in colour only in the online journal)
1. Introduction
Accurate measurement of the Peltier coefficient �Y−�X of a thermocouple X/Y is a laboriousand difficult task [1]. Very few papers dealing with this problem can be found in the literature[1, 2]. Authors prefer to apply the Onsager reciprocal relation (ORR), �Y−�X = T (SY − SX),using the Seebeck coefficient experimental value SY − SX. The latter is measured in a simpleand easy way for obtaining very precise results [3–5]. Nevertheless, the direct measurementof the Peltier coefficient cannot be always ignored: it is convenient to confirm by experimentthe ORR theoretical postulate in more than a few cases [6].
A new method for measuring the Peltier coefficient in a thermoelectric module (TEM),based on the energy balance at the junctions of the materials, was published recently [7].Based on this new approach, we introduce an experiment to be carried out by students in auniversity laboratory, designed for a total duration of about three hours. To this end, we use
1 Author to whom any correspondence should be addressed.
Figure 1. Both the temperature distribution T (x) and the electric current I characterize the non-equilibrium state of the wire X. JU denotes the energy flux along the wire, T0 the ambienttemperature, and q the heat flux from the wire towards the surroundings. The voltage V is measuredthrough probes Z.
a commercial TEM composed of two materials that we label as X and Y in the following.The evolution of the temperatures at the two module sides, Th (hot side) and Tc (cold side),for different electric currents I, provides an evocative idea of the Peltier effect and offers thepossibility of calculating �Y − �X.
For the undergraduate level, or for advanced undergraduate projects, other authors havealready introduced laboratory techniques for determining the Peltier coefficient �Y − �X.Kraftmakher [8] evaluates this coefficient by measuring the heat supplied to the hot side ina TEM when an electric current flows through the module, and the temperature differencebetween the two faces is zero. Guenault et al [9] measure the temperature difference betweenthe two junctions of a thermocouple when I �= 0, and also determine the amount of heat thatneeds to be applied when I = 0 in order to obtain the same temperature difference.
In this paper the thermoelectric phenomena are described in the framework of anobservable theory. In this formulation the measurable quantities are emphasized, that is thetemperature T, the electric current I, the heat flux q which the wire laterally dissipates, thevoltage V measured between probes Z attached to the electric conductor, and the energyflux along the conductor JU (figure 1). In addition, those which cannot be determinedexperimentally, such as the electrical potential φ in the conductor and the electric field strengthE in the conductor, are avoided [10]. To simplify the theory, filiform wires are considered,where only one value provides the cross-section temperature. We will also not distinguishbetween heat or work fluxes along the wire: only the total energy flux JU is considered.
2. Theory
As already stated, we consider a filiform conductor with a temperature distribution T(x) andwhere an electric current flows through the module (figure 1). The transport equations thatdescribe the thermoelectric phenomena are [1, 7]
JU = κAdT
dx+
(� − μ
e
)I (1)
andd(μ/e)
dx= S
dT
dx− ρ
AI, (2)
where κ is the thermal conductivity, A is the cross-sectional area, μ is the electrochemicalpotential of the electron, e > 0 is the magnitude of the electron charge, and ρ is theelectric resistivity. The electrochemical potential distribution μ(x) can be studied applying
Peltier coefficient measurement in a thermoelectric module 1257
d VT 0
← I
Z
x
T
Z
X
d x
d T
VT 0
Figure 2. Two probes Z connect the wire X to the voltmeter which is at ambient temperature T0.The elemental voltage dV measured at the voltmeter provides information about the elementalchange of the electrochemical potential dμ.
XY
x
T
Y XX
Th
Tc
To
To
← I, JU
Figure 3. The Peltier effect appears in an arrangement composed of two materials when an electriccurrent flows through the module. At the junctions X/Y, a jump in the slope of the temperaturedistribution is observed.
d(μ/e) = SZ dT − dV (see figure 2) and the voltage distribution V(x) measured by a voltmeterthrough the probes Z [1, 7, 10].
At every cross-section of the wire, the non-equilibrium state is characterized by thetemperature gradient dT/dx and electric current I. When both of these quantities are zero, thatis dT/dx = 0 and I = 0, the system is in thermodynamic equilibrium: there is no energyflux and the electrochemical potential has a uniform value. Equations (1) and (2) describesix different phenomena: (i) Fourier heat conduction, (ii) Thomson effect, (iii) Joule effect,(iv) Peltier effect, (v) Seebeck effect, and (vi) Ohm’s law [1].
