# Thermal modeling and parametric study of TEG power generation from the exhaust gas of boilers and cold oil tank

Ali Shaito, Hicham El Hage, Jalal Faraj, Khaled Chahine, Mehdi Mortazavi,
Thierry Lemenand, Mahmoud Khaled

► To cite this version:

Ali Shaito, Hicham El Hage, Jalal Faraj, Khaled Chahine, Mehdi Mortazavi, et al.. Thermal modeling and parametric study of TEG power generation from the exhaust gas of boilers and cold oil tank. The International Conference on Technologies and Materials for Renewable Energy, Environment and Sustainability TMREES23, May 2023, Metz, France. pp.51-58, 10.1016/j.egyr.2023.05.248. hal-05437341

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https://univ-angers.hal.science/hal-05437341v1

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TMREES23-Fr, EURACA 06–08 February 2023, Metz-Grand Est, France

# Thermal modeling and parametric study of TEG power generation from the exhaust gas of boilers and cold oil tank

Ali Shaito<sup>a</sup>, Hicham El Hage<sup>a</sup>, Jalal Faraj<sup>a,b</sup>, Mehdi Mortazavi<sup>c</sup>, Thierry Lemenand<sup>d</sup>, Mahmoud Khaled<sup>a,e,*</sup>

<sup>a</sup> Energy and Thermo-Fluid Group, Lebanese International University LIU, Bekaa, Lebanon

<sup>b</sup> Energy and Thermo-Fluid Group, The International University of Beirut BIU, Beirut, Lebanon

<sup>c</sup> Department of Mechanical and Materials Engineering, Worcester Polytechnic Institute, 100 Institute Rd, Worcester, MA 01609, USA

<sup>d</sup> LARIS EA 7315, University of Angers, Polytech Angers, Angers, France

<sup>e</sup> Center for Sustainable Energy and Economic Development (SEED), Gulf University for Science and Technology, Kuwait

Received 17 May 2023; accepted 27 May 2023

Available online 7 June 2023

## Abstract

A new concept of power generation from thermoelectric generators TEGs using the hot exhaust gas of boilers and a cold oil tank is proposed. The suggested concept consists of a flow of exhaust gas of boilers and cold oil in a tank separated by a plate comprising several TEGs in series. The oil tank at the bottom of the system constitutes the cold convection condition for the TEG plate and the upper hot exhaust gas flow constitutes the hot convection condition. Accordingly, a temperature gradient is created across the thickness of the TEGs, which play the role of a separation plate, and converted to an electrical power. To justify the feasibility of this new concept, a suitable thermal modeling is developed and the associated parametric analysis is carried out. The parametric analysis reveals that powers up to 622 W can be generated with a system having a space heating load of 200 kW, an exhaust gas duct height of 0.05 m, and a TEG plate length of 1 m. The temperature difference across each TEG module decreases exponentially when the TEGs plate length increases and decreases exponentially when the exhaust gas duct height increases.

© 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Peer-review under responsibility of the scientific committee of the TMREES23-Fr, EURACA, 2023.

**Keywords:** New concept; Power generation; Thermoelectric generator; Space heating load; Oil tank; Thermal modeling

## 1. Introduction

The need of energy for daily operations in industry, transportation, communication, healthcare, and many other sectors is indispensable. Consequently, many researchers turned their attention to enhance the use of green energy and energy management [1–8]. Moreover, governments, in the developed countries, have been directing the energy research community to concentrate on finding scientific solutions to the reduction of energy consumption

