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Testing a Peltier Element

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									Solid state physics II




                             Testing a Peltier Element




     Ingrid Ajaxon
     Johan Lindahl
     Harald Nyberg
     Q4

     Advisor: C-G. Ribbing
Abstract
The purpose of the experiment was to investigate the cooling properties of a Peltier element
and specifically the relation between the electric current through the element and the
temperature in a refrigerator cooled by the element. The “refrigerator” consisted of a cavity in
a block of polystyrene foam with the Peltier element covering the opening of the cavity. A fan
on top of it cooled the hot side of the element. The temperature inside the cavity was
measured with a thermocouple.

The measurements showed that the temperature depends on the current as a second order
function and that and that there exist a current for which the temperature reaches a minimum
value. For the investigated setup, the lowest measured temperature was 11.1°C
(approximately 12°C below the surrounding temperature). It was achieved at a current of
1.3A, corresponding to a power consumption of 9.7W.


Sammanfattning
Peltier-effekten upptäcktes 1834 av fransmannen Jean C. A. Peltier och beskriver värmeflödet
som uppstår då en elektrisk ström leds genom gränsskiktet mellan två olika ledande material.
Denna effekt utnyttjas idag i kommersiella applikationer för kylning.

I denna artikel presenteras resultaten av en undersökning av en sådan produkt; ett Peltier-
element, med avseende på dess förmåga att kyla ned ett litet hålrum i ett block av
polystyrenskum. I synnerhet undersöktes sambandet mellan den elektriska ström som leddes
genom Peltier-elementet och den temperatur som uppnåddes i det isolerade utrymmet.

Vid mätningen konstaterades att den lägsta uppmätta temperaturen inte uppnåddes vid den
högsta strömmen genom elementet, utan vid en lägre ström. Temperaturen varierar med
strömmen enligt ett kvadratiskt samband, med ett markant extremvärde. Kyleffekten tilltar
alltså inte alltid med ökande ström, utan antar ett maximalt värde vid en viss ström, som kan
antas vara olika för olika experimentella förhållanden (bortledning av värme från den varma
sidan av elementet, isolering på den kalla sidan etc.). Vid det aktuella försöket uppmättes en
lägsta temperatur av 11,1°C (cirka 12°C under omgivande temperatur) vid strömmen 1,3A,
motsvarande effekten 9,7W.




                                                                                                 2
Introduction
The Peltier effect was first observed in 1834 by the Frenchman Jean C.A. Peltier. It describes
the heat current that arises as a result of an electric current through the interface of two
different conductors.

The purpose of this project is to measure the maximum cooling of a commercial Peltier
element, in terms of the lowest achievable temperature inside a small refrigerator built using
the element. The project also includes investigating the limiting factors of Peltier cooling and
presenting the relevant theory behind it.


Theory
                   
The heat current, Q AB , at an interface between two conductors (A and B) can be expressed as
a function of the electrical current, I, through the interface, and the Peltier coefficients of the
two materials, ΠA and ΠB. The heat current at the interface is:

        
        Q AB  ( A   B )  I                                                      (1)

Heat is generated if ΠA> ΠB and the electrical current flows from A to B. If the direction of
the electrical current is reversed, so is the direction of the heat current.

By combining two interfaces, A to B and B to A, a hot and a cold junction can be created. In
this case, heat is generated at one of the interfaces and the same amount is absorbed at the
other.

In most commercial Peltier elements, three different materials are used (a P-doped
semiconductor (P), a metal (M) and an N-doped semiconductor (N)). The Peltier coefficients
of the three materials are different, ΠN> ΠM> ΠP. If the materials are arranged according to
figure 1, a hot and a cold side are created, using several interfaces between the materials (and
thus maximizing the cooling) with simple serial electrical connections. The arrangement
functions due to the fact that (for the materials given in this example) heat is generated at
junctions of the type M to P and N to M and absorbed at junctions M to N and P to M.




                        Figure 1: Sketch of a commercial Peltier element.

The cooling ability of a Peltier element is limited by several factors. Even though the Peltier
cooling increases linearly with the electric current through the element, an increased current
does not always lead to increased cooling. As the electric current increases, so does the


                                                                                                 3
resistive heating of the entire element. At some point, the resistive heating caused by an
increasing electric current will be larger than the cooling caused by the Peltier effect.

