This paper presents quantitative analysis and practical scenarios of implementation of the thermoelectric module for heat flow detection. Mathematical models of the thermoelectric effects are derived to describe the heat flow from/to the detected media. It is observed that the amount of the heat flow through the thermoelectric module proportionally induces the conduction heat owing to the temperature difference between the hot side and the cold side of the thermoelectric module. In turn, the Seebeck effect takes place in the thermoelectric module where the temperature difference is converted to the electric voltage. Hence, the heat flow from/to the detected media can be observed from both the amount and the polarity of the voltage across the thermoelectric module. Two experiments are demonstrated for viability of the proposed technique by the measurements of the heat flux through the building wall and thermal radiation from the outdoor environment during daytime.

1. ISA Transactions 51 (2012) 345–350
Contents lists available at SciVerse ScienceDirect
ISA Transactions
journal homepage: www.elsevier.com/locate/isatrans
Applications of thermoelectric modules on heat flow detection
Thananchai Leephakpreeda∗
School of Manufacturing Systems and Mechanical Engineering, Sirindhorn International Institute of Technology, Thammasat University, P.O. Box 22,
Thammasat-Rangsit Post Office, Pathum Thani, 12121, Thailand
a r t i c l e i n f o
Article history:
Received 13 February 2011
Received in revised form
12 April 2011
Accepted 13 November 2011
Available online 7 December 2011
Keywords:
Thermoelectric module
Heat flow
Thermal detection
Measurement
a b s t r a c t
This paper presents quantitative analysis and practical scenarios of implementation of the thermoelectric
module for heat flow detection. Mathematical models of the thermoelectric effects are derived to describe
the heat flow from/to the detected media. It is observed that the amount of the heat flow through the
thermoelectric module proportionally induces the conduction heat owing to the temperature difference
between the hot side and the cold side of the thermoelectric module. In turn, the Seebeck effect takes
place in the thermoelectric module where the temperature difference is converted to the electric voltage.
Hence, the heat flow from/to the detected media can be observed from both the amount and the polarity
of the voltage across the thermoelectric module. Two experiments are demonstrated for viability of the
proposed technique by the measurements of the heat flux through the building wall and thermal radiation
from the outdoor environment during daytime.
© 2011 ISA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Nowadays, no one can refuse that there are various advanced
engineering applications of thermoelectric modules in both indus-
try and laboratory scale, even though thermoelectric modules are
widely used as thermoelectric coolers for all cooling needs in com-
mon forms of thermoelectric plates [1,2]. For example, recently, in
developed envelopes of a building, the thermoelectric module is
integrated with photovoltaic cells supplying electrical power to it
so as to have the cooling/heating ability to actively control the flow
of the heat across their closure surface through the building, which
is exposed to solar radiation during daytime [3]. On the other hand,
the thermoelectric module can be applied in reversal by simply
making temperature difference on both sides of the thermoelectric
module from available heat sources instead and then the electrical
current is induced due to the thermoelectric effect [4]. This inci-
dent actually yields alternatives of electricity generation. Analyti-
cal studies of [5] reported that the thermoelectric module can be
applied in an automobile to recover waste heat discharged from an
exhaust pipe or a radiator to the surroundings with promising out-
come. Other heat sources such as biomass can be alternatively im-
plemented so as to cause such a temperature difference to produce
electricity as well [6]. Additionally, in the open literature, there is a
very interesting application of the thermoelectric module on ther-
mal sensing. The experimental work of [7] reported that the ther-
moelectric module arranged in specific instrumentation design has
∗ Tel.: +66 2 9869009x2204; fax: +66 2 9869009x2201.
E-mail address: thanan@siit.tu.ac.th.
high sensitivity to heat while it is exposed to infrared radiation in
industrial furnaces.
In this study, the contribution of the works is to provide quan-
titative analysis from a mathematical modeling point of view so as
to understand the principles on physical behaviors of heat flow de-
tection via the thermoelectric module. Additionally, the practical
experiments confirm the applicability of the thermoelectric mod-
ule in determining the heat flow in two modes for case studies:
(1) heat conduction from the building wall and (2) thermal radi-
ation in the outdoor environments. The paper is organized as fol-
lows. In Section 2, the details of experimental setups are described.
Section 3 provides the mathematical modeling of the thermoelec-
tric module. Results and discussion are given in Section 4. Finally,
the conclusion is remarked in Section 5.
2. Experimental setups
Two practical scenarios are performed in this study. Initially,
the thermoelectric module is developed by simply attaching a heat
sink on one side. The other surface of the thermoelectric module is
used for the detection of the heat flow. In the first case study, the
heat flow through an accessible concrete wall of a building during
the day is observed by mounting the thermoelectric module on the
indoor surface of the wall as shown in Fig. 1. The voltage signal
of the thermoelectric module is recorded in order to determine
the corresponding amount of the heat flow from the proposed
technique. In the second case study, the detection of radiation
heat in the outdoor environment is investigated by facing the
black-coated side of the thermoelectric module for detection to the
outdoor atmosphere as depicted in Fig. 2. Again, the voltage signal
is recorded to determine the amount of radiation heat, which is
compared to the measurements from a pyranometer.
0019-0578/$ – see front matter © 2011 ISA. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.isatra.2011.11.003

