1 Introduction

Much of the energy generated today is dissipated to the environment, wasting heat from different industrial sectors. The sustained increase in demand for electricity and the environmental impact of current generation systems have required the study of potential methods for more efficient energy production and optimization of existing mechanisms.

Thermoelectric generation technology can directly transform thermal energy into electricity by using thermoelectric transformation materials. A thermoelectric power converter has no moving parts, and is compact, quiet, highly reliable and environmentally friendly [13]. Owing to these advantages, there has been considerable emphasis on the development of small thermoelectric generators for a variety of aerospace and military applications over the past years [4]. More recently, there is a growing interest for waste heat recovery thermoelectric generator, using various heat sources such as combustion of solid wastes, geothermal energy, power plants and other industrial heat-generating processes [21].

Power generation from waste heat streams using thermoelectric materials has been overlooked due to its low thermal efficiencies (\(\sim 4 (\%)\)) [6]. In the case of a waste heat thermoelectric generator (TEG), there have been many conceptual designs of a power conversion system which is potentially capable of being applied in this field [4, 5, 14, 17, 21,22,23, 27, 28]. For waste heat recovery and subsequent conversion into electricity, it has been used prototypes that used clear fluids and thermoelectric devices, present in many daily industrial processes. An experimental TEG prototype, including a counterflow heat exchanger, was studied in [26], revealing the existence of a direct relationship between the output power and the fluid mass flow rate. In this field, using the thermoelectric effect under different operating conditions and manufacturing material for modules, with an installed power of 1 (kW) and 500 (W), it was established that the cost of the TEG is lower than a photovoltaic system, in terms of an equivalent amount of energy generated [19, 20]. These specific advantages make this type of waste heat recovery technology an option that can still be improved in terms of thermoelectric efficiency, which can contribute to the decrease in fossil fuels consumption thus lowering the environmental impact.

Extensive studies on the topic have generated a solid knowledge base for the main characteristics of this type of thermoelectric generators. However, the vast majority of these numerical studies have developed for waste heat extraction systems without considering turbulent transport and the benefits that it could generate.

2 System description

The system under study consists of a portion of a metal square duct with side \({\text {D}}\) and axis segments \({\text {L}}_{\rm L}\), \({\text {L}}_{\rm C}\) and \({\text {L}}_{\rm R}\), within which a waste heat carrier fluid, such as steam or air, flows. This selection of materials is because they are the most commonly transported work fluids alongside with water found in multiple industrial applications. In the present study, we considered, steam and air, due to the higher temperatures that can be found using these working fluids in industrial operations.

In the flow section, the fluid enters with velocity \(\mathbf{u }_{\rm D0}\) and temperature \(T_{\rm f0}\). On the outer mantle, \(N_{\mathrm{TE}}\) thermoelectric devices have been arranged electrically in series and are confined between a ceramic material that isolates them electrically, as shown in Fig. 1. This structural arrangement allows the recovery of residual thermal energy from the fluid, passing this heat to the thermoelements generating an electric potential \(\varDelta \psi\) due to the Seebeck effect.

Fig. 1
figure 1

Reactor scheme with heat recovery system and thermoelectric modules

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The basic thermoelectric unit is formed by a pair of semiconductor materials, type n and p, whom are electrically connected by copper electrodes. The heat transfer rate is controlled by a ceramic material plate since typically the semiconductor has an upper thermal operational limit at \(\approx 400\,(^\circ \text {C})\), see Fig. 2. The present study is an extension of a previous publication by the authors [11, 12] that considered turbulent reactive flow in porous media, recuperative reactor and thermogeneration. In the present work, we considered 2D plane geometry with variations in the type of fluid carrying residual energy, operational variables and heat extraction conditions.

Fig. 2
figure 2

Thermoelectric modules scheme

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3 Mathematical model

The governing equations necessary to describe the turbulent transport of momentum and energy for a clear fluid and the transfer of energy to its enclosing walls include

The ideal gas law

$$\rho _{\rm f} = \frac{p_0}{\bar{R} T_{\rm f} \sum \frac{m_i}{M_i}}$$
(1)

where \(\bar{R}\) is the universal gas constant, p the operating pressure, \(m_i\) and \(M_i\) are the mass fraction and the molecular weight of species i, respectively.

