INTERNATIONAL JOURNAL OF ENERGY RESEARCH
Int. J. Energy Res. 2004; 28:753–768 (DOI: 10.1002/er.991)
Improving the coefficient of performance of thermoelectric
cooling systems: a review
S. B. Riffatn,y and Xiaoli Ma
Institute of Building Technology, School of the Built Environment, University of Nottingham, Nottingham, NG7 2RD, U.K.
SUMMARY
This paper reviews research carried out to improve the coefficient of performance of thermoelectric cooling
systems during the past decade. This includes development of new materials for thermoelectric modules,
optimisation of module design and fabrication, system analysis and heat exchange efficiency. Several
conclusions are drawn. Copyright # 2004 John Wiley & Sons, Ltd.
KEY WORDS:
thermoelectric cooling system; coefficient of performance; optimisation
1. INTRODUCTION
Thermoelectric modules are solid state heat pumps that utilize the Peltier effect. During
operation, DC current flows through the thermoelectric module, causing heat to be transferred
from one side of the thermoelectric device to other, creating a cold and hot side. A single-stage
thermoelectric module can achieve a temperature difference up to 708C, or can transfer heat at
an utmost rate of 125 W under the extreme conditions.
A thermoelectric cooling system incorporates a power source to provide a direct current
through the electrical circuit, a thermoelectric module with at least one heat sink and at least one
heat source, and a control assembly. The basic arrangement of a thermoelectric module in a
cooling system is shown in Figure 1.
Thermoelectric technology has existed for about 40 years and thermoelectric systems
are employed as cooling devices in many applications including military, aerospace, industrial
and commercial. The main drawback of this technology however, is low coefficient
of performance (COP), particularly in larger capacity applications. The emphasis of
recent research has therefore been the improvement of the COP of thermoelectric
cooling systems by means of developing new materials for thermoelectric modules, optimization
of module system design and fabrication and improvement of the heat exchange (heat sink and
heat rejector) efficiency. Advances in areas are described in the following sections.
n
y
Correspondence to: S. B. Riffat, Institute of Building Technology, School of the Built Environment, University of
Nottingham, Nottingham, NG7 2RD, U.K.
E-mail: saffa.riffat@nottingham.ac.uk
Copyright # 2004 John Wiley & Sons, Ltd.
Received 24 July 2003
Accepted 22 September 2003
754
S. B. RIFFAT AND XIAOLI MA
Q1
Cold side
heat sink
Thermoelectric
device
P
Hot side
heat sink
Q2
Figure 1. Conventional arrangement for thermoelectric cooler. Q1 is the heat to be pumped, P is the
electrical power supplied and Q2 is the heat dissipated to the ambient.
Qc
Tc
Qsb
Th
1/2QJ
1/2QJ
Qcd
_
+
Qh
Figure 2. Schematic diagram of a thermoelectric couple.
2. THERMOELECTRIC MODULE PERFORMANCE
This section provides a basic understanding of the performance of a thermoelectric module.
Thermoelectric heat pumping (Peltier effect) at the cold end of a thermal couple, as shown in
Figure 2, is given by
Qab ¼ aITc
ð1Þ
The term a is the average Seebeck coefficient of the thermoelectric material. It is seen from this
relation that heat is pumped when current flows through the couple. However, the heat pumped
may include other unwanted heat sources. These heat sources are described in the following sections.
Joule heat: Current flow generates resistive or Joule heating (QJ) in the thermoelectric
material. It can be shown that 50 per cent of the Joule heat goes to the cold end and 50 per cent
goes to the hot end. The Joule heating is given by
QJ ¼ I 2 R
ð2Þ
where R is the resistivity of the couple.
Copyright # 2004 John Wiley & Sons, Ltd.
Int. J. Energy Res. 2004; 28:753–768
IMPROVING THE COEFFICIENT OF PERFORMANCE
755
Conducted heat: During operation, heat is conducted from the hot end to the cold end
through the thermoelectric material. The rate of heat conduction is given by
Qcd ¼ kðTh Tc Þ ¼ kDT
ð3Þ
where k is the thermal conductivity of thermocouple.
Equation (3) shows that Qcd increases with the temperature difference across the couple.
Combining Equations (1), (2), and (3) into an energy balance at the end of the thermoelectric
couple gives the following:
Qc ¼ Qsb 0:5QJ Qcd ¼ aITc 0:512 R kDT
ð4Þ
Equation (4) is the standard equation of thermal module performance. This equation shows
that a thermoelectric module no longer operates (Qc=0) when the sum of one half the Joule heat
(0.5QJ) and the conducted heat (Qcd) equals the Peltier heat (Qsb).
The electrical energy consumption of the couple is given by
QE ¼ I 2 R þ aIDT
ð5Þ
Equation (5) shows that the electrical power consumption of a thermoelectric couple is used
to generate the Joule heat and overcome the Seebeck effect, which generates power due to the
temperature difference between the two junctions of the couple.