2. 346 T. Leephakpreeda / ISA Transactions 51 (2012) 345–350
Fig. 1. Experiment on heat flux through the building wall.
Fig. 2. Experiment on thermal radiation within the outdoor environment.
3. Mathematical modeling of the thermoelectric module
This section is to describe mathematical models for governing
physical behaviors of a thermoelectric module so as to approach
practical applications of thermoelectric modules on heat flow
detection. For commercial products, the thermoelectric module is
typically made of two ceramic plates of various sizes and shapes
covering an array of (n − p) sequentially-paired semiconductors
in between those as shown in Fig. 3. In general, the thermoelectric
modules are widely used as heat pumps in electric cooling/heating
when the DC current from a power source flows through the
thermoelectric module, which subsequently causes heat transfer
from one side (cold side) of the thermoelectric module to the other
(hot side). In turn, cooling effects and heating effects are generated
according to thermal demands at the cold side and at the hot side,
respectively. In fact, the thermoelectric module can be considered
a thermal–electrical circuit as depicted on the right side in Fig. 3,
which is mathematically described by:
v = β (Th − Tc ) + RI (1)
where v is the voltage across the thermoelectric module, β is
the Seebeck coefficient, Th is the temperature at the hot side, Tc
is the temperature at the cold side, R is the resistance of the
thermoelectric module, I is the electrical current flowing within
the circuit.
The amount of heat rejected by the thermoelectric module at
the hot side can be determined by:
QH = βITh +
1
2
I2
R − k (Th − Tc ) . (2)
On the other hand, the amount of heat pumped by the thermoelec-
tric module at the cold side can be determined by:
QC = βITc −
1
2
I2
R − k (Th − Tc ) (3)
where k is the thermal conductivity coefficient of the thermoelec-
tric module.
The first term on the right side of Eqs. (2)–(3) is the Seebeck
heating/cooling effects. The second term characterizes the Joule
heating effect associated with electrical power developed in the
resistance. The third term represents the Fourier effect of heat
conduction from the hot side to the cold side.
From the principle of energy balance, the electrical power and
the rate of heat pumped from the cold side as well as the rate of
heat rejected to the hot side can be written as:
QH = QC + IV. (4)
It can be interpreted that the heat can be pumped from the cold
side to the hot side by the electrical drive of the thermoelectric
module. The parametric values of the material properties in the
mathematical models can be determined experimentally with
elaborated details in Section 4.
In this work, the heat-flow detection is proposed by making
use of the thermoelectric effects of the thermoelectric modules.
As illustrated in Fig. 4, without supplying the electrical power,
the circuit of the thermoelectric module is opened (I = 0)
instead. While the amount of the heat, which is to be detected,
transfers to the thermoelectric module instead, it is observed
that the voltage measured across the thermoelectric module is
proportionally varied according to the amount of heat transfered
through the thermoelectric module. In this paper, it is called inflow
heat detection, where the temperature of the detected media is
higher than the thermoelectric module, whereas it is called outflow
heat detection, where the temperature of the detected media is
lower than the thermoelectric module. Without loss of generality,
the inflow heat detection, for which the hot side is facing in this
case, is considered in analytical study while the outflow heat
detection, for which the cold side is facing, can be regarded as a
similar process where the direction of the heat flow is opposite to
the direction of the heat flow through the thermoelectric module
in Fig. 4. Now, let us consider a schematic diagram of the inflow
heat detection presented in Fig. 4.
Since the thermal–electrical circuit is opened so as to obtain
the corresponding condition on that there is no electrical current
within the circuit, the heat rejected from the thermoelectric
module and the heat pumped to the thermoelectric module in Eqs.
(2)–(3) can be reduced to:
QH = QC = −k (Th − Tc ) . (5)
The negative sign indicates the direction of the heat flow, which is
now opposite to the direction in the case that the power source is
used to supply the electrical current to the thermoelectric module

