Peltier Element

7/28/2019 Peltier Element

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Solid state physics II

Testing a Peltier Element

Ingrid AjaxonJohan LindahlHarald NybergQ4

Advisor: C-G. Ribbing


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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 thetemperature 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 11.1C

(approximately 12C below the surrounding temperature). It was achieved at a current of

1.3A, corresponding to a power consumption of 9.7W.

Sammanfattning

Peltier-effekten upptcktes 1834 av fransmannen Jean C. A. Peltier och beskriver vrmefldet

som uppstr d en elektrisk strm leds genom grnsskiktet mellan tv olika ledande material.

Denna effekt utnyttjas idag i kommersiella applikationer fr kylning.

I denna artikel presenteras resultaten av en underskning av en sdan produkt; ett Peltier-

element, med avseende p dess frmga att kyla ned ett litet hlrum i ett block av

polystyrenskum. I synnerhet undersktes sambandet mellan den elektriska strm som leddesgenom Peltier-elementet och den temperatur som uppnddes i det isolerade utrymmet.

Vid mtningen konstaterades att den lgsta uppmtta temperaturen inte uppnddes vid den

hgsta strmmen genom elementet, utan vid en lgre strm. Temperaturen varierar med

strmmen enligt ett kvadratiskt samband, med ett markant extremvrde. Kyleffekten tilltar

allts inte alltid med kande strm, utan antar ett maximalt vrde vid en viss strm, som kan

antas vara olika fr olika experimentella frhllanden (bortledning av vrme frn den varma

sidan av elementet, isolering p den kalla sidan etc.). Vid det aktuella frsket uppmttes en

lgsta temperatur av 11,1C (cirka 12C under omgivande temperatur) vid strmmen 1,3A,

motsvarande effekten 9,7W.

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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, ABQ , at an interface between two conductors (A andB) can be expressed as

a function of the electrical current,I, through the interface, and the Peltier coefficients of thetwo materials,A andB. The heat current at the interface is:

IQBAAB = )(

(1)

Heat is generated ifA> B and the electrical current flows fromA toB. If the direction of the

electrical current is reversed, so is the direction of the heat current.

By combining two interfaces,A toB andB toA, 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, N> M> P. 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 typeMtoPandNto 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 currentdoes not always lead to increased cooling. As the electric current increases, so does the

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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 ofthe 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, A and B (where it is assumed that A>B), 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,T, according to equation 2.

TKIR

IP BA

=2

)(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 elementand relates to the temperature difference between the hot and cold sides, T. The relationship

betweenTand 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 Pin equation 2 with respect to the currentIto zero the

current at maximum cooling can be obtained.

( ) 0==

ITKIR

IP BA (3)

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

R

I

TK

IBA )(

0

=(4)

In equations 3 and 4, the unknown dependence ofTon the current,I, is included. This must

be measured experimentally or estimated in order to calculate an optimum current from

equation 4.

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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.

( ) ( ) TKIR

InInP MNMNPMMPtotal

+=2

2

(5)

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 (A-B):

TKIR

IP totaltotal

=2

2

(6)

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.

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Figure 2:Polystyrene block with Peltier element,

cooling flange and fan on top of it.

The experiment was started at room temperature (23C) 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.

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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).

0

5

10

15

20

25

0 1 2 3

Current [A]

Temp

erature[degreesC]

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 of11.1C (approximately 12C below the surrounding temperature) after which any further

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increase of the current led to a temperature raise.

T= 17.458*I - 6.3663*I2

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Current [A]

Temperaturedifference

[degreesC]

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.

0

5

10

15

20

25

0 10 20 30 40 50

Power [W]

Tem

perature[degreesC]

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.

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

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

0.00 0.50 1.00 1.50 2.00 2.50

Current [A]

Temperaturedifference[degreesC]

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 ofa 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, T.

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) isequal to the thermal flow through the refrigerator walls (including both conducted and

radiated heat). If this flow is assumed to depend linearly on T through some constant C,

equation 6 can be written as:

TKRI

ITCP totaltotal ==2

2

(7)

This implies that Tcan be written as a second order function on the current, I, through the

element.

( )2

2)(I

KC

RI

KCT total

+

+

= (8)

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The constants in equation 8 can be identified as the ones found in the polynomial fitted to the

curve in figure 6.

237,646,17 IIT = (9)

Identification of constants leads to:

37,6)(2

46,17)(

=+

=+

KC

R

KC

total

The electric resistance of the element can be deduced from the measured data (see Appendix

1). An average value was calculated as 5.92. This means that the constants (C+K) andtotal

can be calculated.

46,037,62

92,5

37,62)( =

=

=+

RKC W/K

( ) 12,846,1746,046,17 ==+= KCtotal 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 total 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 theperformance 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.

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

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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 arenumerous 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.

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http://www.ferrotec.com/products/thermal/modules/http://www.ferrotec.com/products/thermal/modules/


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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 ()

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 5.904.66 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 5.769.86 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) T (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

Peltier Element

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