Continuity equation

$$\frac{\partial }{\partial t} \left( \rho _{\rm f} \right) + \nabla \cdot \left( \rho _{\rm f} {\mathbf {u}}_{\mathrm{D}} \right) = 0$$
(2)

where t is time and \({\mathbf {u}}_{\mathrm{D}}\) is the velocity vector.

Fluid phase energy equation

$$\frac{\partial }{\partial t} \left( \rho _{\rm f} c_{p\text {f}} T_{\rm f} \right) + \nabla \cdot \left( \rho _{\rm f} {\mathbf {u}}_{\mathrm{D}} c_{p\text {f}} T_{\rm f} \right) = \nabla \cdot \left( {\mathbf {K}}_{\rm eff,f} \cdot \nabla T_{\rm f} \right)$$
(3)

with, \(c_{p\text {f}}\) is fluid heat capacity, and \({\mathbf {K}}_{\rm eff,f}\) is the effective conductivity tensor for the fluid phase.

Solid phase energy equation

$$\frac{\partial }{\partial t} \left( \rho _{\rm s} c_{p\text {s}} T_{\rm s} \right) = \nabla \cdot \left( {\mathbf {K}}_{\rm eff,s} \cdot \nabla T_{\rm s} \right)$$
(4)

where \(\rho _{\rm s}\) is the density, \(c_{p\text {s}}\) is the heat capacity and \({\mathbf {K}}_{\rm eff,s}\) is the effective conductivity tensor for the solid phase.

Macroscopic turbulent flow momentum equation

$$\frac{\partial }{\partial t} \left( \rho _{\rm f} {\mathbf {u}}_{\mathrm{D}} \right) + \nabla \cdot \left( \rho _{\rm f} {\mathbf {u}}_{\mathrm{D}} {\mathbf {u}}_{\mathrm{D}} \right) = - \nabla p + \nabla \cdot \left( \overline{\overline{ \varvec{\tau }}} \right) + \rho _{\rm f} \mathbf {g}$$
(5)

with \(\overline{\overline{ \varvec{\tau }}}\) the molecular and turbulent stress tensor.

Turbulent kinetic energy and its rate of dissipation equations

$$\frac{\partial }{\partial t} \left( \rho _{\rm f} k \right) + \nabla \cdot \left( \rho _{\rm f} {\mathbf {u}}_{\mathrm{D}} k \right) =\nabla \cdot \left[ \left( \mu + \frac{\mu _{\mathrm{t}} }{\sigma _k} \right) \nabla k \right] + G_k - \rho _{\rm f} \varepsilon$$
(6)
$$\frac{\partial }{\partial t} \left( \rho _{\rm f} \varepsilon \right) + \nabla \cdot \left( \rho _{\rm f} {\mathbf {u}}_{\mathrm{D}} \varepsilon \right) =\nabla \cdot \left[ \left( \mu + \frac{\mu _{\mathrm{t}}}{\sigma _\varepsilon } \right) \nabla \varepsilon \right] + c_{1\varepsilon } \frac{\varepsilon }{k} G_k - c_{2\varepsilon } \rho _{\mathrm{f}} \frac{\varepsilon ^2}{k}$$
(7)

with \(G_k\) represent the turbulent kinetic energy generation due to the mean velocity gradients, \(\mu _{\mathrm{t}}\) is the turbulent viscosity computed as follows

$$\mu _{\mathrm{t}} = c_\mu \rho _{\rm f} \frac{k^2}{\varepsilon }$$
(8)

here \(\sigma _k\), \(\sigma _\varepsilon\), \(c_{\mathrm{1}\varepsilon }\), \(c_{\mathrm{2}\varepsilon }\) and \(c_\mu\) are dimensionless constants.