The COP of the thermoelectric module for cooling is given by
e ¼ Qc =QE ¼
aITc kDT 0:5I 2 R
I 2 R þ aIDT
ð6Þ
It is seen that the COP is a function of the material dimension property of thermocouple, the
temperature of the hot side and cold side Th, Tc and the current input. There exists an optimum
current for maximum COP, if Th, Tc and the thermoelectric material are fixed.
Solving the equation @e=@I ¼ 0; the optimum current for the maximum (optimum) COP can
be given by
aDT =R
Iopt ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ ZTm 1
ð7Þ
Replace I in Equation (6) by Iopt, the optimum COP can be given by
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Th
1
þ
ZT
m
Tc
Tc
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
eopt ¼
ðTh Tc Þ ð 1 þ ZTm þ 1Þ
ð8Þ
where
Tm ¼ 1=2ðTh þ Tc Þ
ð9Þ
Z ¼ a2 =kR
ð10Þ
It is seen that the optimum COP under the optimum current is a function of Th, Tc and the
figure of merit of thermoelectric material.
Copyright # 2004 John Wiley & Sons, Ltd.
Int. J. Energy Res. 2004; 28:753–768
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S. B. RIFFAT AND XIAOLI MA
3. DEVELOPMENT OF NEW THERMOELECTRIC MATERIALS
Equation (10) express the performance of a thermoelectric materials:
Z ¼ a2 =kR
ð10Þ
where Z is a figure of merit, a the Seebeck coefficient, R the electric resistivity and k the thermal
conductivity.
Z depends only on material properties and should be maximized to increase the module
efficiency. This parameter may be made dimensionless by multiplying by T (average temperature
of the hot side and cold side of the thermoelectric module, K):
ZT ¼ a2 T =kR
ð11Þ
Over the past four decades, improvement in the conversion efficiency has been marginal. The
challenge has been the development of thermoelectric materials with an improved dimensionless
figure of merit. Effort has been concentrated on improving the performance of the thermocouple
materials. Currently, bismuth telluride (Bi2 Te3 ), which is the best low temperature thermoelectric material and is widely employed in thermoelectric generators and coolers. Bi2Te3 possess
a maximum value of ZT1 (Min et al., 2002).
If the ZT could be raised to 2 or 3, the thermoelectric cooling device would be competitive
with vapour compression cooling systems. Furthermore, if the ZT could be raised to 6,
thermoelectric devices would be able to cool to cryogenic temperature (77 K) from room
temperature. Recent advances have indicated the possibility of overcoming classical limitations
and increasing the figure of merit significantly. Most of the advances involve tailoring the
microstructure of a material to increase phonon scattering in order to decrease thermal
conductivity. These materials include skutterudites, clathrates, half-Heusler alloys and
chalcogenides. Another approach to the problem is to reduce the dimensionality of the
material so that quantum size-effects alter the ratio between the electrical and thermal
conductivity. A reported calculation for 2D quantum well structures, as well as 1D quantum
( . In addition, experiments
wires, predicted values of ZT beyond 10 for wire diameters below 10 A
carried out on quantum wells synthesized by molecular beam epitaxy showed that the Seebeck
coefficient (times the carrier concentration) increased as the well thickness decreased (Hillhouse
et al., 2001).
Many other new approaches to the design of improved thermoelectric materials have also
been suggested. However, these are yet to be realised in practice.
Entrique Macia (in press) presented a theoretical study into the possible use of quasicrystals
as potential thermoelectric materials. By considering a suitable model for the spectral
conductivity, it was shown high values of the thermoelectric figure of merit, well beyond the
practical upper limit ZT ¼ 1; may be expected for certain quasicrystalline alloys.
Anatychuk et al. (1996) gave a number of examples supporting the concept of using
inhomogeneous materials (with functional gradients) to improve the module efficiency.
Development of thin-film thermoelectric materials offers many advantages including
extending the possibility of a variety of designs for lower heat-flux modules; enabling mass
production; reducing manufacturing costs; and performance enhancement. Venkatasubramanian et al. (2001) reported thin-film thermoelectric materials that demonstrated a significant
enhancement in ZT at 300 K, compared to state-of-the-art bulk Bi2 Te3 alloys. This amounts to a
maximum observed factor of approximately 2.4 for p-type Bi2 Te3 =Sb2 Te3 superlattice devices.
Copyright # 2004 John Wiley & Sons, Ltd.
Int. J. Energy Res. 2004; 28:753–768
IMPROVING THE COEFFICIENT OF PERFORMANCE
757
The enhancement is achieved by controlling the transport of phonons and electrons in the
superlattices. At present, this thin-film thermoelectric material has only been used in electronic
device cooling.
4. OPTIMIZATION OF MODULE DESIGN AND FABRICATION
One approach to improve the COP of thermoelectric modules is to examine all the aspects of
their design and fabrication that affect the overall performance of the thermoelectric system.