At a constant current the temperature difference between the hot and the cold side, ∆T, will be
constant. This gives rise to another limiting factor, namely the heat dissipation on the hot side.
If the heat generated on the hot side is not dissipated into the environment, the temperature of
the hot side will be increased. Since the temperature difference between the sides is constant,
this leads to an equal increase in the temperature of the cold side. The heat conduction
through the element depends linearly on the temperature difference between the sides. Since
the temperature difference increases with the electric current through the element, so does the
conduction of heat through the element.

For each pair of hot/cold interfaces (eg. metal-semiconductor-metal), the cooling, P, (eg. the
flow of thermal energy from the cold to the hot side) is related to the Peltier coefficients of the
two materials, ΠA and ΠB (where it is assumed that ΠA>ΠB), the electric resistance of the
element, R, the electric current, I, the thermal conductivity of the element, K, and the
temperature difference between the sides of the element, ΔT, according to equation 2.

                               RI2
        P  ( A   B )  I        KT                                            (2)
                                2

In this case, since cooling is the parameter of interest, the heat flow is described in this
slightly unusual way (strictly speaking as flow of “cold”, or negative flow of heat).

As seen from equation 2, the Peltier cooling (the first term) depends linearly on the electric
current, whereas the resistive heating (the second term) is related to the square of the
electrical current. The third term describes the conduction of heat through the Peltier element
and relates to the temperature difference between the hot and cold sides, ΔT. The relationship
between ΔT and the electrical current is unknown. At low electric currents, the Peltier cooling
is the dominating term, but as the electric current increases, the resistive heating will increase
faster than the Peltier cooling. At a certain value of the electric current, the resistive heating
will be larger than the Peltier cooling, and any further increase in electric current will actually
decrease the cooling.

By setting the derivative of the cooling P in equation 2 with respect to the current I to zero the
current at maximum cooling can be obtained.

        P                            T
             A   B   R  I  K     0                                         (3)
        I                             I

From equation 3, the current at maximum cooling, I0, can be determined.

                    T
               K        ( A   B )
        I0          I                                                              (4)
                         R

In equations 3 and 4, the unknown dependence of ΔT on the current, I, is included. This must
be measured experimentally or estimated in order to calculate an optimum current from
equation 4.


                                                                                                 4
It should be noted that the above stated equations are valid for a single pair of material
interfaces. For a commercial Peltier element, the contribution from all interfaces must be
added in order to obtain total values of cooling power, current at optimum cooling etc. This
requires knowledge of the number of interfaces in the element, as well as the Peltier
coefficients of all participating materials.

For an element consisting of nMP pairs of interfaces between metal and p-doped
semiconductor, and nMN pairs of interfaces between metal and n-doped semiconductor, the
total cooling power would be described by equation 5 (obtained by modification of equation
2). For a symmetrically built Peltier element, it is of course true that nMP=nMN.

                                                                     RI2
        Ptotal  nMP   M   P   I  nMN   N   M   I          K  T   (5)
                                                                      2

In equation 5, the Peltier element is considered as a single unit regarding the heat conduction
and resistive heating. The resistance, R, in the equation describes the total electrical resistance
of the Peltier element. It is worth noting that the current is the same through each of the
interfaces as through the entire element (since they are connected in series). For practical
purposes, it would also be possible to assign a total Peltier coefficient to the entire element,
thus incorrectly regarding it as a single pair of material interfaces. In this case, equation 2 can
be used, with the total Peltier coefficient replacing the term (ΠA-ΠB):

                                 RI2
        Ptotal   total  I          K  T                                       (6)
                                  2


Experimental set-up
The cold side of a Peltier element was mounted to cover a cavity enclosed by polystyrene
foam, thus creating a small “refrigerator” (see figure 2). A cooling flange was placed on the
hot side of the element and on top of it a fan was mounted to ensure maximum heat
dissipation. The fan was run at the same speed during all measurements. Silicon paste was
applied between the Peltier element and the cooling flange, to ensure good heat conductivity.
One of the thermocouples of a FLUKE 52 was inserted into the cavity and the other was
placed in a container of ice water as a temperature reference. The experimental set-up is
shown in figures 2-4.




                                                                                                 5
                   Figure 2: Polystyrene block with Peltier element,
                   cooling flange and fan on top of it.

The experiment was started at room temperature (23°C) and zero current. A direct current was
led through the Peltier element and increased stepwise from 0 to 2.5A in steps of 0.1A. The
voltage, current and temperature in the cavity were registered after each step, giving sufficient
time for stationary temperature to establish. The current was increased until the temperature
reached its minimum value and started increasing.




                          Figure 3: Sketch of the experimental setup.