The boundary conditions considered were

$$\begin{aligned}&x = 0 \nonumber \\&{\text {u}}_{\mathrm{D}} = {\text {u}}_{\rm D0}, \quad T_{\rm f} = T_{\rm 0}, \quad k = k_0, \quad \varepsilon = \varepsilon _0 \end{aligned}$$
(9)
$$\begin{aligned}&x = \text {L} \nonumber \\&\nabla T_{\rm f} = \nabla k = \nabla \varepsilon = 0, \quad \ p = p_L \end{aligned}$$
(10)

at walls no-slip velocity condition was established. The standard wall functions were used for turbulent variables treatment near the wall [1, 30]. In the inlet and outlet domain, the specification method of transported turbulence quantities intensity and viscosity ratio was implemented. On the axis, the boundary conditions include zero normal velocity and zero normal gradients of all variables in the symmetry plane.

The physical properties of air are computed using the following correlations [15].

$$c_{p\text {f}}= 947.0 \ e^{1.83 \times 10^{-4} T_{\rm f} }$$
(11a)
$$\lambda _{\rm f}= 4.82 \times 10^{-7} c_{p\text {f}} T_{\rm f}^{0.7}$$
(11b)
$$\mu _{\rm f}= 3.37 \times 10^{-7} T_{\rm f}^{0.7}$$
(11c)

The physical properties of the steam are calculated using exponential adjustments to the data series in the temperature range 400–600 (K), presented in [29]. The deviation in the prediction of the physical properties is in the order of [0.005–1.5] (%).

$$c_{p\text {f}}= 1780.3 \ e^{2.89 \times 10^{-4} T_{\rm f} }$$
(12a)
$$\lambda _{\rm f}= 1.01 \times 10^{-2} e^{2.39 \times 10^{-3} T_{\rm f} }$$
(12b)
$$\mu _{\rm f}= 5.754 \times 10^{-5} e^{2.15 \times 10^{-3} T_{\rm f} }$$
(12c)

The effective thermal conductivity and diffusivity included molecular and turbulent transport

$$\lambda _{\mathrm{eff,f}}= \lambda _{\rm f} + \frac{c_{p\text {f}} \mu _{\mathrm{t}}}{{\text {Pr}}_{\rm t}}$$
(13)
$$D_{\rm eff,f}= D_{\rm f} + \frac{\mu _{\mathrm{t}}}{\rho _{\rm f} {\text {Sc}}_{\rm t}}$$
(14)

where \(D_{\rm f}\) is the molecular mass transport coefficient, \({\text {Pr}}_{\rm t}\) is the turbulent Prandtl number, and \({\text {Sc}}_{\rm t}\) is the turbulent Schmidt number. The last two latter were taken as constant [1].

The fluid and solid phases effective transport properties tensors are given by

$${\mathbf {D}}_{\rm eff,f}= \left[ D_{\rm eff,f} \right] \mathbf {I}$$
(15a)
$${\mathbf {K}}_{\mathrm{eff,f}}= \left[ \lambda _{\rm eff,f} \right] \mathbf {I}$$
(15b)
$${\mathbf {K}}_{\mathrm{eff,s}}= \left[ \lambda _{\rm eff,s} \right] \mathbf {I}$$
(15c)

It should be noted that for the effective transport properties and their respective tensors, the subscript \(\text {f}\) is modified by the one corresponding to the air or steam, as appropriate.

3.1 Thermoelectric generation

Modeling the thermoelectric generation phenomenon in solids (TEG) is based on the theory of non-equilibrium thermodynamics [7,8,9]. The modeling approach includes the solution of the equations of conservation of energy and conservation of charge in each of the thermoelectric devices and the coupled transport phenomena which gives origin to the Seebeck effect among others. The equations used in this work correspond to the form proposed by Antonova and Looman [3].

The equation of energy for the solid phase is

$$\frac{\partial }{\partial t} \rho \left( \rho _{\rm E} c_{p\text {E}} T_{\rm E} \right) = \nabla \cdot \varvec{q} + \dot{q}$$
(16)

with \(\rho _{\rm E}\) the density, \(c_{p\text {E}}\) the heat capacity, \(T_{\rm E}\) the temperature, \(\varvec{q}\) the total heat flux vector including the Peltier effect and \(\dot{q}\) the heat generation rate due to the Joule effect and work done against the Seebeck electric field.

