Design, modeling and parametric optimization of thermoelectric cooling systems for high power density electronic devices
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Design, modeling and parametric
optimization of thermoelectric cooling
systems for high power density electronic
devices
Downloaded from https://academic.oup.com/ijlct/advance-article/doi/10.1093/ijlct/ctab032/6248809 by guest on 28 August 2021
..............................................................................................................................................................
Mohammed Barrubeeah*, Mohamed Rady, Alaa Attar, Faisal Albatati and
Abdullah Abuhabaya
Mechanical Engineering Department, Faculty of Engineering at Rabigh, King Abdelaziz
University, KSA
.............................................................................................................................................
Abstract
The present article reports on the design, modeling and parametric optimization of a thermoelectric cooling
system for electronics applications. An analytical model based on energy equilibrium is developed for
cooling a microprocessor using a thermoelectric module with an air-cooled finned heat sink. The proposed
analytical model is validated by experimental measurements and by comparison with detailed 3D numerical
simulations. Estimation of effective material properties of the thermoelectric module using manufacturer-
reported performance characteristics is found to reduce the uncertainty in the calculation of module input
power as compared to experimental measurements. A parametric optimization of the thermoelectric module
and heat sink is carried out to maximize the coefficient of performance (COP) and achieve the required
cooling capacity of the microprocessor. The effectiveness of the proposed methodology is demonstrated
for cooling current high power microprocessors. At a constant input current, the cooling capacity and
COP of the thermoelectric cooling system increase with increasing thermoelectric module geometric ratio.
Furthermore, at a constant geometric ratio, the cooling power increases with increasing input current to
reach a maximum value and then decreases. The present study highlights the importance of designing and
fabricating high-performance thermoelectric cooler modules with optimum parameters for cooling specific
electronic components. The results indicate that the cooling capacity can be increased by ∼70% using
thermoelectric modules with optimized parameters as compared to using non-optimized commercially
available thermoelectric modules.
Keywords: thermoelectric; heat transfer; microprocessor
*Corresponding author: Received 29 January 2021; revised 12 March 2021; editorial decision 23 March 2021; accepted 23 March
mbalrbeah@stu.kau.edu.sa 2021
.................................................................................................................................................................................
1. INTRODUCTION of devices. For example, the TDP value for the recent Intel i9 X
series processors is as high as 165 W, with a maximum allowed
The large amount of heat generated during operation from cur- junction temperature of 94◦ C [14]. The primary challenge with
rent electronic devices poses significant challenges for efficient using conventional bulk cooling systems is the limited available
thermal management to ensure safe and reliable operation. These space in electronic packages. The high effective heat dissipation
challenges relate to the need to maintain the electronic device requirements are difficult to meet using conventional air or water
junction temperature below the maximum allowable temperature passive cooling technologies; therefore, active cooling methods
at the processor die, known as the junction temperature. In the should be applied.
area of microprocessor cooling, thermal design power (TDP) Thermoelectric coolers (TECs) associated with hot side air
represents the average power the processor dissipates when oper- or liquid cooling solutions have shown promise for electronics
ating at base frequency with all cores active. The values of TDP cooling. The advantages of TECs include their small size, high
continue to increase with the development of new generations reliability and low noise. The use of TECs in military, aerospace,
International Journal of Low-Carbon Technologies 2021, 00, 1–17
© The Author(s) 2021. Published by Oxford University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which
permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
doi:10.1093/ijlct/ctab032 1
M. Barrubeeah et al.
and micro-electromechanical systems. These studies include the
use of TEGs for generating electricity in micro-power generation
systems [3, 23, 39] and self-cooling systems of computer chips [6,
32]. Novel techniques have been proposed to extract maximum
heat from the hot combustion products of thermoelectric power
generators [3]. In the field of electronics cooling, Lee et al. [32]
proposed placing TEGs on the cold chip areas to generate electri-
cal power from the wasted heat from the CPU that can be used to
power TECs located on the hotspot areas to maintain local tem-
peratures to equal or below a certain temperature threshold [6].
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Cai et al. [6] showed that increasing the figure-of-merit, ZT, of the
TEG from 0.5 to 3.0 resulted in decreasing the chip temperature
from 92.44 to 74.55◦ C. The results of a 3D numerical study for
Figure 1. Schematic of a thermoelectric air-cooling module comprised of a TEC performance optimization of cascaded and non-cascaded TEGs
and an air-cooling heat sink. and TECs used in developing a self-cooling system for cooling
chip hotspots showed that the system can successfully cool down
the hotspot to an acceptable temperature [31]. The focus of the
instruments and industrial products has been supported by the present study is on the use of TECs in electronics cooling.
commercial availability of TECs in small sizes [27, 29]. Ther- TEC performance depends on several parameters, which can
moelectric modules consist of p-type and n-type semiconductor be classified as thermoelectric module design parameters, cooling
pellets wired electrically in series and thermally in parallel to system thermal design parameters and cooling system working
function as a solid-state energy converter. A thermoelectric air- condition parameters. Thermoelectric module design parameters
cooling module comprised of a TEC and an air-cooling heat include the number of thermocouples (thermoelectric elements)
sink is shown in Figure 1. Whenever direct current passes in and the thermoelectric element length to cross-sectional area
the appropriate direction through the circuit, a thermoelectric ratio. The cooling system thermal design parameters include
cooling effect is generated; as a result, one TEC face is cooled and the geometry of the heat sink, available heat transfer area, heat
the opposite face is simultaneously heated. In electronics cooling transfer coefficient and thermal and electrical contact resistance.
applications, a TEC is used as a solid-state energy converter for In addition, the cooling system working condition parameters
removing heat from the high-temperature surface to the low- include electric current input, heat sink coolant type and mass
temperature environment. The TEC pumps heat away from the flow rate. Enhancement of TEC system performance can be
device to maintain the electronic device junction temperature obtained by optimizing each category of these parameters for
below the safe design threshold. a specific application. Proper design of a TEC system involves
In recent years, researchers have used TECs for electronics identifying the optimal balance between system cooling capacity
cooling and have developed many approaches for thermoelectric and cooling coefficient of performance (COP).
cooling modules. Some studies have investigated the effective Previous research work on TECs has focused on the effect
operating range of TEC modules using an air-cooling heat sink of different parameters on thermoelectric system performance
and water-cooling device for different values of heat load and [37]. Luo et al. [10] presented a recent parametric study of a
input current [7, 13]. Using a square 40 × 40 mm2 TEC module, thermoelectric module used for power generation and cooling.
higher performance was reported for heat load values below A theoretical model was used to study the influences of height,
50.5 W and 57 W for an air-cooled heat sink and water-cooling cross-sectional area, number of couples, ceramic plate and heat
device, respectively [7, 13]. loss on the generator and cooler performance [10].