<footnote>* Corresponding author at: Energy and Thermo-Fluid Group, Lebanese International University LIU, Bekaa, Lebanon. E-mail address: mahmoud.khaled@liu.edu.lb (M. Khaled).</footnote>
and carbon emissions [9–11]. This cannot be accomplished without performing extensive research in renewable energy and energy management [12,13]. Energy management reflects the global need to save energy and cut the operational costs by planning energy saving measures, monitoring energy utilization, and controlling and conserving energy. Since large amounts of heat are released from engineering systems as constrained by the second law of thermodynamics, recovery of waste heat and its conversion into new forms of energy have become an integral factor in the realm of energy management [14–17]. One widespread means to recover heat is by thermoelectric generators. The thermoelectric technology has been implemented for various sources such as internal combustion engines [18–21], stoves [22–24], vehicles [25–28], biomass gasifier [29], chimneys [30], diesel engines [31–34] and fuel cells [35]. Although thermoelectric generators have low conversion efficiency, they serve as simple and rapid means to recover heat by generating electricity wherever a gradient of temperature is present or can be created [36,37]. As a result, thermoelectric generators present an excellent addition to hybrid heat recovery systems since they can be coupled with any heat recovery heat exchanger wherever a gradient of temperature is possible [38–41]. However, comprehensive research about TEG reveals that challenges, encountered during physical applications, lie in creating significant temperature differences [42,43]. In this context and to increase the temperature difference while using TEGs, the present work proposes a new concept of power generation using the hot exhaust gas of boilers and a cold oil tank. The originality of the proposed concept resides mainly in finding new applications/configurations in engineering applications where one can generate significant temperature gradient and then electrical power using TEGs. The proposed design employs a flat plate composed of several TEG modules in series having at its upper surface a flow of hot exhaust gas of a boiler and at its bottom surface a cold oil tank. Therefore, the upper surface of each TEG module is heated by the hot exhaust gas flow, whereas the lower surface is cooled by the cold oil. Consequently, a temperature gradient is created and an electrical power is generated. To validate the aforementioned new concept, thermal modeling of the proposed design is developed to predict the power generation performance as a function of the space heating load of the conditioned space, the thickness and conductivity of each TEG module, the exhaust gas duct height, and the TEGs plate length.

The rest of the paper is organized as follows. Section 2 describes the concept of the new system and labels its different components. Section 3 details the thermal modeling and governing equations of the proposed TEG power generation system. The analysis of the obtained results is presented in Section 4. Finally, conclusions of this work are drawn in Section 5.

## 2. New suggested concept

One of the optimum configurations of thermoelectric generators when exposed to heat flux, temperature, and convection boundary conditions was found when exposing the TEG to convection at upper and lower sides simultaneously [42,43]. In other words, exposing the upper side to hot convection while exposing the lower side to cold convection [42,43]. Therefore, the current study suggests an original system of power generation using thermoelectric generators subjected to convection conditions generated deliberately on both sides. In the new suggested concept shown in Fig. 1, the TEGs lower sides are placed in series on a cold oil tank while their upper sides are exposed to boilers hot exhaust gas. This implies that the oil tank, at the bottom of the system, constitutes the cold convection condition for the TEGs plate, whereas the upper hot exhaust gas flow constitutes the hot convection condition. Accordingly, a temperature gradient is generated and converted to electrical power.

## 3. Thermal modeling and calculations

The thermal modeling is depicted in Fig. 2 where each TEG is assumed to be a plane wall subjected to convection conditions on both sides, with hot convection taking place on the upper side and cold convection on the lower side. The TEGs are placed next to each other on the same plane where their total area is referred to as the TEG plate hereafter.

In Fig. 2, $T_{\infty c}$ is the temperature of the oil in the cold oil tank, $T_{\infty h}$ is the temperature of the exhaust gas exiting the boiler, $h_c$ is the convective heat transfer coefficient of the cold oil, $h_h$ is the convective heat transfer coefficient of the exhaust gas, and finally $t$ and $k$ are the thickness and thermal conductivity of each TEG module, respectively.

The heat diffusion equation is employed to firstly calculate the temperature distribution and then deduce the temperature difference. As previously mentioned, the TEG plate is considered as a plane wall and assuming steady state and no heat generation conditions, the heat diffusion equation reduces to the following form [44]:

$$ \frac{d^2 T}{dx^2} = 0 \qquad (1) $$
<figure><img src="image_3.png" /><figcaption>Fig. 1. Schematic of the proposed system of power generation.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 2. Thermal representation of the TEG plate situation.</figcaption></figure>