A second measurement was performed, measuring the temperature difference between the hot
and cold side of the element, instead of the actual temperature on the cold side. The cold
temperature was actually measured inside the cavity and not in direct contact with the
element. For practical reasons, the hot temperature was measured on the cooling flange and
not directly on the element. This measurement was performed for four different currents
between 0.5 and 2.0A.



                                                                                               6
        Figure 4: Experimental set-up.



Results
The measured parameters in the first measurement are the temperature inside the cavity below
the cold side of the Peltier element, the current through the Peltier element and the voltage
over the Peltier element. From these values, the power consumption of the element was also
calculated. The registered data is presented in appendix 1. The results from the first
measurement are presented graphically in the following figures (5-7).


                                       25
             Temperature [degrees C]




                                       20


                                       15


                                       10


                                        5


                                        0
                                            0   1                 2        3
                                                    Current [A]


           Figure 5: The temperature inside the cavity as a function of the current
           through the Peltier element.

Figure 5 shows that the temperature decreased rapidly as the current was increased from zero.
However, at higher currents the temperature decreased more slowly for a given increase in
current. At a current of approximately 1.3A, the temperature reached its minimum value of



                                                                                           7
11.1°C (approximately 12°C below the surrounding temperature) after which any further
increase of the current led to a temperature raise.



                       Temperature difference [degrees   14.00
                                                                               ΔT= 17.458*I - 6.3663*I2
                                                         12.00

                                                         10.00

                                                             8.00
                                     C]




                                                             6.00

                                                             4.00

                                                             2.00

                                                             0.00
                                                                0.00    0.50   1.00   1.50        2.00   2.50   3.00
                                                                                 Current [A]


           Figure 6: The temperature difference between the cavity and the
           surroundings. The equation in the figure describes a second order
            polynomial fitted to the measurement data.

Figure 6 shows the temperature difference between the cavity and the surroundings. This is
basically the same results as already shown in figure 5. The presentation does however allow
calculations to be done on the data more easily. A second order polynomial is fitted to the
data and the equation of the polynomial is presented in the figure.



                                        25
              Temperature [degrees C]




                                        20


                                        15


                                        10


                                           5


                                           0
                                                         0             10       20           30          40       50
                                                                                  Power [W]

           Figure 7: The temperature inside the cavity as a function of the power
           consumption of the Peltier element.

As shown in figure 7, the temperature inside the cavity depends on the power consumption of
the Peltier element in a similar way as on the current. The figure is included because it would
be a better aid in the construction of a practical device, since the power consumption is
usually a more critical parameter than the current.


                                                                                                                       8
The results of the second measurement are presented in figure 8 below.

                                                   35.0

              Temperature difference [degrees C]
                                                   30.0



                                                   25.0



                                                   20.0



                                                   15.0



                                                   10.0



                                                    5.0



                                                    0.0
                                                      0.00   0.50         1.00           1.50   2.00   2.50

                                                                           Current [A]


           Figure 8: The temperature difference between the two sides of the
           Peltier element as a function of the electric current through it.

Figure 8 shows the relation between the current through the Peltier element and the
temperature difference between the sides of the element.


Discussion
The cooling behaviour of Peltier elements described in the theory section (i.e. the existence of
a temperature minimum) is confirmed by the measurements. A clear minimum temperature
can be found for both temperature vs. current and temperature vs. power consumption.

The thermal conductivity of the entire refrigerator and the total Peltier coefficient of the
element can be roughly estimated using equation 6 and the polynomial fitted to the curve in
figure 6, together with the assumptions that the thermal flow through the refrigerator walls are
linearly dependent on the temperature difference between the cavity and the surroundings, ΔT.
It is also assumed the thermal conductivity of the Peltier element and the refrigerator walls do
not vary with temperature.

For a stationary temperature, the cooling power of the Peltier element (from equation 6) is
equal to the thermal flow through the refrigerator walls (including both conducted and
radiated heat). If this flow is assumed to depend linearly on ΔT through some constant C,
equation 6 can be written as:

                                                                    RI 2
         Ptotal  C  T   total  I                                   K  T                             (7)
                                                                     2

This implies that ΔT can be written as a second order function on the current, I, through the
element.




                                                                                                                    9
                     total          R
         T                I               I2                                   (8)
                   (C  K )      C  K   2
The constants in equation 8 can be identified as the ones found in the polynomial fitted to the
curve in figure 6.

         T  17 ,46  I  6,37  I 2                                               (9)

Identification of constants leads to:

           total
                    17,46
         (C  K )
               R
                       6,37
         2  (C  K )

The electric resistance of the element can be deduced from the measured data (see Appendix
1). An average value was calculated as 5.92Ω. This means that the constants (C+K) and Πtotal
can be calculated.