Chein and Huang [9] theoretically investigated the heat sink The performance optimization of TEC systems has been
thermal resistance requirement for high TEC performance using discussed in many studies [1, 16, 17, 38], and a recent review
a commercially available square 55 × 55 mm2 TEC module. was reported in [36]. In addition to the exploration of high-
The maximum obtained cooling capacity and chip junction tem- performance thermoelectric (TE) materials, structure-based
perature were reported as 207 W and 88◦ C, respectively. The optimization approaches are also reported to enhance the
performance of the TEC was shown to be restricted by the TEC performance of TE modules. A variety of system optimization
cold side temperature and heat sink thermal resistances. Studies methods have been adopted by Lee [20]. In order to reduce
on improving the performance of TECs by decreasing the thermal the number of optimum design parameters, a dimensionless
resistance of the heat sink have proposed the use of novel cooling analytical method has been adopted by several authors. Attar
technologies; these include adopting heat sinks that are cooled and Lee [4] presented a method for optimizing each parameter to
using microchannels [8, 9, 22], phase change materials [12, 30], maximize the cooling capacity of the TEC system as well as COP.
heat pipes [25, 33], water jet [15] and nanofluids [2, 26, 28]. By considering both the first and second laws of thermodynamics,
Many recent studies have also explored the potential capa- Wang et al. [34] introduced a dimensionless entropy generation
bilities of using thermoelectric generators (TEGs) in electronics number based on thermal conductance to evaluate the external
2 International Journal of Low-Carbon Technologies 2021, 00, 1–17
Design, modeling and parametric optimization
irreversibility in the thermoelectric cooling system. Lee [20] et al. [35] is shown to be simple and robust. The present study
adopted the use of a thermal conduction ratio, convection highlights the importance of the optimal design and fabrica-
conduction ratio and load resistance ratio as new dimensionless tion of high-performance TEC modules specifically for cooling
groups to represent important parameters of the thermoelectric electronic components. The use of commercially available TE
devices. Zhu et al. [24] conducted a theoretical study focused modules may limit the performance of these electronic devices.
on the optimal heat exchanger configuration of a TEC system.
The analytical results indicated that the highest COP, highest
heat flux pumping capability of the TEC and lowest cold side 2. DESIGN AND MODELING
temperature can be achieved by selecting an optimal heat transfer
area allocation ratio. Elarusi et al. [11] investigated the optimum The thermoelectric system used to cool the microprocessor in
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design of a TEC with heat sinks based on a modification of this study consists of a thermoelectric module placed between
the dimensional technique developed by Lee [20]. The analysis a microprocessor and a heat sink, as shown above in Figure 1.
showed that an optimal design of a TEC can be determined if two The microprocessor considered in the present study is the Intel
®
fluid temperatures at the heat sinks are known. Optimization of Core™ i9-9820X X-series Processor with a total power dissipa-
the TEC cooling power and COP were achieved by optimizing tion of 165 W, junction temperature of 94◦ C and a surface area
the dimensionless current and thermal conductance. 50 × 50 mm2 [14]. Intel recommends the use of a liquid cooling
In designing and developing a TEC for electronic cooling appli- high-performance thermal solution attached to the entire surface
cations, its purpose is to maintain the electronic device junction area of the microprocessor. In the present design, the surface area
temperature below a safe temperature by rejecting the heat from of the TEC is considered equal to the microprocessor area, as
the electronic device. Due to the fact that the parameters for com- shown in Figure 1. This design represents the minimum solution
mercially available TEC modules vary based on the manufacturer, as constrained by space limitations; increasing the TEC module
the key design task is to find the optimum thermoelectric ele- area results in more heat dissipation from the microprocessor.
ment geometry and structure parameters and the relevant design The microprocessor generates the heat, Qc , at the bottom of the
constraints. Despite the numerous parametric analyses and opti- microprocessor layer, and the heat subsequently transfers to the
mizations of TEC systems discussed above, efficient design tools TEC module by conduction. The TEC module then absorbs the
are needed that can assist developers to select and design suitable Qc at the cold junction and rejects the heat at the hot junction via
TECs for cooling electronic components, reducing the need for thermoelectric cooling effects. Finally, the heat rejected from the
costly and time-consuming experimental evaluation tests. TEC module, Qh , dissipates into the surroundings by convection.