Recent investigations have demonstrated the effect of size of the thermoelements the COP of the
thermoelectric module.
Min et al. (2000) has developed an improved theoretical model of a Peltier module which
takes into account both the electrical and thermal contact resistances (conventional module
theory neglects contact resistances).
Instead of the conventional performance formula, as given in Equation (8), the COP of a
Peltier module, which takes into account both electrical and thermal contact resistances, may be
given by
l
Tc b Th =Tc rlc
eopt ¼
ð12Þ
l þ 2rlc Th Tc 1 þ b
l
where
lZTM 1=2
b¼ 1þ
nþl
n¼
2Rc
R
r¼
k
kc
TM ¼ ðTh þ Tc Þ=2
ð13Þ
Theoretical calculations based on this model indicate that both the COP and heat pumping
capacity are dependent on thermoelement length. This dependence becomes increasingly
significant with a decrease in thermoelement length. As a result, a relatively long thermoelement
is required to obtain a large COP, while a relatively short thermoelement is desirable for
achieving maximum heat pumping capacity. It is apparent that the optimum module design will
be a compromise between the requirements of COP and heat pumping capacity. Min also
showed that reducing the contact resistances, in particular, the thermal contact resistance, is an
essential requirement to achieve a further improvement in both COP and heat pumping
capacity.
In addition, a precise manufacturing technique is required to provide high quality
thermoelectric modules, with high performance. Precise manufacturing technique requires
exact determination of module parameters.
The requirements include: precision measurement of each module internal resistance at the
ambient temperature; consideration of the resistance of the module supply leads; determination
of optimum current and voltage of each module; determination of thermal efficiency of each
module; calculation of temperature difference Tmax, maximum cooling capacity Qmax according
to the measurement results and figure of merit Z; certification of the module main parameters,
values of internal resistance Rmin, Rmax and Tmin, Qmax, etc.
Copyright # 2004 John Wiley & Sons, Ltd.
Int. J. Energy Res. 2004; 28:753–768
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S. B. RIFFAT AND XIAOLI MA
Methods for precise and rapid determination of parameters governing the performance of
thermoelectric cooling and generation modules, as well as software and hardware used in the
realization of these measurements are reviewed by Anatychuk et al. (1998).
5. OPTIMIZATION OF THE DESIGN OF THERMOELECTRIC COOLING SYSTEMS
AND NOVEL METHODOLOGY FOR SYSTEM ANALYSIS
The methodology of system design and system analysis is very important to the design of highperformance thermoelectric cooling systems.
5.1. Exact system design method
The design procedure of a thermoelectric cooling system usually follows the performance curves
of the thermoelectric module provided by the manufacturer. Usually, the design of a
thermoelectric cooling system starts from a given temperature difference across the hot and
cold sides of the module DT (=THTL) and the required cooling capacity QL. The current I for
the thermoelectric module is determined from a measured DT–I curve at a fixed QL. The V–I
curves at zero cooling capacity (QL=0) and at zero temperature difference (DT=0) are then
used to determine the voltages V. The required thermal resistance of the heat sink is then
evaluated. An iteration procedure is necessary since the heat sink design may not be feasible and
the assumed DT may not be practical. In addition, this design method only determines the range
of the applied voltage. The actual value of V needs to be determined experimentally. In general,
this method is more suitable for the selection of the thermoelectric module as it does not take
into account the effect of the thermal resistance of heat sink (Huang et al., 2000).
In addition, the above design procedure can give rise to several difficulties. Most
manufacturers do not supply the performance curves of the thermoelectric module.
Furthermore, the thermal performance of a thermoelectric module depends on physical
properties such as the Seebeck coefficient a; the electric resistance R, and the thermal
conductivity K. In general, these properties may vary with operating temperature.
Manufacturers of thermoelectric module do not usually provide this type of data for their
customer, or if provided, the data are not accurate due to variations in the manufacturing
process (Huang et al., 2000).
A high quality design procedure is therefore required for the design of high-performance
thermoelectric cooling systems.
Huang et al. (2000) developed novel system design method for thermoelectric cooling systems.
The performance curve and the basic physical properties of a thermoelectric module were first
measured from a module test. An automatic test apparatus was designed and built to carry out
the testing. System analysis was then carried out using the measured results and a computer
model was developed to assist system design. The thermal resistance of the heat sink was
selected as one of the key parameters in design of a thermoelectric cooling system. This
eliminated the need to carry out the complicated heat transfer analysis of a heat sink during the
system analysis and thus simplified the system design procedure. This system design method
allows the derivation of more accurate relations for determining the optimum COP and
optimum cooling capacity, (it was found that the extreme value of COP represents the design
Copyright # 2004 John Wiley & Sons, Ltd.