Then, applying following boundary conditions [44]:

$$-k \frac{dT}{dx} \Big|_{x=0} = h_c (T_{\infty c} - T(0)) \qquad (2)$$

$$-k \frac{dT}{dx} \Big|_{x=t} = h_h (T(t) - T_{\infty h}) \qquad (3)$$

the temperature distribution and temperature gradient across the TEGs can be obtained as follows:

$$T(x) = \frac{h_c h_h (T_{\infty h} - T_{\infty c})}{k (h_c + h_h) + h_c h_h t} x + T_{\infty c} + \frac{kh_h (T_{\infty h} - T_{\infty c})}{k (h_c + h_h) + h_c h_h t} \qquad (4)$$

$$\Delta T = \frac{h_c h_h (T_{\infty h} - T_{\infty c})}{k (h_c + h_h) + h_c h_h t} t \qquad (5)$$

In Eq. (5), $h_c$ is obtained from heat transfer references for oil in natural convection [44] and $T_{\infty c}$ value is set. $t$ and $k$ are taken as input to the calculations in the intended parametric study. However, $T_{\infty h}$ and $h_h$ depend on the operational parameters of the boiler. To proceed, the gas flow rate, $\dot{m}_g$, and exhaust gas temperature, $T_{\infty h}$, should be calculated using energy balances on the boiler operational mode side. The efficiency of a boiler is defined as the ratio of the space heating load provided to the space $\dot{Q}_{heating}$ (and calculated in HVAC designs) and the heat of combustion $\dot{Q}_{combustion}$ [45]:

$$\eta_b = \frac{\dot{Q}_{heating}}{\dot{Q}_{combustion}} \qquad (6)$$
The difference between the heating load $\dot{Q}_{heating}$ and $\dot{Q}_{combustion}$ is lost in the exhaust gases and then the energy rate contained in the exhaust gases is:

$$ \dot{Q}_{ex} = \dot{Q}_{combustion} - \dot{Q}_{heating} \qquad (7) $$

Combining equations (6) and (7) yields:

$$ \dot{Q}_{ex} = \left( \frac{1 - \eta_b}{\eta_b} \right) \dot{Q}_{heating} \qquad (8) $$

At the same time, the energy rate of the exhaust gases can be written as:

$$ \dot{Q}_{ex} = \dot{m}_g C_{p,g} (T_{\infty h} - T_{amb}) \qquad (9) $$

where $T_{amb}$ is the ambient temperature.

The fuel (diesel) flow rate averaged per day can be calculated from [45]:

$$ \dot{m}_f = \frac{\dot{Q}_{combustion}}{q_c} = \frac{\dot{Q}_{heating}}{\eta_b q_c} \qquad (10) $$

where $q_c$ is the heat of combustion of the fuel (diesel).

Noting $A_{af}$ the air to fuel ratio, the gas mass flow rate can be written as [45]:

$$ \dot{m}_g = (A_{af} + 1) \dot{m}_f = \frac{(A_{af} + 1) \dot{Q}_{heating}}{\eta_b q_c} \qquad (11) $$

Combining equations (8), (9), and (11), one can write for the exhaust gas temperature:

$$ T_{\infty h} = T_{amb} + \frac{(1 - \eta_b) q_c}{(A_{af} + 1) C_{p,g}} \qquad (12) $$

Knowing the mass flow rate of exhaust gas, the convective heat transfer $h_h$ can be calculated using standard heat transfer correlations that can be found in [44]. Considering now the exhaust gas flow below the TEG plate, the infinite flow velocity is calculated as follows:

$$ u_{\infty} = \frac{4\dot{m}_g}{\rho\pi D_h^2} \qquad (13) $$

where $\rho$ is the density of the exhaust gas and $D_h$ is the hydraulic diameter calculated from the relation below:

$$ D_h = \frac{4S}{P} = \frac{2HL}{H + L} \qquad (14) $$

Then, the Reynolds number at the edge of the upper plate is estimated as follows:

$$ \text{Re}_L = \frac{\rho u_{\infty} L}{\mu} = \frac{4 \dot{m}_g L}{\pi D_h^2 \mu} \qquad (15) $$

where $\mu$ is the dynamic viscosity of the exhaust gas. Furthermore, to estimate the heat transfer coefficient of exhaust gas on the upper surface of the TEG plate, $h_h$, the flow regime should be checked: (i) the flow is considered as a laminar for $\text{Re}_L$ lower than $5 \times 10^5$ (ii) the flow is mixed (laminar then turbulent) in case of $\text{Re}_L$ is greater than $5 \times 10^5$. Table 1 shows the correlation that can be used to estimate the Nusselt number and then the convective heat transfer coefficient [44].