The goal of this study is to develop an analytical model for the Different modeling approaches for TEC have been reported in the
design and optimization of TECs for microprocessor cooling. This literature. Three-dimensional modeling involves solving govern-
study’s major contribution is a simple and robust design tool that ing nonlinear partial differential equations to capture the tem-
can be easily used by electronics developers to design an effective perature distribution both along and across the thermoelectric
TEC system for current high power density microprocessors. element; however, this requires significantly more computational
In the present study, optimization techniques are employed effort. In contrast, energy equilibrium models (EEMs) are simple
for optimizing the thermoelectric module design parameters and and, when they are validated, can be used as an analytical design
heat sink cooling system. A case study involving the cooling of an tool for thermoelectric cooling applications. In the present study,
Intel i9 microprocessor is utilized to demonstrate the capability of an analytical model based on energy equilibrium is validated by
the proposed design and analytical approach. Commercial TEC comparison with the results obtained from a 3D numerical model
modules are investigated and their performance is predicted by and experimental measurements.
estimating the effective material properties from the performance
curves typically provided by the manufacturers. The performance
of the TEC module depends on a set of parameters such as the 2.1. TEC energy equilibrium model
electrical current, the thermal conductivity of the semiconduc- An EEM is developed based on governing equations that describe
tors, the number thermoelectric elements and its geometric ratio. the thermoelectric effects to evaluate the performance of TEC
Likewise, the heat sink performance depends on the number and modules. An EEM is a compact model that can be applied to
thickness of the fins as well as the fin spacing, which influence simplify the design process of the TEC. The calculations of heat
the heat transfer rate. The thermoelectric parameters are stud- flux at the cold and hot sides of the TEC take into account
ied simultaneously with the heat sink parameters in which the the Seebeck effect, Joule heating and heat conduction. They are
optimum cooling power is analyzed along with the heat sink written as follows [21]:
dimensions, electrical current and leg length of the thermoelec- 1
tric module. The proposed analytical models are validated with Qc = n αTc I − I 2 R − K (Th − Tc ) (1)
2
detailed 3D numerical simulations. In addition, the predictions
from the theoretical model are compared with the experimen-
tal results. The optimal design using the developed analytical 1
Qh = n αTh I + I 2 R − K (Th − Tc ) (2)
model with the effective material properties obtained by Weera 2
International Journal of Low-Carbon Technologies 2021, 00, 1–17 3
M. Barrubeeah et al.
where Qc is the cooling capacity at cold side,Qh is the heat rejec-
tion rate, n is the number of thermoelectric elements, α is the
Seebeck coefficient,Tc is the cold junction temperature,Th is the
hot junction temperature, I is current, R is the electrical resistance
of the thermoelectric element and K is the thermal conductance of
the thermoelectric element. The values of R and K are calculated
using the following:
ρLe
R= (3)
Ae
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kAe
K= (4)
Le
where ρ is the electrical resistivity (Ω cm), k is the thermal Figure 2. Cross-sectional area and length of a thermoelectric element.
conductivity,Ae is the cross-sectional area of the thermoelectric
element and Le is the length of thermoelectric element.
Alternatively, from the perspective of the power supply, assum-
The performance of thermoelectric devices is measured by the
ing no losses in the circuit, the power consumption of the TEC
figure of merit, Z, with units of 1/K, written as follows:
can be calculated using the voltage, V, and current, I, as follows:
α2 α2σ
Z= = (5)
ρk k Pin = VI. (10-b)
−1
where σ is electrical conductivity Ωcm . The dimensionless The COP is given by the following:
figure of merit is defined by ZT, where T is the absolute tem-
perature; it is practically limited to values of ZT ≈ 1. Higher
values of ZT indicate greater energy conversion efficiency of Qc
COP = . (11)
the TEC material. The quantity of α 2 σ is defined as the power Pin
factor and is a function of the Seebeck coefficient, α, and the
electrical conductivity, σ. Therefore, it is preferable to increase the
electrical conductivity and minimize the thermal conductivity.
Improving a material’s ZT is challenging due to the well-known
interdependence among these physical properties [29]. 2.2. TEC effective material properties
Assuming that the n- and p-type thermoelectric elements have Solving Equations (7) and (8) requires the determination of prop-
the same leg length and cross-sectional area [21], and considering erties of the thermoelectric module. The design of a TEC module
the heat transfer rate from the heat sink by convection and con- for cooling applications is usually based on commercially available
duction in the processor, the governing equations are written as elements in the market. The manufacturers of thermoelectric
follows: modules typically provide the maximum values for parameters
such as temperature difference, T max , the electrical current,
Qh = ηhA (Th − T∞ ) (6) I max , the cooling power, Qmax , and the voltage, V max . However,
the material properties of the module such as the Seebeck coef-
2 ρ
Qh = n αI Th + 0.5 I − Ge k (Th − Tc ) (7) ficient, α, the electrical resistivity, ρ, and the thermal conduc-
Ge tivity, k, are not given. Material property values can be obtained
2 ρ
Qc = n αI Tc − 0.5 I − Ge k (Th − Tc ) (8) using the effective material equations, where the properties are
Ge
kp Ap extracted from the maximum parameters provided by the man-
Qc = Tp − Tc (9) ufacturers [35], as defined in Equations (12) to (15). The effective
tp
figure of merit, Z∗, is given by the following [21]:
where T∞ is the average air temperature between the air inlet and
outlet, Ge is the geometric ratio of the thermoelectric element,
which is equal to ALee ,Ae is the cross-sectional area of the thermo- 2Tmax
Z∗ = . (12)
electric element, Le is the length of the thermoelectric element, (Th − Tmax )2
kp is the thermal conductivity of the processor, Ap is the heat
transfer area of the processor, tp is the processor thickness and
The effective Seebeck coefficient, α ∗ , is given by the following:
Tp is the processor temperature.
The input power to the TEC module is given by the following:
2Qmax
α∗ = . (13)
Pin = Qh − QC . (10-a) n Imax (Th + Tmax )
4 International Journal of Low-Carbon Technologies 2021, 00, 1–17
Design, modeling and parametric optimization
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Figure 3. Detailed schematic of a single couple model and module design.
Table 1. Module specifications used in the present study.