3. T. Leephakpreeda / ISA Transactions 51 (2012) 345–350 347
Fig. 3. Schematic diagram of the thermoelectric module and the thermal–electrical circuit.
Fig. 4. Installation during inflow heat detection.
in Fig. 3. To continue the analysis, let us consider the amount of the
heat transfer through the thermoelectric module to be:
Q o
H = Q o
C = k (Th − Tc ) . (6)
By applying the principle of heat balance to the thermal system in
Fig. 4, the dynamics of the temperatures of the hot side and the
cold side as well as the heat sink can be governed by the following
three equations.
ρcV
dTh
dt
= Q − Q o
H (7)
ρcV
dTc
dt
= Q o
C − Qs (8)
ρscsVs
dTs
dt
= Qs − Qa (9)
where Q is the detected heat flow to the thermoelectric module, ρ
is the density of the ceramic substrate, c is the specific heat of the
ceramic substrate, V is the volume of the ceramic substrate, and the
subscript s indicates those properties belonging to the heat sink.
Eqs. (7)–(9) are applied in order to describe each lumped
solid temperature considered in the heat flow direction from the
detected media to the heat sink as shown in Fig. 4, since the heat
transfer area of the thermoelectric module is noticeably larger
than the perimeter area. Explicitly, Eq. (7) represents the rate of
change in the internal energy stored within the hot-side control
volume of the thermoelectric module due to the rates at which
heat transfer enters and leaves the hot-side control volume. The
same consideration is applied for the cold-side control volume and
the heat sink, which are governed by Eqs. (8)–(9), respectively.
However, there are temperature differences across the interfaces
between the cold side of the thermoelectric module and the
heat sink as well as the heat sink and the air. The temperature
differences are attributed to the thermal contact resistance and
the thermal resistance of the natural convection, as expressed in
Eqs. (10)–(11), respectively.
The heat conduction from the cold side of the thermoelectric
module to the heat sink can be expressed as:
Qs =
Tc − Ts
rs
. (10)
The heat convection from the heat sink to the air can be written as:
Qa =
Ts − Ta
ra
(11)
where rs is the thermal contact resistance between the thermoelec-
tric module and the heat sink, ra is the thermal resistance of the
natural convection at the heat sink, Ts is the temperature of heat
sink, and Ta is the temperature of air.
It can be seen from Eqs. (7)–(11) that the temperatures of the
hot side, the cold side, and the heat sink can be changed with
respect to time according to the capability of heat capacity, heat
conduction among the contact materials, and heat convection by
cooling air. In fact, temperatures of the hot side, the cold side and
the heat sink rise up until the heat transfer from the thermoelectric
module to the air is the same as the amount of the heat flow
from the detected media. Without loss of generality, an ideal case
of perfect heat dissipation is considered in such a way that the
heat sink can draw the temperature of the cold side and the
temperature of the heat sink itself to the temperature of air. In
other words, the thermal resistances in Eqs. (10)–(11) are assumed
to be sufficiently small, where the heat sink is designed for efficient
cooling. The temperature at the cold side is to be retained at a

4. 348 T. Leephakpreeda / ISA Transactions 51 (2012) 345–350
Fig. 5. Response of temperature difference after contacting detected media.
Table 1
Parameters of the thermoelectric module and the copper plate.
Parameters Numerical values
Seebeck coefficient β, (V/K) 0.0488
Thermal conductivity k, (W/K) 0.831
Size of alumina substrate V, (cm × cm × cm) 4 × 4 × 0.09
Specific heat of alumina c, (J/g K) 0.88
Density of alumina ρ, (g/cm3
) 3.89
Heat capacitance of copper plate (J/K) 32.725
constant temperature until the steady state is reached. With the
hypothesis (dTc /dt = 0), this yields mathematical manipulations
of Eqs. (6)–(7) to be expressed as Eq. (12).
ρcV
d (Th − Tc )
dt
= Q − k (Th − Tc ) . (12)
Therefore, the analytical solution of Eq. (12) for a given amount of
the heat flow can be obtained by:
Th − Tc =
Q
k