<table><caption>**Table 1.** Heat transfer correlations for the Nusselt Number of the exhaust gas flow [44].</caption><thead><tr><th>Flow nature</th><th>Correlation</th><th></th></tr></thead><tbody><tr><td>Laminar flow</td><td>$Nu_h = \frac{h_h L}{k} = 0.664Re_L^{0.5} Pr^{1/3}$</td><td>(16)</td></tr><tr><td>Mixed flow</td><td>$Nu_h = \frac{h_h L}{k} = (0.037Re_L^{4/5} - 871.32) Pr^{1/3}$</td><td>(17)</td></tr></tbody></table>

In Table 1, $Nu_h$ represents the Nusselt number of the exhaust gas flow, $k$ is the thermal conductivity, and $Pr$ is the Prandtl number.
The effects of space heating load and thickness to the thermal conductivity of each TEG are investigated by adopting a first set of calculations performed by fixing the height of exhaust gas duct *H* at 0.05 m, the length and width of the plate composed of TEGs at 0.4 m, the cold oil temperature, *T*<sub>∞c</sub>, at 10 °C, and the ambient temperature, *T*<sub>amb</sub> at 5 °C.

To perform the aforementioned parametric study, the cold oil convective heat transfer coefficient is set to 200 W m⁻² K⁻¹ [44]. Twenty-five calculations corresponding to similar number of configurations of space heating load and ratio of TEG thickness over TEG thermal conductivity are performed. Five space heating loads of 50, 100, 150, 200, and 250 kW and five ratios *t/k* of 0.002, 0.004, 0.006, 0.008, and 0.01 are considered. Previous literature [46,47] revealed that the ratio *t/k* varies between 0.002 and 0.005. The higher ratios of *t/k* are taken as a parametric testing for potential suggestion of new ratios for temperature gradient enhancement and consequently power production enhancement should *t/k* future production be feasible. The conversion temperature difference – power of the TEG obtained in [46] is considered.

To investigate the effects of the exhaust gas height and TEGs plate length, a second set of calculations is performed by fixing the space heating load at 200 kW, the cold oil temperature at 10 °C, and the ambient temperature *T*<sub>amb</sub> at 5 °C. The cold oil convective heat transfer coefficient is set equal to 200 W m⁻² K⁻¹ [44]. The optimum ratio *t/k* of 0.01 is considered. Likewise, twenty-five calculations corresponding to a similar number of configurations of exhaust gas height and TEGs plate length are performed by considering the width equal to the length of the TEGs plate. Five heights of exhaust gas duct *H* of 0.05, 0.1, 0.15, 0.2, and 0.25 m and five lengths of the TEGs plate *L* of 0.2, 0.4, 0.6, 0.8, and 1 m are considered.

## 4. Results and analysis

Fig. 3a depicts the variation of the temperature difference across each TEG module. Fig. 3b portrays the total power (sum of power generated by each TEG), obtained by the generator of the proposed design, as a function of the space heating load for different *t/k* ratios.

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Variation of (a) temperature difference across each TEG module and (b) power generated by the assembly of TEG modules as function of the heating load for different ratio of thickness and thermal conductivity of each TEG.</figcaption></figure>

As clearly revealed in Fig. 3, the temperature difference across each TEG module and the associated power generated by the assembly of TEGs increases linearly when simultaneously both the space heating load and the ratio *t/k* increases. As illustration for a ratio *t/k* of 0.002, when the space heating load increases from 50 to 250 kW, the temperature difference across each TEG module increases from 13.8 to 27.6 °C and the associated power generated by the assembly increases from 6.9 to 13.8 W (43.1 to 86.3 W m⁻²). Additional illustration for a ratio *t/k* of 0.01 along with space heating load increase from 50 to 250 kW, the temperature difference across each TEG module varies from 62.3 to 114.1 °C and the associated power generated by the assembly varies from 77.9 to 213.8 W (from 486.9 to 1336.3 W m⁻²). As a conclusion, as the ratio *t/k* increases in addition to increasing the
space heating load, the increase in temperature difference and power is more considerable. As a final illustration for a space heating load of 250 kW, when the ratio *t*/*k* increases from 0.002 to 0.01, the temperature difference increases from 27.6 to 114.1 °C, and the power generated increases from 13.8 to 213.8 W (from 86.3 to 1336.3 W m⁻²).