Geometry Value Units
p-type element
Thermal cross-section area (E-D × E-W) 1 mm × 1 mm mm2
Length (E-L) 0.7 mm mm
Seebeck coefficient (α) 209.88 μV/K
Thermal conductivity (k) 0.011 W/m K
Electrical resistivity (ρ ( 6.27 × 10−3 Ω.mm
n-type element
Thermal cross-section area (E-D × E-W) 1 mm ∗ 1 mm mm2
Length (E-L) 0.7 mm mm
Seebeck coefficient (α) 209.88 μV/K
Thermal conductivity (k) 0.011 W/m K
Electrical resistivity (ρ ( 6.27 × 10−3 Ω.mm
Copper conductor
Electrical cross-section area (Cu-W × Cu-t) 0.1 mm × 1 mm mm2
Electrical length (Cu-L) 3 mm
Thermal conductivity 400 W/m K
Electrical resistivity 1.7 × 10−5 Ω.mm
Ceramic insulation
Thermal cross-section area (Cr W × Cr L) 50 mm × 50 mm mm2
Thickness (Cr-t) 0.1 mm
Thermal conductivity 30 W/m K
The effective electrical resistivity, ρ ∗ , is given by the following: Thomson effect, which could be observed when the intrinsic
material properties are used [35]. Comparing the performance of
α ∗ (Th + Tmax ) Ae /Le the TEC module using the effective material properties calculated
ρ∗ = (14) by Equations (12) to (15) with both commercially provided data
Imax
and experimental results supports the validity of the developed
where Ae is the cross-sectional area of the thermoelectric element method as a highly utilizable analytical tool in predicting the
and Le is the length of the thermoelectric element, as shown in performance of commercial thermoelectric modules [35].
Figure 2.
The effective thermal conductivity, k∗ , is given by the following:
2.3. Couple and module design
Geometric models of the TEC couple and module designs and
∗ α ∗2 specifications for the theoretical and 3D analysis of the present
k = ∗ ∗. (15)
ρ Z study are shown in Figure 3 and Table 1, respectively. The dimen-
sion values listed in Table 1 are representative values and are
Thus, after determining the values of effective properties (k∗ , varied for the purpose of optimization of the TEC module. The
ρ∗ , α ∗ ) using Equations (12) to (15), they are used to replace their fill factor, F, is the ratio of the area covered by the active thermo-
corresponding values (k, ρ, α) in Equations (7) to (9). Using the electric material to the plate area. The value of F is determined
effective material properties in the ideal equations to evaluate the by the dimensions of the p-type and n-type elements and the
performance of thermoelectric modules accounts for a majority copper conductor. The couple leg length and cross-sectional area
of parasitic losses and uncertainties associated with electrical are varied to achieve for the optimum value of geometric ratio
and thermal contact resistances, material degradation and the (Ge). The length of the copper conductor varies according to the
International Journal of Low-Carbon Technologies 2021, 00, 1–17 5
M. Barrubeeah et al.
The single-fin efficiency, η∗ , is given by the following:
tanh(mb)
η∗ = (20)
bm
1
2h 2
m= . (21)
kalu t
The heat transfer coefficient, h, is calculated using the following
equations:
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Nu kair
h= (22)
Figure 4. Schematic of the heat sink and the key design parameters [ 19 ]. Dh
4
Nu = 0.023Re 5 Pr0.4 (23)
leg dimensions in order to maintain a constant fill factor of 0.66, Uair Dh
which is normally recommended and used in commercial TEC Re = (24)
ν
modules [18]. The module surface area is fixed at 50 × 50 mm2 4zb
to equal the surface area of the microprocessor implemented in Dh = (25)
2 (z + b)
the case study. The number of couples in the module can be easily
determined when distributed over this fixed area. where Nu is the Nusselt number, kair is the thermal conductivity
of air, Dh is the hydraulic diameter, Pr is the Prandtl number, Re
is the Reynolds number, Dh is the hydraulic diameter, U air is the
2.4. Heat sink design and optimization air velocity and ν is the kinematic viscosity of air. Equation (23)
The heat sink plays an important role in the overall performance is applicable to turbulent flow, which is dominant for the range
of the TEC system. It is placed above the TEC to reject the heat of air flow velocity and heat sink dimensions encountered in the
from the TEC’s hot side. A heat sink is a device that absorbs and present study.
rejects heat into the surrounding air by increasing the heat transfer It is important to emphasize that the higher the heat transfer
surface area with the use of fins or spines. The objective of this coefficient value, the greater the heat dissipation. Increasing the
section is to optimize the heat sink parameters, ηhA, in Equation heat transfer coefficient can be achieved by increasing the air
(6) to maximize the heat rejection, Qh . Figure 4 depicts the design velocity, which correspondingly increases the required fan power.
parameters of the heat sink, where b is the profile length, the base Therefore, the fan power is calculated using the following:
area is W × L and the material used is aluminum. The heat sink
is designed and optimized following the optimization technique Ppower = ΔPVt (26)
developed by Lee [19].
The heat sink dimensions (width, W, length, L, and profile where Vt is the total volume flow rate and ΔP is the pressure drop
length, b) are fixed by the available space associated with the across the sink, given by the following:
microprocessor. Therefore, the present optimization focuses on
optimizing the fin thickness, t, fin spacing, z, and number of fins,
Vt = Uair z b (n − 1) (27)
n, in order to minimize the thermal resistance, Rt , given by the
following [19]:
2
L ρair Uair
1 ΔP = f . (28)
Rt = . (16) Dh 2
ηhA
The friction factor is a function of Reynolds number:
The overall efficiency, η, is given by the following:
−1
f = 0.316Re 4 (29)
Af
η =1−n 1 − η∗ (17)
A Equations (8) to (26) relating to the heat sink design are solved
as a function of the fin thickness, t, with iterations to find the
where A is the total area and Af is a single-fin area calculated as optimal design, which maximizes the heat transfer rate. The alu-
follows: minum and air properties used in the equations are listed in
Table 2. The fin base area (L × W) is equal to that of the micro-
A = n (2 (L + t) b + Lz) (18) processor dimensions (50 × 50 mm2 ). Figure 5 shows that the heat
dissipation rate first increases with increasing fin thickness. How-
Af = 2 (L + t) b. (19) ever, the increase in fin thickness reduces the spacing between the
6 International Journal of Low-Carbon Technologies 2021, 00, 1–17
Design, modeling and parametric optimization
Table 2. Aluminum and air properties.