Int. J. Energy Res. 2004; 28:753–768
IMPROVING THE COEFFICIENT OF PERFORMANCE
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limit which corresponds to heat exchanger thermal resistance Re=0). The main drawback of this
method is that it needs an automated test apparatus and therefore may not be convenient to use.
5.2. Convenient optimization thermoelectric system design form
It is important to design a system so that it operates with a maximum COP for a specified heat
exchanger thermal resistance and at a constant temperature difference. There have been several
investigations into optimum design to maximize the COP of a thermoelectric cooling system,
but many methods are not in a convenient form to allow simulation of the optimum
thermoelectric cooling system. The present interest is to develop a form convenient for this type
of simulation.
Yamanashi et al. (1996) investigated an optimum design to maximize the COP of a
thermoelectric cooling system when the thermal resistances of the heat exchangers are given and
the system operates under a constant temperature difference. The optimization was performed
using non-dimensional entropy flow equations, which are an extension of the heat balance
equations of a thermoelectric cooling system. The thermoelectric cooling system absorbs the
heat flow (Qc) at the cold side and emits the heat flow (Qh) at the hot side. Therefore, the
entropy flows at the cold and hot sides are Qc/Tc and Qh/Th, respectively. The non-dimensional
entropy flows at the cold and hot side are derived from normalizing these entropy flows by the
thermal conductance of the thermoelectric module. The non-dimensional thermal resistances of
the hot side and the cold side heat exchangers are the ratio of the thermal resistances of the hot
side and the cold side heat exchangers to the thermal resistance of the thermoelectric module. In
these equations, the COP becomes a function of the non-dimensional thermal resistance of
the cold side heat exchanger, and the non-dimensional entropy flow at the cold side of the
thermoelectric cooling system. Therefore, the COP of the thermoelectric cooling system can be
shown as a contour graph based on these two variables. This graph allows not only
determination of the thermoelectric cooling design parameters for the maximum COP of the
thermoelectric cooling system, but also evaluation of the degrading effect on the COP of the
thermal resistance of the system. The maximum COP was found to decrease rapidly as the ratio
of the cold side thermal resistance and the hot side thermal resistance increased.
In these simulations, the thermoelectric properties of thermoelements are based on values
determined from the average operating temperature of the thermoelectric module. This
convenient design method is therefore an approximate method.
5.3. Novel system analysis method
Chen et al. (1996) investigated the heat transfer rate and efficiency of thermoelectric cooling
systems. The study focused on the use of large-scale thermoelectric refrigerators for air
conditioning applications. A one-dimensional heat transfer analysis was performed to determine
the cooling power and electricity consumption of the thermoelectric elements. The constantproperty results were in good agreement with the variable-property solutions for the
thermoelectric materials and temperatures typical for air conditioning applications. A heat
transfer analysis was also carried out for thermoelectric refrigerators equipped with a heat
exchanger. Both parallel- and counter-flow heat exchangers were considered. Fluid temperature
variations of these two flow arrangements were found to be quite different, but the efficiencies
and cold fluid exit temperatures differed only slightly when a uniform current was used for all
thermoelectric elements. If the length of the heat exchanger exceeds an optimum value, the cold
Copyright # 2004 John Wiley & Sons, Ltd.
Int. J. Energy Res. 2004; 28:753–768
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S. B. RIFFAT AND XIAOLI MA
fluid temperature begins to rise and the efficiency drops for both parallel- and counter-flow
arrangements. The second law of thermodynamics was applied to the optimization of
thermoelectric refrigerators operating between two constant-temperature reservoirs and
between two flowing fluids. It was found that if a thermoelectric cooling system incorporates
a heat exchanger, a non-uniform current distribution should be used to achieve the maximum
efficiency and the lowest cold fluid temperature. The optimization results for thermoelectric
refrigerators operating between two constant-temperature reservoirs are not applicable to
thermoelectric cooling systems operating between two flowing fluids.
Heat transfer at a finite rate, and electrical resistive losses, are necessarily irreversible
processes and unavoidable in a thermoelectric device. Go. ktun et al. (1995) suggested that the
internal and external irreversibilities in a thermoelectric refrigerator might be characterised by a
single parameter named the device-design parameter. The presence of this parameter in the
equations for the refrigeration effect and the maximum input power, shows that a real
refrigerator has a smaller cooling capacity and needs more input power than an ideal
refrigerator.
6. IMPROVEMENT OF EFFICIENCY OF THE HEAT EXCHANGE SYSTEM
As described previously, the COP of a thermoelectric module (the optimum COP on the
condition of optimum current) can be expressed by Equation (8). This indicates that the COP of
a specific thermoelectric module is a function of module’s hot and cold side temperatures, i.e, Th
and Tc, respectively. Increasing the Tc and decreasing the Th will improve the COP.
For a fixed Th or Tc, the COP of a thermoelectric module typically decreases with an increase
in the temperature difference between the module’s hot and cold side.