1 − e
−

k
ρcV

t

. (13)
It should be noted that obtaining the analytical solution is to
give insight on how fast the response time of the theoretical
case is to reach the steady-state conditions. In actual cases, the
characteristics of dynamic responses may vary. From Eq. (13), once
the heat flow is detected while the detected media is attached
by the thermoelectric module, the magnitude of the temperature
difference starts increasing with respect to time and then it
reaches steady-state heat conduction with a magnitude of the
ratio of the heat flow to the conductivity coefficient. The dynamic
response time to the heat flow to reach the steady condition is
dependent on the properties of the thermoelectric module, that
is, the density, specific heat, volume of the ceramic plate and the
conductivity coefficient. With property parameters in Table 1 of
materials used in this study, Fig. 5 shows the dynamic response
of the temperature difference of the thermoelectric module after
contacting the detected media. The response time to reach the
steady condition is estimated to be slightly less than 30 s. In fact,
it is sufficiently fast to thermally detecting for general purpose. It
should be noted that the actual response time deviates from these
ideal results based on the dissipative efficiency of the heat sink
as mentioned earlier. It can be noted that the more the amount
of the heat flow, the larger the temperature difference it requires.
Therefore, it is better to maintain the temperature of the heat sink
to be as low as possible to cover the ranges of the amount of the
heat flow to be detected.
Under the opened thermal–electrical circuit (I = 0) at
steady-state condition, the model of Eq. (13) at (t → ∞) can be
substituted to Eq. (1) or the model of Eq. (6) can be substituted to
Eq. (1) in order to yield the relations of the heat flow to the voltage
measured across the thermoelectric module.
Q =
k
β
v. (14)
It can be interpreted form Eq. (14) that the amount of heat that
transfers to a given area of the thermoelectric module causes
proportionally the voltage across the thermoelectric module. The
thermal–electrical relation in Eq. (14) can be applied to determine
the heat flow from the detected media to the thermoelectric
module and vice versa. It should be noted that the inflow heat
detection and the outflow heat detection can be indicated in the
polarity of voltage measurement.
4. Results and discussion
This section is to demonstrate examples of how the proposed
technique of heat flow detection via a thermoelectric module is
applied in practical uses. Initially, a thermoelectric module coupled
with a heat sink, which is commonly available in product market,
is experimentally tested in order to determine its properties for
thermoelectric relation in Eq. (14), that is, the Seebeck coefficient
and the thermal conductivity coefficient. In fact, the details of
parametric determination can be found as follows. Fig. 6 shows the
plots of the measured voltage against the temperature difference
between the temperature at the hot side and the temperature
at the cold side after the circuit of the thermoelectric module
is cut off from the DC source (open circuit or I = 0). It is
observed that the voltage decreases as the temperature difference
reduces. From Eq. (1), the slope of the linear relation in Fig. 6 is
quantified, by the best fitting method, to be the Seebeck coefficient
of 0.0487 V/K, which is listed in Table 1. To determine the thermal
conductivity coefficient, a hot copper plate with the same size
of the thermoelectric module is well insulated at one side and
another side is attached to the thermoelectric module so that all
the internal energy of the copper plate is only transferred to the
thermoelectric module. Therefore, the heat conduction through
the thermoelectric module takes place due to the decrement of the
internal energy within the hot copper plate as expressed in Eq. (6).
Fig. 7 shows plots of the decreasing temperature of the copper plate
against time, which can be used to determine the rate of change in
the temperature of the copper plate. With the heat capacitance of
the copper plate in Table 1, the heat rejected to the thermoelectric
module can be determined and then it is plotted with respect to the
corresponding temperature difference between the temperature at
the hot side and the temperature at the cold side as illustrated in
Fig. 8. The slope of the linear relation in Eq. (6) is quantified to be
the thermal conductivity coefficient of 0.831 W/K, which is listed
in Table 1. To verify the thermoelectric relation with those obtained
parameters in Eq. (14), the plate-type heaters with different power
capacities are prepared as known heat sources. Fig. 9 illustrates
the comparisons of the results between the heat flow determined
from Eq. (14) corresponding to measured voltages, illustrated in
the solid line and the known heat flow from the plate-type heaters
to the thermoelectric module as well as the known heat flow from
the thermoelectric module to the cooled plates, depicted in dotted
marks. It is found that results from the proposed model in Eq. (14)
have good agreement on the actual heat inflow and the actual heat
outflow of the thermoelectric module, where the average value of
the absolute relative differences is 6.7% with a standard deviation
of 2.7% in the testing experiments.
Now, two practical scenarios are demonstrated as real appli-
cations of the thermoelectric module on heat flow detection. The
thermoelectric module is used to measure the heat flux (W/m2
),
which is determined from the heat flow through the thermoelec-
tric module in Eq. (14) per the area of the thermoelectric module