Property Symbol Unit Air Aluminum
Thermal conductivity k W/m K 26.3 × 10−3 177
Density ρ kg/m3 1.16 2700
Prandtl number Pr 0.707
Kinematic viscosity ν m2 /s 15.89 × 10−6
Air velocity U air m/s 17.38
3. THREE-DIMENSIONAL NUMERICAL
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SIMULATION
The EEM described above is validated by comparison with
the results obtained from a 3D numerical simulation. The
3D numerical model is developed using ANSYS,2017-R1 CFX
integrated with ANSYS,2017-R1 Thermal-Electric software
packages for fluid flow and thermoelectric analysis, respectively.
SOLIDWORKS 2016 software is also used to create the part
models and assemble the system components, namely, the TEC
module and the heat sink. Figure 6 shows the complete system
implemented in ANSYS using a mesh size of 0.5 mm.
After the system components are drawn and assembled, the
geometry is imported into Ansys CFX to simulate air passing
through the heat sink fins by placing the heat sink inside an air
duct, as shown in Figure 7. The boundary condition at the air
duct inlet is air velocity at room temperature, while the boundary
Figure 5. Total heat transfer rate from the heat sink vs. fin thickness (base area condition at the exit is zero gauge pressure.
50 × 50 mm2 , base temperature 85◦ C). The thermoelectric analysis was then conducted using Ansys
Thermal-Electric. This software allows the manual input of
Table 3. Heat sink design parameters. material properties of thermoelectric elements, as well as the
input of electrical current to the TEC module. The TEC couple
Parameter Symbol Value
and module design parameters and specifications, shown in
Fin thickness t 0.76 mm Figure 3 and Table 1, respectively, were implemented for the
Fin spacing z 2.78 mm thermoelectric analysis. Two boundary conditions were set for
Number of fins ns 18 this simulation. The first boundary condition was set as electrical
Mass of heat sink m 56.27 g
Profile length b 30 mm
current at one of the TEC module’s poles and zero volts at the other
Base length L 50 mm pole, representing ground. The second boundary condition was
Base width W 50 mm the temperature at the bottom of the block which was set at 94◦ C,
Total heat rejected qt 205.52 W representing the microprocessor temperature. The boundary
Total area of the heat sink A 5.76 × 104 mm2 conditions of the ANSYS Thermal-Electric model are shown in
Total heat sink resistance Rt 0.23 K/W
Heat sink efficiency η 0.74
Figure 8.
Heat sink effectiveness ε 55.11 The simulation procedure and integration of the CFX model
Heat transfer coefficient h 109.39 W/m2 . K with the Thermal-Electric model are as follows:
Pressure drop ΔP 82.48 Pa
Fan power Ppower 2.2 W 1. Set the airflow temperature and velocity in the CFX toolbox to
calculate the convective heat transfer coefficient, h.
2. Import the resulting value of the heat transfer coefficient to the
Thermal-Electrical toolbox.
fins and the number of fins resulting in a decreasing in the surface 3. Use the heat transfer coefficient as a boundary condition in
area for convective heat transfer. At the optimum fin thickness of Thermal-Electrical analysis.
0.76 mm, the maximum heat rejected by the heat sink is 205.52 W, 4. Calculate the junction’s temperature (Tc is the module’s junc-
which exceeds the power dissipated from the microprocessor. The tion’s temperature from the microprocessor side, and Th is the
heat sink design parameters at the optimum condition are listed module’s junction’s temperature from the heat sink side) for
in Table 3. input current values from 1A to 7A.
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M. Barrubeeah et al.
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Figure 6. ANSYS model of the overall system including microprocessor, TEC module and heat sink using a mesh size of 0.5 mm.
Figure 7. ANSYS CFX model of heat sink flow.
5. Calculate the cooling power, Qc , and heat rejection, Qh , by Figure 8. ANSYS Thermal-Electric model boundary conditions: arrow A is the
integrating the heat fluxes at the cold and hot sides of the TEC. input current position, arrow B is the input voltage position, which is set at 0 Volts
to define the grounding system, and arrow C is the microprocessor temperature.
6. Calculate the input power, Pin , and COP using Equations
(10-b) and (11).
7. As a cross-check for the accuracy of the solution, substitute the
resulting values of the junction’s temperatures, Th and Tc , into the microprocessor surface and the design shown in Figure 1.
the design Equations (8) to (11) to obtain Qc , Qh , Pin and COP, Also, the TEC module parameters are not optimized for cooling of
and evaluate the error in the calculations. the selected microprocessor. Therefore, the experimental results
are only used for the purpose of validating the analytical and 3D
simulations. The selected heat sink is 40 × 40 × 20 mm and is
made from aluminum. The values shown in Table 4 are used to
4. EXPERIMENTAL SETUP calculate the effective material properties used in the analytical
model while comparing with the experimental results. The
An experimental setup using a commercially available TEC geometric parameters of the experimental module are measured
module is also built for the purpose of validating the pro- and used as inputs in the models.
posed EEM. The UT15-200-F2-4040 thermoelectric module is The complete experimental set up is shown in Figure 9. An
purchased from Laird Thermal Systems [18] and is assembled adjustable DC power supply (0–30 V/0–10 A) is also used to
using bismuth telluride as the semiconductor material. The supply the TEC module with varying electrical currents. The TEC
performance characteristics and data sheet specifications of the module is placed between two aluminum blocks with dimensions
module are provided in Table 4. It should be noted that the surface of 40 × 40 × 20 mm3 and 40 × 40 × 200 mm3 . Two K-type
area of the TEC module is 40 × 40 mm2 , which is different from thermocouples with a diameter of 2 mm and a depth of 20 mm
8 International Journal of Low-Carbon Technologies 2021, 00, 1–17
Design, modeling and parametric optimization
Table 4. TEC module performance specifications, Laird UT15-200-F2-4040 [ 18 ].