Figure 3 shows the calculated COP of a commercially available module as a function of
temperature difference between the hot and cold side, at a hot side temperature of 300 K, which
is a typical condition for domestic refrigeration.
For a typical domestic refrigerator, a temperature difference between the ambient and the
cabinet of about 25–30 K at Th=300 K is usually required to achieve satisfactory cooling
performance. This indicates that the maximum COP of a thermoelectric refrigerator comprised
of a commercially available module is around 0.9–1.2, as shown in Figure 3. However, the
practical COP of a thermoelectric refrigerator is much lower than this because the temperature
difference between the hot and cold side of the thermoelectric module is larger than the
temperature difference between the ambient and the cabinet. In other words, the hot side
temperature is higher than the ambient and the cold side temperature is lower than the cabinet
temperature.
For a practical thermoelectric cooling system, the hot side heat exchanger rejects the heat
produced on the hot side of the thermoelectric module to the ambient and so reduces the hot
side temperature. The cold side heat exchanger removes the heat from the cold region to the cold
side of thermoelectric module and so increases the temperature of the cold side. Because the
thermoelectric module is very high heat intensity equipment, the high efficiency thermoelectric
heat exchangers is necessity.
The efficiency of the heat exchange system strongly influences the COP of the thermoelectric
cooling system. If the efficiency of the heat exchange system is high, the temperature difference
between hot and cold side of the thermoelectric cooling system may be reduced significantly, and
Copyright # 2004 John Wiley & Sons, Ltd.
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IMPROVING THE COEFFICIENT OF PERFORMANCE
3
Th =300K
Z=2.8×10-3K-1
2.5
COP
2
1.5
1
0.5
0
0
5
10
15
20
25
30
35
40
45
50
Temperature difference, Th-Tc, (K)
Figure 3. COP as a function of temperature difference across the module at
hot side temperature Th=300 K.
the COP will be increased. If the efficiency of the heat exchange system is low, the temperature
difference between hot and cold side will be greater, and the COP will be lower.
Heat is rejected from the hot side across a heat exchanger to the ambient. Heat exchanger
thermal resistance is defined by
Qh ¼
Th Ta
Re
or
Th ¼ Qh Re þ Ta
ð14Þ
As shown in Equation (14), the hot side temperature may be calculated as a function of the
heat exchanger thermal resistance, Re under specific heat flow at hot side Qh and ambient
temperature Ta. The Re determines how high the thermoelectric cooling system rises above the
ambient temperature.
In principle, heat exchangers in thermoelectric cooling systems should be designed to
minimise their thermal resistance under restrictions such as the size of the system and heat
transfer method and system design method, because as the thermal resistance of the heat
exchangers increases, the efficiency of thermoelectric cooling systems decreases.
Typical heat exchanger designs include natural convection, and forced convection heat
exchangers for heat rejection to air, and forced convection heat exchangers for heat rejection to
water flow, as shown in Figure 4.
Of these common types of heat exchanger, shown in Figure 4, the liquid cooled system is the
most efficient. The typical heat exchanger thermal resistance for a 45 45 mm square
thermoelectric module is:
(1) Natural convection: 0.853–13.075 m2 K kW1, depending on the fin density and the ratio
of the heat exchanger base plate area to the thermoelectric module area. Higher ratios of the
Copyright # 2004 John Wiley & Sons, Ltd.
Int. J. Energy Res. 2004; 28:753–768
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S. B. RIFFAT AND XIAOLI MA
Figure 4. Common heat exchanger designs: (a) natural air convection, (b) forced air convection (heat sink
not shown for clarity) and (c) water-cooled forced convection.
heat exchanger base plate area to the thermoelectric module area result in a lower thermal
resistance;
(2) Forced air convection: 0.531–5.759 m2 K kW1, depending on the air flow rate. Larger air
flow rates result in a lower thermal resistance;
(3) Water-cooled exchanger: 0.348–0.737 m2 K kW1, depending on the water flow rate.
Larger water flow rates result in a lower thermal resistance.
A ducted, forced-air, convection system has a higher performance than an un-ducted system.
The data provided by Melcor shows the typical allowances of temperature difference between
the hot side and ambient, with respect to the heat exchange mode. That is:
(1) Natural convection 20–408C;
(2) Forced air convection: 10–158C.
(3) Liquid exchangers: 2–58C above liquid temperature.
Since the heat flux densities on the cold side of the system are considerably lower than those
on the hot side, an allowance of about 50% on the afore-mentioned hot side data can be used.
Various types of heat pipe may be used to conduct heat from the small ceramic area to the
convection surface, which is an alternate to the metal heat spreader plate. A heat pipe may also
be used to assist the distribution of heat within the spreader plate. A heat pipe system must still
reject heat to air or water. Hence, it must use one of the previously discussed convective heat
rejection systems. Assuming a 12.7 mm diameter aluminum/methanol heat pipe, and using a
high performance wick structure, one can have a heat pipe resistance as low as 0.02 K W1.