                            R         5,92
         (C  K )                           0,46 W/K
                        2  6,37 2  6,37
          total    C  K   17 ,46  0,46  17 ,46  8,12 V

The constant (C+K) describes the total heat loss through the refrigerator walls and the Peltier
element. It is a strictly experimental parameter, consisting of contributions from several
different mechanisms of heat transport.

The calculated Peltier coefficient Πtotal is a practical parameter and does not give any
information about the Peltier coefficients of the materials in the element. It is a measure of the
performance of the element and is related to the construction of the element, as well as on the
materials in it.

The second measurement (figure 8) shows a relation between current through the Peltier
element and the temperature difference between the two sides of the Peltier element that is
suspiciously close to linear. This result should however be treated with a great deal of caution,
since the conditions during the measurement were far from ideal, as noted above in the results
section. A proper measurement of this relation would require an experimental setup better
suited for the task, as well as a larger series of collected data.

The temperature minimum in the refrigerator is limited by a number of mechanisms. The
insulation of the refrigerator is one key factor. If the heat flow from the surroundings through
the polystyrene walls and through the gaps in the enclosure could be reduced, the temperature
in the cavity would be lowered. A thin metallic film (e.g. aluminium foil) covering the inside
of the cavity would reduce losses through radiation and have a positive effect on the cooling
of the cavity.




                                                                                               10
If the heat on the hot side could be dissipated in a more efficient way (by means of a better
cooling flange, fan etc.) the temperature in the cavity would be reduced since the temperature
difference between the hot- and the cool side is constant, as stated in the theory part.

A more efficient Peltier element would be another way to reach a lower minimum. This can
be achieved by larger differences between the Peltier coefficients of the participating
materials and a lower thermal conductivity between the two sides of the element. Two or
more Peltier elements stacked on top of each other provide an easy way to make the whole
cooling device more efficient, since each element lowers the temperature by a certain value.

To conclude, the possibilities of optimising a cooling device based on a Peltier element are
numerous and a comprehensive description of the influences of the different parameters
would require a multitude of measurements, far beyond what would be reasonable in a limited
study as this.


References
   1.   Thermoelectric Materials and Devices, Cadoff and Miller, 1960.
   2.   Theoretical Solid State Physics, vol. 2, Albert Haug, 1972.
   3.   Transportegenskaper hos fasta kroppar, C-G. Ribbing och O. Beckman, 1990
   4.   Thermoelectric Cooling Systems Design Guide, Marlow Industries Inc., 1994.
   5.   http://www.ferrotec.com/products/thermal/modules/ , 2008-09-18.




                                                                                           11
                                                                              APPENDIX I

All measured data, as well as parameters calculated from the measurements, are presented in
the following tables. The power is calculated as the product of the voltage over the Peltier
element and the current through it.

Measurement 1:

U (V) I (A)   T (°C)   Power (W) Resistance (Ω)
  0.00    0.0     23.0        0.00              -
  0.59    0.1     21.9        0.06          5.90
  1.18    0.2     20.2        0.24          5.90
  1.84    0.3     18.6        0.55          6.13
  2.43    0.4     17.2        0.97          6.08
  3.01    0.5     15.8        1.51          6.02
  3.55    0.6     14.9        2.13          5.92
  4.13    0.7     13.9        2.89          5.90
  4.66    0.8     13.1        3.73          5.83
  5.21    0.9     12.3        4.69          5.79
  5.78    1.0     12.1        5.78          5.78
  6.30    1.1     11.8        6.93          5.73
  6.88    1.2     11.5        8.26          5.73
  7.46    1.3     11.1        9.70          5.74
  8.00    1.4     11.1       11.20          5.71
  8.61    1.5     11.2       12.92          5.74
  9.21    1.6     11.1       14.74          5.76
  9.86    1.7     11.7       16.76          5.80
 10.50    1.8     12.0       18.90          5.83
 11.16    1.9     12.4       21.20          5.87
 11.87    2.0     13.2       23.74          5.94
 12.57    2.1     14.0       26.40          5.99
 13.36    2.2     15.2       29.39          6.07
 14.13    2.3     16.5       32.50          6.14
 15.08    2.4     18.1       36.19          6.28
 15.87    2.5     19.8       39.68          6.35



Measurement 2:

U (V)          I (A)           ΔT (°C)
        3.03            0.50               8.1
        5.74            1.00              15.0
        8.57            1.50              22.8
       11.67            2.00              31.5

								
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