Hot side temperature (◦ C) 25 50
Qmax (W) 236.6 254.9
Tmax (◦ C) 68 75
Imax (A) 15.4 15.4
Vmax (V) 25.0 28.6
Module resistance (Ohms) 1.37 1.54
Thickness 3.3 mm
Area 40 × 40 mm
Number of couples 200
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Figure 9. Assembly of experimental setup as well as the schematic diagram of the experiment.
are inserted in each aluminum block at the location of interest,
as illustrated in the schematic Figure 9. Thermal paste is used at
the interfaces between the blocks and the TEC module to obtain
better heat conduction and minimize the thermal resistance. An
adjustable 1000 W electrical heater is used to generate heat. A
dimmer (4000 W, AC 220 V) variable voltage controller is used
to adjust the air blower speed. It should be noted that the lower
aluminum block in contact with the electric heater is long enough
(200 mm length) to ensure 1D and uniform heat flux at the bottom
surface of the TEC module and minimize errors associated with
the calculation of heat flux using temperature measurements. The
measured value of heat flux is used in the analysis and there no
need to insulate the electric heater at the bottom. The experimen-
tal setup components also include an air blower with a capacity
of 170 m3 /h and a 3D-printed air duct containing the heat sink,
which ensures that the air passes through the fins of the heat sink.
A digital anemometer is also used to measure the airflow speed at
the outlet of the duct.
To emulate the heat generated from microprocessors, the input
power to the electrical heater installed at the bottom of the lower
Figure 10. Comparison of TEC input power measurements and Pin, using heat
aluminum block was controlled. The amount of heat is adjusted balance and voltage and current measurements.
to keep T 2 , the equivalent of the microprocessor junction temper-
ature, Tp , constant for all experiment tests. Tp is also considered
constant in the TEC model. The experimental procedure is carried 1. Set the flow velocity of air to a constant value throughout the
out as follows: experiment to maintain a constant thermal conductance.
International Journal of Low-Carbon Technologies 2021, 00, 1–17 9
M. Barrubeeah et al.
2. Record temperature readings of T 5 and T 6 to find the average
air temperature, T ∞ .
3. Set the desired electrical current and adjust the heater to main-
tain a constant temperature of T 2 until other temperatures
reach steady state.
4. Record temperature readings of T 3 and T 4 and apply the
extrapolation method to find the hot junction temperature
Th . Record temperature readings of T 1 and T 2 and apply the
extrapolation method to find the cold junction temperature Tc .
Substitute the Tc and Th in Equations (7), (8), (10-a) and (11)
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to findQh , Qc , Pin and COP, respectively.
5. The input power, Pin , can be also calculated using Equation
(10-b) to ensure the thermal balance and accuracy of measure-
ments.
The uncertainty of the measurement of the junction temper-
atures, Tc and Th , by extrapolation depends on the uncertainty
in the temperature measurement and the distance measurements
of the actual thermocouple locations. The manufacturing uncer- Figure 11. Performance curves of the Laird UT15-200-F2-4040 TEC module;
the solid line is calculated using the effective material properties; points represent
tainty associated with machining these holes was estimated to be the manufacturer data for different values of electric current.
±0.1 mm. Cumulatively, the total uncertainty of the 5 mm dis-
tance between the thermocouples is ±4%. The thermocouples T 2
and T 3 are placed at distances of 5 and 10 mm from the TEC sur-
face, respectively. The thermocouples have a measurement error
5.1. Effective material properties
of ±0.5◦ C, corresponding to an uncertainty of ±1%. Using the
Effective material properties for the thermoelectric module used
theory of uncertainty propagation [5], the resulting uncertainty
in the present study are first estimated using Equations (12) to
in the calculation of Tc and Th is about ±0.8%. Using Equations
(15) by using the maximum parameters from the manufacturer’s
(7), (8) and (10), the uncertainty in Qc , Qh and input powerPin
datasheet, listed in Table 5 below.
is between ±1 and ±2%. The errors in the voltage and current
The maximum cooling power, Qmax , is the maximum thermal
measurements are ±0.5 mA and ± 5 μV, respectively, which
load, which occurs at I = Imax and Tc = Th ; this can be obtained
results in a maximum uncertainty of ±2% in the input power
by substituting both I and Tc in Equation (1) with Imax and Th .
value using the measured voltage and current. Comparisons of the
Then, using the calculated material properties, the values of Qmax
power measurement as the difference between Qh and Qc using
can be obtained. Figure 11 provides a comparison between the
Equations (10-a) and as the product of V and I using Eq. (10-b) are
calculations (solid lines) and the manufacturer’s performance data
shown in Figure 10. It can be seen that the power measurements
(triangles) for the TEC module. As can be seen, the calculated
using Equations (10-a) and (10-b) agree very closely, with a small
effective maximum parameters, Tmax , Imax and Qmax , are in
deviation between the two methods occurring at relatively high
good agreement with the manufacturer’s performance curves.
electric current values. This can be explained by temperature-
Using the effective material properties in the ideal equations
independent effective TEC properties, as discussed in Section 5.1,
accounts for uncertainties associated with electrical and thermal
which occur at high input currents. Also, small differences (less
contact resistances and the Thomson effect [35]. The uncertainty
than 5%) in input power measurements using the two methods
associated with using the effective material properties can be eval-
can be attributed to the effects of thermal and electrical contact
uated by comparing the TEC input power using measurements of
resistances in the experimental setup. Overall, close agreement
input, V × I and Qh –Qc , as given by Equations (10-a) and (10-b),
in the measurement of Pin using temperature measurements and
and as shown in Figure 10. The maximum difference between the
V × I confirms the thermal balance and accuracy of the experi-
TEC input power values obtained using the EEM model and Qh –
ments.