Coupling this with a liquid heat exchanger with a thermal resistance of 0.172 K W1 will result
in a heat pipe/convection resistance of 0.132 K W1. Use of a heat pipe will not be of benefit for
natural convection, because the dominant thermal resistance in this case is the convection
resistance (Webb et al., 1998).
As mentioned previously, water-cooled forced convection heat exchangers have excellent
performance. The main drawback of a water-cooled heat exchanger is that it needs a convenient
Copyright # 2004 John Wiley & Sons, Ltd.
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IMPROVING THE COEFFICIENT OF PERFORMANCE
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source of cooling water. Without a source of cooling water, a forced convection water heat
exchanger would require a pump and radiator and associated fittings and tubing. The added
resistance of the radiator would increase the overall resistance. Air-cooled systems are therefore
often more desirable.
Many heat exchange systems based on the afore-mentioned forced air convection exchangers
and the use of heat pipes have been reported.
Sofrata (1996) reported that using a double fan in an appropriate position could significantly
increase the efficiency of the forced air exchanger compared to using the single fan in a
refrigerator. A long chimney for a natural-convection heat exchanger may also improve the
performance of the refrigerator without the need to use fans that, of course, require the electrical
power input.
A novel, air-cooled thermosyphon reboiler-condenser system has been reported (Webb et al.,
1998) and has been used as a heat exchanger of a thermoelectric refrigerator (Gilley et al.,
1999). This system is capable of providing very low heat sink resistance values with aircooling and a thermal resistance as low as 0.0194–0.0505 K W1 was obtained for cooling a
45 mm square module. The system promises significantly higher COP for thermoelectric coolers
than is possible using existing heat exchange technology. The high performance is obtained
using of enhanced heat transfer surfaces and its operation is summarised as follows.
As shown in Figure 5(a), the heat exchanger includes a boiling chamber, and a condensing
chamber. The boiling surface inside the boiling chamber has a porous metal coating to enhance
its heat transfer. The working fluid, which has been heated in boiling chamber to its vapour
phase, can flow upwardly through the hollow tube into the condensing tube in condensing
chamber. As shown in Figure 5(b), each condensing tube includes partitions, which provide the
required structural strength for respective tubes and also increase the total surface area
contained within each condensing tube. Enhanced heat transfer surfaces are preferably formed
on the interior surface of each condensing tube. The working fluid that has been condensed into
its liquid phase in the condensing chamber will flow through the hollow tube downward into the
boiling chamber.
Riffat et al. (2001) have reported a thermoelectric refrigeration system, which employs a phase
change material (PCM) as a cold side heat exchanger for cooling storage and improvement of
the COP. The refrigeration system was first fabricated and tested using a conventional heat sink
system (bonded fin heat sink system) at the cold heat sink. In order to improve the performance
and storage capability, the system was reconstructed and tested using an encapsulated phase
change material (PCM) as a cold sink. Both configurations used heat pipe embedded fins as the
heat sink on the hot side, as shown in Figure 6. Results of tests on the latter system showed an
increased performance. This was because the PCM had a large storage capacity allowing most
of the cooling energy to be absorbed by the PCM, and therefore the cold side temperature fell
more slowly than when the PCM was not used. During the phase change process, the
temperature of the refrigeration system was almost constant until the phase change process was
complete. This helped to keep the temperature difference across the thermoelectric module to a
minimum, thus improving its performance.
In general, thermoelectric modules are very high heat intensity equipment, which need high
efficiency heat exchangers to lower the hot side temperature and increase the cold side
temperature in order to improve the COP. Use of a greater number of modules would also
improve the COP of the system. Use of more modules would reduce the heat load on each
module, and so lower the heat flux densities of both the hot and cold side of each module. The
Copyright # 2004 John Wiley & Sons, Ltd.
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S. B. RIFFAT AND XIAOLI MA
Figure 5. (a) Air cooled, thermosyphon reboiler-condenser assembly, and (b) cross-section of the hollow
condensing tube with enhanced heat transfer surface.
Figure 6. Schematic description of an experimental thermoelectric refrigeration system.
hot side temperature could therefore be reduced more by the heat exchange system. The main
disadvantage of this is however, that the use of many modules would increase both cost and
space requirements.
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7. OTHER APPROACHES
7.1. Multistage thermoelectric cooling system
The COP of a thermoelectric cooling system decreases rapidly with increasing temperature
difference but its performance can be improved by the use of multistage thermoelectric modules.
Figure 7 shows typical designs of a single-stage module and a multistage module.