The continuity of charge is expressed by the following equation

$$\nabla \cdot \left( \varvec{J} + \frac{\partial {\mathbf {D}}}{\partial t} \right) = 0$$
(17)

where \(\varvec{J}\) is the electric current density vector and \({\mathbf {D}}\) is the electric flux density vector.

The constitutive relations and final form of the heat generation term are

$$\varvec{q} =T {\varvec{\alpha }} _{\mathrm{E}} \cdot \varvec{J} - {\mathbf {K}}_{\rm E} \cdot \nabla T$$
(18)
$$\varvec{J} =\varvec{\sigma }_{\mathrm{E}} \cdot \left( {\mathbf {E}} - {\varvec{\alpha }}_{\mathrm{E}} \cdot \nabla T \right)$$
(19)
$${\mathbf {D}} =\varvec{\xi } \cdot {\mathbf {E}}$$
(20)
$${\mathbf {E}} =- \nabla \psi$$
(21)
$$\dot{q} =\varvec{J}^2 / \varvec{\sigma }_{\mathrm{E}}$$
(22)

with \(\varvec{\sigma }_{\mathrm{E}}\) the electric conductivity tensor, \({\varvec{\alpha }}_{\mathrm{E}}\) the Seebeck coefficient tensor, \({\mathbf {K}}_{\rm E}\) the thermal conductivity tensor, \(\varvec{\xi }\) the permittivity tensor and \(\psi\) the voltage.

The governing equations will be expressed in its extended form by combining the energy and charge equations with the constitutive relations, resulting in the expressions 23 and 24 for the conservation of energy and charge, respectively.

$$\frac{\partial }{\partial t} \left( \rho _{\rm E} c_{p\text {E}} T_{\rm E} \right) = \nabla \cdot \left[ \left( \varvec{\sigma }_{\mathrm{E}} \cdot {\varvec{\alpha }}_{\mathrm{E}}^2 T_{\rm E} + {\mathbf {K}}_{\rm E} \right) \cdot \nabla T_{\rm E} \right] + \varvec{\sigma }_{\mathrm{E}} \cdot \left[ \left( \nabla \psi \right) ^2 + 2{\varvec{\alpha }}_{\mathrm{E}} \cdot \nabla T_{\mathrm{E}} \cdot \nabla \psi + \left( {\varvec{\alpha }}_{\mathrm{E}} \cdot \nabla T_{\mathrm{E}} \right) ^2 \right] + \nabla \cdot \left( \varvec{\sigma }_{\mathrm{E}} \cdot {\varvec{\alpha }}_{\mathrm{E}} T_{\rm E} \cdot \nabla \psi \right)$$
(23)
$$\nabla \cdot \left( \varvec{\xi } \cdot \nabla \frac{\partial \psi }{\partial t} \right) + \nabla \cdot \left( \varvec{\sigma }_{\rm E} \cdot {\varvec{\alpha }}_{\rm E} \cdot \nabla T_{\rm E} \right) + \nabla \cdot \left( \varvec{\sigma }_{\rm E} \cdot \nabla \psi \right) = 0$$
(24)

In Fig. 3, thermoelectric elements connected electrically in series are shown. Thermoelectric elements are essentially devices operating between reservoirs of high temperature and a low temperature, where \(Q_H\) and \(Q_C\) represent their respective heat flows.

Fig. 3
figure 3

Scheme Nn thermocouples electrically connected in series [10]

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Using the relation given by the extended Ohm’s Law [16], the electric current intensity can be determined from the following equation

$$I = \frac{ {\varvec{\alpha }}_p \cdot \sum _{i=1}^{Nn} \varDelta T_{p,i} - {\varvec{\alpha }}_n \cdot \sum _{i=1}^{Nn} \varDelta T_{n,i} }{\left( 1 + R_{e,o}^ * \right) \sum _{i=1}^{Nn} R_{e,i} }$$
(25)

where \(\varDelta T_p\) and \(\varDelta T_n\) are temperature differences in the semiconductor p and n, respectively. \(R_{e,i}\) is the internal electrical resistance, and \(R_{e,o}^*\) is the internal to external electrical resistance ratio. For a maximum power output, \(R_{e,o}^* = 1\) must be set [24].