The Peltier effect appears at the junctions of two different wires X and Y when an electriccurrent flows through the module (figure 3). As the Peltier component of energy flux is differentin each conductor �
junctX I �= �
junctY I, the temperature evolves towards the stationary distribution
shown in figure 3. Then, the Peltier coefficient can be evaluated from the values of the twotemperature gradients [1]
�junctY − �
junctX = A
[κ
junctX (dT/dx)
junctX − κ
junctY (dT/dx)
junctY
]I
. (3)
Here, we have considered two values of the temperature derivative in the immediate vicinityof the junction, (dT/dx)
junctX and (dT/dx)
junctY , each one in a branch. A scheme of the energy
balance at the junction can be seen in figure 4. Only one component of the energy �junctY I enters
the junction, while the three other components, κjunctX A (dT/dx)
junctX , κ
junctY A (dT/dx)
junctY , and
�junctX I, leave the junction.
1258 J Garrido et al
κ Xjunct A dT dx( )X
junct ← ← κ Yjunct A dT dx( )Y
junct
Π Xjunct I ← ← Π Y
junct I
T
T0
Th
Figure 4. The Peltier effect is a consequence of the energy balance at the junction X/Y, that is�
junctX I + κ
junctX A (dT/dx)
junctX = �
junctY I + κ
junctY A (dT/dx)
junctY .
T h
T c
← connectors
dies →
Figure 5. Scheme of a TEM. The dies X and Y, and the copper connectors, are sandwiched betweenthe ceramic substrates.
3. Experimental task
In this proposal of undergraduate work the measurement of the Peltier coefficient is to be carriedout in a TEM, where the two materials X and Y are arranged alternately in series (figure 5).Copper connectors are placed at the ends of each die in order to form an electric circuit.Two ceramic substrates, which are good heat conductors but electric insulators, constitute themodule shell and provide structural consistency. When an electric current flows through themodule, the temperature of the two sides of the module evolves from the ambient temperatureT0 to the steady values Th and Tc.
For simplicity, only one thermocouple of the module is considered, as we can see atfigure 6. We denote as cross-sections I and II the junctions X/Cu and Cu/Y, respectively. Atthe steady state, the energy fluxes hold JII
U − JIU = Qh/N, where Qh is the heat that departs
from the hot connectors towards the environment, and N is the number of couples X/Y in themodule. For small currents, a linear temperature gradient at the pellets can be assumed(
dT
dx
)I
X
= −(
dT
dx
)II
Y
= Th − Tc
L, (4)
where L is the height of these elements. Then, from equations (1), (2) and (4) we deduce
I(�II
Y − �IX
) + RconnI2 = Qh
N+ (KX + KY) (Th − Tc) , (5)
where Ki = κiA/L is the thermal conductance of the pellet i = X, Y. A scheme of this balanceis provided in figure 7 [11]. The energy that the copper connector receives due to the Peltiereffect �II
YI −�IXI, plus that absorbed by the Joule effect RconnI2, equals the components Qh/N
and (KX + KY) (Th − Tc) given out by the connector.The heat flux Qh/N can be calculated by the temperatures Th, Tc, and T0. To avoid spurious
losses, a thermal insulation material laterally covers the module, except for the two faces thatare in contact with the aluminium blocks (figure 8). A clamp provides a strong structure to the
Peltier coefficient measurement in a thermoelectric module 1259
↑ I
↑ Qh N ↑
I
↑ x
↑ JU
II
↓ JU
↓ x
↓ I
↓ Qc N ↓
Th
Tc
Tc
Th
Y
III
x
X
T
Figure 6. Temperature distribution in one of the thermocouples of the TEM in the steady state. Forsmall currents a linear temperature gradient can be assumed.
↑ ↑ ↑ ↑ ↑ Qh N ↑ ↑ ↑ ↑ ↑
↓K X Th − Tc( )
Rconn I 2
↓
Π XI I
↓
K Y Th − Tc( )↑
Π YII I
Figure 7. Energy fluxes which enter or leave a copper connector at the steady state. The Joule termis the energy absorbed by the connector due to the balance (μI
X − μIIY)I/e = RconnI2.