Lindler (1998) investigated the improvement in performance that could be obtained using a
multistage module. The results showed a comparison of COP as a function of hot side
temperature (with a fixed cold side temperature of 208C) for a single, commercially available CP
1.0-17-08L module, and two CP 1.0-17-08L cascaded modules. For a hot side temperature
around 508C (temperature difference of 308C), the improvement in COP was too small to justify
the added cost of a second module. For a hot side temperature of 608C, the single module
operated at a COP of 0.670 compared to a COP of 0.719 for the cascaded module. This
represents a 7.3% improvement in COP. For hot side temperature above 908C, the improvement
in COP is significant. At a hot side temperature of 1008C, the single module COP is 0.151
compared to 0.232 for the cascaded module. This represents a 54% improvement in COP. The
results also show that a cascaded system consisting of a CP1.0-17-08L module on the cold side
with a CP 1.0-31-08L module on the hot side, yielded essentially the same COP as two CP 1.017-08L modules cascaded for hot side temperatures less than 908C. For higher hot side
temperatures, the cascaded system with a CP 1.0-31-08L module on the hot side outperformed
the cascaded system consisting of two CP 1.0-17-08L modules.
It has also been reported that at low temperature cooling (200–250 K) and for a given
temperature difference, using a multistage module with an appropriate number of stages may
lead to sharp increase in the cooling efficiency (Anatychuk et al., 1996).
Optimum temperature staging has been investigated to minimise entropy generation in a
multi-stage cryogenic refrigeration cycle (Jeong et al., 1994). It was found that the best
intermediate temperature distribution was to have the same high to low temperature ratio at
each stage of the system. As an example, the result could be applied to the design of a cryogenic
cascade thermoelectric cooling system to find the optimum size distribution of each stage.
7.2. Optimization of module location
Welling et al. (1997) reported an experiment designed to evaluate the effect of thermoelectric
module location on cooling system efficiency. An experimental device was conceived, which was
to employ thermoelectric modules in the duct attached to an enclosure with a heat load, similar
in function to an automobile air conditioner. The hot air flowed through the duck and it was
found that the positions of the thermoelectric modules in the duct had an effect on the air
Figure 7. Typical thermoelectric module designs. (a) single-stage module and (b) multistage module.
Copyright # 2004 John Wiley & Sons, Ltd.
Int. J. Energy Res. 2004; 28:753–768
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S. B. RIFFAT AND XIAOLI MA
cooling rate. It can therefore be concluded that it is important to optimise module location in
order to increase system efficiency and reduce operating costs.
7.3. Further investigation
Buist et al. (1996) reported a theoretical analysis of thermoelectric cooling performance
enhancement via thermal and electrical pulsing. The cooling enhancement was by virtue of the
fact that Peltier cooling is a surface effect and extremely concentrated at the cold junction,
whereas, Joule heating is a volume effect and is distributed throughout the volume of the
thermoelement. As a result, most of the Joule heat takes a longer time to reach the cold side,
than heat from the Peltier effect. This phenomenon was demonstrated theoretically by modelling
a high-current pulse applied after the minimum steady-state cold side temperature had been
established. Calculations showed that cold side temperatures could be reduced by 16 K
compared to temperatures achieved by steady-state means. These transient enhancements are
admittedly short-lived and have limited effectiveness. However, the results presented suggest
that further investigation of the fundamental differences between Peltier and Joule heat may be
useful.
8. CONCLUSIONS
(1) Recent advances have indicated the possibility of overcoming classical limitations and
increasing the figure of merit of the thermoelectric materials significantly. The investigations
include the following aspects: tailoring the microstructure of a material to increase phonon
scattering in order to decrease thermal conductivity; reducing the dimensionality of the material
so that quantum size-effects alter the ratio between the electrical and thermal conductivity; use
of quasicrystals as potential thermoelectric materials; use of inhomogeneous materials (with
functional gradients) and development of thin-film thermoelectric materials which has achieved
a figure of merit of approximate 2.4.
(2) Investigations have demonstrated the effect of size of the thermoelements on the COP and
heat pumping capacity of the thermoelectric module. A relatively long thermoelement is
required to obtain a large COP, while a relatively short thermoelement is desirable for achieving
maximum heat pumping capacity. The optimum module design will be a compromise between
the requirements of COP and heat pumping capacity. The investigations also showed that
reducing the contact resistances, is an essential requirement to achieve a further improvement in
both COP and heat pumping capacity of a thermoelectric module.
(3) The new methodologies of system design and system analysis to the design of
high-performance thermoelectric cooling systems include the following main points: use
of the performance curve and the basic physical properties of a thermoelectric module measured
from an accurate module test; use of non-dimensional entropy flow equations to determine
the thermoelectric cooling design parameters for the maximum COP of the thermoelectric cooling system; one-dimensional heat transfer analysis; use of the ‘‘device-design
parameter’’ which characterise the internal and external irreversibilities in a thermoelectric
refrigerator.
(4) Of the common types of heat exchanger for thermoelectric cooling systems, water-cooled
forced convection heat exchangers have excellent performance. The air-cooled heat exchange
Copyright # 2004 John Wiley & Sons, Ltd.