Qc is less than ±0.5% and increases to ±2.5% as compared to the
measured value of V × I. These low uncertainty values indicate
the accuracy of the measurements carried out in the present study
and the importance of using effective material properties of TEC
5. VALIDATION OF TEC EEM modules in the design models.
In this section, results obtained using the EEM are compared
with the experimental and 3D numerical results. After the EEM 5.2. Comparisons with 3D numerical results
is validated, it can be widely used for design and optimization of Comparisons of the EEM and 3D numerical model are carried
TECs for microprocessor cooling applications. out. The TEC module and heat sink characteristics used in this
10 International Journal of Low-Carbon Technologies 2021, 00, 1–17Design, modeling and parametric optimization
Table 5. Material properties of the Laird UT15-200-F2-4040 module.
α∗ R∗ K∗ Z∗
419.77 μV
K 6.27 × 10−3 Ω 0.011 W
K 0.77
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Figure 12. Effects of mesh size on the calculated values of Qh, Qc and input power.
study are listed in Tables 1 and 3. After defining the boundary in a maximum difference in calculated input power of 2.3%. The
conditions in Ansys CFX and integrating the ANSYS Thermal- difference in calculations of Pin , Qh and Qc using different mesh
Electrical simulation software, the electrical current is manually sizes is smaller at values of input current less than 5 A. The
input for each simulation run and the system is solved. A mesh temperature distribution throughout the heat sink and the TEC
refinement study is carried out using mesh sizes of 1.5 mm, module for different mesh sizes is presented in the simulation
1.25 mm, 1.0 mm, 0.75 mm and 0.5 mm. The effects of mesh results shown in Figure 13. The results obtained using a 0.5 mm
size on the calculated values of Qh and Qc for different values of mesh size are considered accurate and grid independent.
input current are shown in Figure 12a. Refining the mesh from The junction cold and hot temperatures for each input current
1.5 to 1.0 mm, and from 1.0 mm to 0.5 mm, results in differences and for every simulation run were recorded and compared to
in the Qh and Qc calculation of about 10% and 3%, respectively. those obtained using the EEM. Figures 14 and 15 show com-
An accurate measure of grid size independence results can also be parisons of Qh and Qc , and TEC module junction temperatures,
evaluated by comparing the calculated input power Pin using (Qh – Th and Tc , for a range of electrical currents. Good agreement
Qc ) and (V × I). Figure 12b shows the difference in calculated can be observed between the EEM and the 3D model numerical
input power for different mesh sizes and different values of input results. It can be observed from Figure 15 that input current
current. It can be observed that using a mesh size of 0.5 mm results values higher than 4.6 A are necessary to achieve effective cooling
International Journal of Low-Carbon Technologies 2021, 00, 1–17 11M. Barrubeeah et al.
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Figure 13. Temperature distribution in the system using a 3D numerical model with a mesh size of 0.5 mm; the model geometric and thermophysical parameters
are listed in Tables 1 and 3.
Figure 14. Comparisons of Qh and Qc for different values of electrical current
obtained using the EEM (solid lines) and 3D simulation results (symbols), with Figure 15. Comparisons of TEC module cold and hot junction temperatures, Th
a mesh size of 0.5 mm, and model geometric and thermophysical parameters as and Tc, for different values of electrical current obtained using the EEM (solid
listed in Table 1. lines) and 3D simulation results (symbols), with a mesh size of 0.5 mm, and
model geometric and thermophysical parameters are listed in Table 1.
with an increase in the delta between the hot and cold junction
temperatures with increasing input current.
between the measured and predicted TEC heat transfer rates,
Qh and Qc , and junction temperatures, Th and Tc , respectively.
5.3. Comparisons with experimental results Relatively small differences in the values are observed, which are
Further comparisons of the EEM and 3D numerical models with likely a result of the contact resistance between the TEC module
experimental results were carried out. The experimental setup and the upper and lower aluminum blocks, meaning a non-perfect
components’ properties and geometric parameters of the TEC insulation. In general, the comparison of results shows good
module and the heat sink reported in Tables 3 and 4 were used agreement. Thus, the EEM model can be used as a simple and
in the analysis. The TEC module and heat sink contact surface reliable tool for design optimization, as explained in the following
area is 40 × 40 mm2 . Figures 16 and 17 illustrate comparisons section.
12 International Journal of Low-Carbon Technologies 2021, 00, 1–17Design, modeling and parametric optimization
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Figure 16. Comparisons of the TEC module (Qh, Qc) for different values of elec- Figure 17. Comparisons of TEC module cold and hot junctions temperatures
trical current obtained using the EEM, 3D simulation results and experimental (Th, Tc) for different values of electrical current obtained using the EEM, 3D sim-
results; the model geometric and thermophysical parameters are listed in Tables 3 ulation results and experimental results; the model geometric and thermophysical
and 4. parameters are listed in Tables 3 and 4.
6. ANALYSIS AND OPTIMIZATION OF TEC the optimum values for Ge within the available surface area of
PERFORMANCE FOR MICROPROCESSOR 50 × 50 mm2 . The heat sink design optimum parameters are listed
COOLING in Table 3.