5. T. Leephakpreeda / ISA Transactions 51 (2012) 345–350 349
Table 2
Statistical summaries of absolute relative differences of experimental results and simulated results.
Figure Minimum values (%) Maximum values (%) Average values (%) Standard deviations (%) Numbers of data
6 0.1 14.6 5.4 4.7 13
8 0.2 8.6 4.0 3.1 6
9 0.1 10.5 6.7 2.7 13
11 0.3 11.7 4.8 3.9 18
Fig. 6. Plots of voltage against temperature difference.
Fig. 7. Temperature evolution of copper plate during decrease in internal energy.
Fig. 8. Plots of the heat flow to the thermoelectric module against temperature
difference.
itself (4 cm×4 cm, listed in Table 1). Fig. 10 shows the implementa-
tion of the proposed technique in determining the heat flux passing
Fig. 9. Comparison of simulated results from the model in Eq. (14) with the actual
heat flow.
Fig. 10. Detected heat flux through the building wall during daytime.
through a side of the building wall exposed to sunlight against the
time. It is observed that the amount of heat flux through the wall
increases and decreases corresponding to the time from sunrise to
sunset. It is a fact that the thermoelectric module is used to mea-
sure the amount of the heat transfer through the detected-media
facing area, which is not identical to the amount of the heat transfer
through the wall (without the thermoelectric module). However,
those measurements can be used as proportional indicators of the
heat flow in system design techniques. There are two main factors
causing such differences: 1. changes in boundary conditions due
to attaching the thermoelectric module to the wall and 2. contact-
ing effect on thermal resistance between the detected media and
the thermoelectric module. In turn, the relationship may change
from one scenario to another. Fig. 11 shows variations of thermal
radiation obtained from the thermoelectric module during day-
time when the equipment is exposed to the outdoor atmosphere
as mentioned in Section 2. Results from the proposed technique
yield good agreement with the measured results from a pyranome-
ter, where the average value of the absolute relative differences
is 4.8% with a standard deviation of 3.9%. For Figs. 6, 8, 9 and 11,
the statistical summaries of absolute relative differences between
the experimental results and the simulated results such as min-
imum value, maximum value, average value, standard deviation,
and numbers of data are reported in Table 2.

6. 350 T. Leephakpreeda / ISA Transactions 51 (2012) 345–350
Fig. 11. Detected heat flux within the outdoor environment during daytime.
5. Conclusion
The proposed technique is analytically presented for viability
of simple-to-use and effective application of the low-cost thermo-
electric module on heat flow detection. To implement, the thermo-
electric module is typically coupled with a heat sink and then it is
well attached to the detected media. The heat flow from/to the de-
tected media is observed from both the amount and the polarity of
the voltage across the thermoelectric module. Two practical sce-
narios in heat conduction through the building wall and thermal
radiation within the outdoor environment are demonstrated as
examples of hands-on implementations. Likewise, the identifica-
tion on heat-flow thresholds can be applied to trigger appropriate
action of real-time control.
Acknowledgments
The author sincerely thanks Tanawat Boonpanya for assistance
in experiments. Also, the author appreciates the reviewers’ com-
ments and suggestions for improvement.
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