Int. J. Energy Res. 2004; 28:753–768
IMPROVING THE COEFFICIENT OF PERFORMANCE
767
systems are however generally the most desirable at present due to its convenience to use. And
some novel air-cooled heat exchangers with higher performance have been developed.
(5) For large temperature temperature difference applications, the COP can be improved
significantly by use of multistage thermoelectric modules.
NOMENCLATURE
Qab
a
I
QJ
R
Qcd
K
Th
Tc
DT
Qc
Qh
QE
e
Iopt
eopt
Z
Rc
l
lc
kc
Ta
Re
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Peltier heat pumping rate (W)
seebeck coefficient of thermoelectric material (W/A-K)
current (A)
joule heat generation rate (W)
electrical resistivity of the thermocouple (V A1)
heat conduction from the hot end to cold end (W)
thermal conductivity of thermocouple (W m-K1)
hot end temperature (8C)
cold end temperature (8C)
temperature difference between hot and cold end (8C)
heat flow at cold side (W)
heat flow at hot side (W)
power consumption (W)
COP of the thermoelectric couple
optimum current (A)
optimum COP of the thermoelectric couple
figure of merit of thermoelectric material (K1)
electrical contact resistivity between the thermoelements and copper strips (R)
thermoelement length (mm)
thickness of contact layers between thermoelements and copper strips (mm)
thermal conductivity of the contact layers (W m-K1)
ambient temperature (8C)
heat exchanger thermal resistance (K W1)
REFERENCES
Anatychuk LI et al. 1996. Optimal functions as an effective method for thermoelecric devices design. 15th International
Conference on Thermoelectrics, Chernivtsi, Ukraine, 223–226.
Anatychuk LI et al. 1998. Methods and means of precise and rapid determinations of thermoelectric cooling and
generating modules parameters. 17th International Conference on Thermoelectrics, Chernivtsi, Ukraine, 270–272.
Buist RJ et al. 1996. Theoretical analysis of thermoelectric cooling performance enhancement via thermal and electrical
pulsing. 17th International Conference on Thermoelectrics, Traverse City, Michigan, 234–237.
Chen K et al. 1996. Analysis of the heat transfer rate and efficiency of thermoelectric cooling systems. International
Journal of Energy Research 20(5):399–417.
Entrique Macia. Quasicrystals as thermoelectric materials: a theoretical prospective. Journal of Alloys and Compounds
342(1–2):460–463.
Gilley et al. 1999. Thermoelectric refrigerator with evaporating/condensing heat exchanger. United States Patent, No.
6003319, December 21.
Go. ktun S et al. 1995. Design considerations for a thermoelectric refrigerator. Energy Conversion and Management
36:1197–1200.
Copyright # 2004 John Wiley & Sons, Ltd.
Int. J. Energy Res. 2004; 28:753–768
768
S. B. RIFFAT AND XIAOLI MA
Hillhouse HW et al. 2001. Modelling the thermoelectric transport properties of nanowires embedded in oriented
microporous and mesoporous films. Microporous and Mesoporous Materials 47:39–50.
Huang BJ et al. 2000. A design method of thermoelectric cooler. International Journal of Refrigeration 23:208–218.
Jeong S et al. 1994. Optimum temperature staging of cryogenic refrigeration system. Cryogenics 34(11):923–933.
Lindler KW 1998. Use of multi-stage cascades to improve performance of thermoelectric heat pumps. Energy Conversion
and Management 39:1009–1014.
Min G et al. 2000. Improved model for calculating the coefficient of performance of a Peltier module. Energy Conversion
and Management 41:163–171.
Min G et al. 2002. ‘‘Symbiotic’’ application of thermoelectric conversion for fluid preheating/power generation. Energy
Conversion and Management 43:221–228.
Riffat SB et al. 2001. A novel thermoelectric refrigeration system employing heat pipes and a phase change material: an
experimental investigation. Renewable Energy 23:313–323.
Sofrata H 1996. Heat rejection alternatives for thermoelectric refrigerators. Energy Conversion and Management 37:
269–280.
Venkatasubramanian R et al. 2001. Thin-film thermoelectric devices with high room-temperature figures of merit.
Nature 413:597–602.
Webb-RL et al. 1998. Advanced heat exchange technology for thermoelectric cooling. Journal of Electric Packing
120(1):98–105.
Welling TE Jr, et al. 1997. The effect of thermoelectric cooler mounting orientation on cooling efficiency. Aes-vol.37,
Proceedings of the ASME Advanced Energy Systems Division ASME, Middletown, Ohio, 303–307.
Yamanashi M et al. 1996. Optimum design in thermoelectric cooling systems. 15th International Conference on
Thermoelectrics, Kanagawa-Ken, Japan, 220–222.
Copyright # 2004 John Wiley & Sons, Ltd.
Int. J. Energy Res. 2004; 28:753–768