Considering the TEG length (*L*) and exhaust gas duct height (*H*) as parameters, Fig. 4 displays the variation of the temperature difference across each TEG module in addition to the total power obtained by the suggested generator as a function of the TEGs plate length for different exhaust gas duct height.

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Variation of (a) temperature difference across each TEG module and (b) power generated by the assembly of TEG modules in function of the TEGs plate length for different exhaust gas duct height.</figcaption></figure>

Fig. 4a reveals that when the TEGs plate length increases, the temperature difference across each TEG module decreases exponentially. Likewise, when the exhaust gas duct height increases, the temperature difference decreases exponentially as well. As illustration for an exhaust gas duct height of 0.05 m, when the TEGs plate length increases from 0.2 to 1.0 m, the temperature difference across each TEG module decreases from 141.6 to 71.2 °C. For an exhaust gas duct height of 0.25 m, when the TEGs plate length increases from 0.2 to 1 m, the temperature difference across each TEG module decreases from 68.8 to 20.1 °C. As evidenced by equations 16 and 17, when the length of the flow bed increases, the Reynolds number increases and consequently the Nusselt number increases as well. However, the associated average convective heat transfer coefficient decreases. Similarly, as Eqs. (14) and (15) reveal, when the exhaust height increases, the hydraulic diameter increases, and thus the Reynolds number for the same mass flow rate of exhaust gas decreases. Consequently, the average convective heat transfer coefficient decreases. This results in a decrease in the temperature difference across each TEG module.

As revealed in Fig. 4b, the power generated by the assembly of TEGs increases linearly when the TEGs plate length increases and decreases exponentially when the exhaust gas duct height increases. As illustration for an exhaust gas duct height of 0.05 m, when the TEGs plate length increases from 0.2 to 1.0 m, the power increases from 74.2 to 621.6 W (the power per unit area decreases from 1855 to 621.6 W m⁻²). For a TEG plate length of 0.2 m, when the exhaust gas duct height increases from 0.05 to 0.25 m, the power decreases exponentially from 74.2 to 23.4 W (from 1855 to 585 W m⁻²). Also, when the TEG plate length increases, the temperature difference across each TEG module decreases since the average convective coefficient of exhaust gas decreases. Simultaneously, the number of TEG modules increases when the TEGs plate length increases. The increase in the number of TEGs dominates the decrease of the temperature difference decrease to result finally in a linear increase in the power variation when the TEGs plate length increases.

**5. Conclusions**

In this paper, a new concept of power generation from TEGs using the hot exhaust gas of boilers and a cold oil tank is proposed. To validate the feasibility of the proposed concept, a proper thermal modeling is developed and associated parametric analysis is performed. The parametric analysis reveals the following conclusions:
1. The temperature difference across each TEG module and the associated power generated by the assembly of TEGs increase linearly when both the space heating load and ratio of the thickness to the thermal conductivity of each TEG increase.

2. The temperature difference across each TEG module decreases exponentially when the TEGs plate length increases and decreases exponentially when the exhaust gas duct height increases.

3. The power generated by the assembly of TEGs increases linearly when the TEGs plate length increases and decreases exponentially when the exhaust gas duct height increases.

As practical recommendations, one should find ways to increase the temperature difference between the exhaust gas and the cold oil in the tank but more importantly the convective heat transfer coefficients in both gas and oil sides should be augmented. For example, one can use vortex generators/fins in the exhaust gas flow side and in the cold oil tank.

Finally, one of the most important future work is to design and implement an experimental setup that permits to test experimentally, in a parametric way, the feasibility of the system and suggest optimum configurations.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

The authors are unable or have chosen not to specify which data has been used.

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[47] https://thermoelectric-generator.com/wp-content/uploads/2014/04/SpecTEG1-12611-6.0Thermoelectric-generator1.pdf.