Further insights into the performance of the TEC module for
The results and comparisons presented above demonstrate the microprocessor cooling regarding the significance of the obtained
ability of the EEM to accurately predict the TEC module perfor- optimum design values can be gained by analyzing the effects of
mance. The present EEM has been used to conduct parametric the geometric ratio and input current on cooling power and COP,
analyses and optimization for the design of the TEC module and as shown in Figure 18. It can be observed that, for constant input
heat sink for microprocessor cooling. As a case study, a micro- current, the cooling power and COP increase with increasing
processor power of 165 W representing the newest generation geometric ratio. In contrast, for values of Ge, the cooling power
of the technology is considered. The analysis shows that, if two increases with increasing input current to a maximum value and
temperatures at the microprocessor surface and cooling fluid are then decreases, as shown in Figure 19. As expected, the COP
known, an optimal design always exists and can be determined always decreases with increasing input current. The range of Ge
[11]. The objective of design optimization for our case study is to values is limited by the surface area of the TEC module available
use the thermophysical properties of the module listed in Table 1, to distribute the TE couples; Ge = 0.2 for a 50 × 50 mm2 TEC
and the heat sink optimum design parameters listed in Table 3, module. Drawing a horizontal line at Qc = 165 in Figure 18 allows
to optimize the input current and geometric ratio to maximize the identification of the minimum input current and maximum
the cooling power. The constraints for this optimization task are geometric ratio values to achieve this required cooling power. It
a required microprocessor cooling power of 165 W, a surface area can be inferred from Figure 18 that the optimum value of cooling
of the TEC module of 50 × 50 mm2 , a cooling air temperature power is achieved at lower COP values and higher input power
of 30◦ C and a microprocessor junction temperature of 94◦ C. values. The curves representing the selected optimum design
The EEM governing equations can be easily used to solve this values for input current, 4.69, and Ge, 0.144, were obtained using
optimization problem. A Mathcad program is implemented in Mathcad and are shown on Figures 18 and 19. Figure 20 shows
the present study to search for the solution of this optimization cooling power and COP as a function of heat sink thermal con-
problem. The optimum values for input current and geomet- ductance, η h A, for varying input electric current. For all values
ric ratio of the TEC module are determined to be 4.69 A and of electric current, it can be seen that the values of QC and COP
0.144 cm, respectively. Based on these results, the optimum design initially increase with increasing heat sink thermal conductance.
parameters of the TEC for a microprocessor power of 165 W are The increase in COP and QC is relatively small for high values of
shown in Table 6. The number of couples, n, is determined using η h A. Curves representing QC and COP obtained using optimum
International Journal of Low-Carbon Technologies 2021, 00, 1–17 13M. Barrubeeah et al.
Table 6. Details for the optimum design parameters of a TEC module for cooling a 165 W microprocessor.
Parameter Optimization goal Optimization constraint Optimum design (50 × 50) mm2
Qc (W) Maximize Qc Required cooling capacity 165
COP Maximize COP Required cooling capacity 2.4
ηhA = 1/Rt (W/K) Maximize Qh Surface area of TE module Refer to Table 3 for details of heat
50 × 50 mm2 sink optimization
Tp (◦ C) Maximum allowable microprocessor 94
junction temperature
T ∞ (◦ C) Ambient air temperature 30
α( μV
K ) TE module effective properties; 419.77
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R (Ω) refer to Table 5 6.27 × 10−3
K ( mWK ) 0.011
Ge (cm) Results of optimization 0.144
n Surface area of TE module 204
50 × 50 mm2
Tc (◦ C) 74
Th (◦ C) 77.60
I (A) 4.69
Figure 18. System performance using EEM: (a) cooling power (solid lines) and COP (dotted lines) vs. electrical current (A) for different input currents; the TEC
parameters are listed in Table 1.
values of Ge and input current are also shown on Figure 19. From module would offer the advantages of low cost, low noise and high
the design perspective, the heat sink thermal conductance can reliability.
be minimized as far as possible. However, for a given required The present study focused on the design of a customized TEC
cooling power of the present microprocessor (165 W) and opti- module and heat sink for a particular microprocessor. The com-
mized heat sink geometry, listed in Table 3, a heat sink thermal mon practice of selecting commercially available TEC modules
conductance of about 5 W/K is considered sufficient. Increasing and heat sinks would result in poor performance or an inabil-
the heat sink thermal conductance would result in more capacity ity to meet the microprocessor cooling requirements. Figure 21
to dissipate heat from the TEC module; however, this would be at compares the performance obtained using the commercial TEC
the expense of higher heat sink fan power requirements. module, listed in Table 4, and the TEC module with optimized
It should be noted that liquid cooling solution is typically used parameters, listed in Table 6, obtained using the EEM model
for cooling the processor used in the present study [14], consisting as recommended in the present study. Higher performance was
of a combined heat sink with a liquid pump and a radiator. The obtained using the TEC module with optimized parameters. It can
small unit circulates water to keep the CPU cool when it is idling be observed that, for the same input power, the cooling capacity of
and when it is under full load. It automatically adjusts the rate the TEC system with optimized parameters is ∼70% higher than
of cooling based on the CPU temperature. The use of a TEC that of commercially available TEC modules of equivalent surface
14 International Journal of Low-Carbon Technologies 2021, 00, 1–17Design, modeling and parametric optimization
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Figure 19. Cooling power (solid line) in watts and COP (dotted lines) vs. geometric ratio in cm; the TEC parameters are listed in Table 1.
Figure 20. System performance using EEM: cooling power (solid lines) and COP (dotted lines) vs. heat sink thermal conductance (η h A) for different values of input
electric current, TEC parameters listed in Table 1.
area. In addition, the COP of the optimized module is slightly TEC systems for electronic devices aim to meet the high cool-
higher than that of the commercial module. ing requirements and maximize the COP. To demonstrate the
capability of the proposed model and to analyze the performance
of a microprocessor thermoelectric cooling system, a case study
involving the cooling of recent available microprocessor with a
7. CONCLUSION power dissipation requirement of 165 W is considered. The main
findings of the present study are summarized as follows:
The major contribution of the present study is the development
of a simple and robust design tool to optimize thermoelectric • Using effective material properties in the model equations
cooling systems for current high power density microprocessors. reduces the uncertainty in the calculation of TEC input power
The developed model considers different design and operation to less than ±2.5%.
parameters affecting the performance of a TEC module with an • At a constant input current, the cooling power and COP
air-cooled heat sink. The model was validated by comparison increase with increasing geometric ratio. In addition, at a
with the results obtained from detailed 3D numerical simulations constant geometric ratio, the cooling power increases with
and experimental measurements. Design and optimization of increasing input current to a maximum value and then
International Journal of Low-Carbon Technologies 2021, 00, 1–17 15M. Barrubeeah et al.
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Figure 21. Comparisons of performance of a commercial TEC module and an optimum TEC module design.
decreases; the COP always decreases with increasing input [7] Chang Y-W, Chang C-C, Ke M-T et al. Thermoelectric air-cooling module
current. for electronic devices. Appl Therm Eng 2009;29:2731–7.
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