Figure 8. Picture of the experimental device.
assembly. To provide good thermal contact between the module and the blocks a conductingpaste is placed between them. Temperature probes embedded in the aluminium blocks measureTh and Tc. To evaluate the ambient temperature T0 an aluminium radiator is placed in the base ofthe module. The temperatures Tc, Th and T0 are measured by digital millimetres using K-typethermocouples with a precision of 0.1 ◦C.
1260 J Garrido et al
Figure 9. Change of temperatures Th, Tc and T0 versus time during the first stage. The constantcurrent I = 50 mA is applied at t ≈ 2 min. Due to the Peltier effect, one of the metal blocks isheated and the other is cooled.
The module is placed in a vertical position thereby providing an identical heat transfercoefficient on both sides. Therefore, only one coefficient � determines the heat fluxesQh = � (Th − T0) and Qc = � (Tc − T0). At the steady state, the heat balance equals theelectric power, Qh + Qc = V I, where V is the voltage applied to the TEM. Then, we deduce
� = V I
Th + Tc − 2T0. (6)
We work with a Ferrotec 9501/071/085 B TEM. The module is composed of N = 71thermocouples of an alloy of bismuth telluride suitably doped to provide distinct n and pproperties. Its characteristics are reported in the Ferrotec Thermoelectric Technical ReferenceGuide [12]: module dimensions of 29.8 × 29.8 × 3.94 mm3, and each die is 1.56 mmfor base dimensions, and 1.30 mm in height L. The ceramic substrate has a good thermalconductance of about five times better than bismuth telluride. For a n/p thermocouple at anaverage temperature of 300 K, the thermal conductance is Kn + Kp = 5.86 mW K−1, and theSeebeck coefficient Sp−Sn = 0.419 mV K−1. The electric resistance of the copper connectingthe p and n branches of the thermocouple is estimated at Rconn = 8.5 × 10−6�.
The experiment is developed in six stages, each one lasting 20 min. At the beginning themodule is at ambient temperature T0. Then, a current of 50 mA is applied. The temperaturesTc and Th change over time, as shown in figure 9. At each new step the current is increasedby 50 mA, up to 300 mA. The difference Th − Tc increases at each stage and reaches thesteady-state value quickly, as shown in figure 10. Figure 11 provides complete informationabout the module’s behaviour during the experiment.
4. Results
From these temperature data we evaluate the Peltier coefficient of the thermocouple n/p(see table 1). At each stage of the experiment, we obtain the steady temperatures Tc and Th,together with the mean value of the ambient temperature T0. The mean calculated heat transfercoefficient is � = 66 ± 10 mW K−1, and the Peltier coefficient �p − �n = 101 ± 5 mV.This latter result may be compared with that deduced from the ORR. For T = 300 K weobtain the value (�p − �n)ORR = 126 mV. The deviation between these two values is about20%.
Peltier coefficient measurement in a thermoelectric module 1261
Figure 10. Change of the difference Th − Tc versus time during the experiment. In each stage, aconstant value is soon reached.
Figure 11. Evolution of Th, Tc and T0 during the experiment. A constant electric current is appliedin each stage.
Table 1. Steady-state temperatures Th, Tc, and T0 measured at the TEM. Each stage is characterizedby the electric current. The values for the coefficients � and �p − �n are also given.
The values of � given in table 1 need a comment. They show a high dispersion about themean. It is evident that the design of the arrangement can be improved in order to increase theprecision of �. But this effort may be unnecessary because the weight of the term Qh/N inequation (5) is approximately 15% of the term
(Kn + Kp
)(Th − Tc) [7].
1262 J Garrido et al
In conclusion, a simple and well-founded experiment for determining the Peltiercoefficient in a laboratory at undergraduate level has been presented. The proposed methodis based on the energy balance at the junctions X/Y, and the Peltier coefficient is obtainedfrom the steady-state temperature of hot and cold blocks at constant current and ambienttemperature.
Acknowledgments
We thank the useful recommendations given by the referee, and to Benjamın Sanchıs andSantiago Gonzalez who gave the initial suggestions in this work.
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