The overall efficiency of the process is defined as the generated electric power over the fluid enthalpy change times the mass flow rate

$$\eta =\frac{{\text {P}}}{\dot{m} \left( H_0 - H_L \right) } = \frac{I ^2 \left( \sum _{i=1}^{Nn} R_{e,i} + R_{e,o} \right) }{ {\text {D}}^2 \ \mathbf{u }_{\rm D0} \rho _{\rm f0} \left( H_0 - H_L \right) }$$
(26)
$$\eta =\frac{I ^2 N_n R_{e,i}(1 + R_{e,o} ^*)}{ {\text {D}}^2 \ \mathbf{u }_{\rm D0} \ \rho _{\rm f0} \ \overline{c}_{p\text {f}} \ \varDelta T_{\rm f}}$$
(27)

with \(R_{e,o}\) external electrical resistance, H fluid specific enthalpy.

4 Numerical method

The standard FLUENT interface does not cover all the modeling needs of the user. Complementary, the software provides two extensions for modeling purposes in the form of user-defined functions (UDF) and user-defined scalars (UDS). The former allows for customization of boundary conditions, source terms, reaction rates, physical properties, among others, while the latter can be used to solve generic transport equations for arbitrary scalars \(\varphi\) in the form [2]

$$\frac{\partial }{\partial t} \left( \rho \varphi \right) + \nabla \cdot \left( \rho {\mathbf {u}}_{\mathrm{D}} \varphi - \varvec{\varGamma } \cdot \nabla \varphi \right) = S$$
(28)

where \(\varvec{\varGamma }\) and S are the diffusion tensor and the source term, respectively, which must be defined for each scalar equation.

We implement the equations set for estimation of physical properties, Eqs. 11 – 12 and the voltage related source terms in Eq. 23, in the form of UDFs. The conservation of electric charge, Eq. 24, was incorporated into the FLUENT solver through the use of UDS.

The system of differential equations was discretized with the finite volume method with upwind scheme for convective terms, and pressure–velocity coupling is solved using the SIMPLE algorithm for incompressible fluid [1, 25].

Thermoelectric model validation was conducted replicating the results of Jaegle [18] and were presented by the authors in a previous publication [12].

The model was solved using axial symmetry, and, based on the complexity of the phenomena to be modeled, differential meshing was performed by region. The input channel was discretized with a size equal to \(2\times 10^{-3}\) (m), whereas element sizes were \(5.0 \times 10^{-4}\) (m) in the thermoelectric region. A good compromise between accuracy and computation time was found with the grid size of \(\sim\) 80.000 elements.

All simulations were based on the standard parameters presented in Table 1.

Table 1 Standard case values
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5 Results and discussion

The fluid flows through the interior of the duct and yields sensible heat to the thermoelectric devices attached to the mantle only in the solid–fluid interface. Due to the Seebeck effect, an electric potential is generated and the fraction of heat not converted into electricity is rejected to the surroundings. Two heat transfer coefficients were used to analyze their influence on heat conversion to electricity, h and \(h' = 100 h\). Different values of inlet velocity \(\mathbf{u }_{\rm D0} = [1, 2, 3]\) (m/s) and incoming fluid temperature \(T_{\rm f0} = [400, 450, 500, 550, 600]\) (K) were used to study the residual heat recovery. Normalized values of electric potential, efficiency and power will be presented in the form

$$\eta _{norm} =\frac{\eta - \eta _{\min }}{\eta _{\max } - \eta _{\min }}$$
(29)
$$\varDelta \psi _{norm} =\frac{\varDelta \psi - \varDelta \psi _{\min }}{\varDelta \psi _{\max } - \varDelta \psi _{\min }}$$
(30)
$${\text {P}} _{norm} =\frac{{\text {P}} - {\text {P}} _{\min }}{{\text {P}} _{\max } - {\text {P}} _{\min }}$$
(31)

where the min and max subindexes refer to the minimum and maximum values for the complete set of results.

Figures 4 and 5 show the variation of electric potential as function of the operational variables (\(\mathbf{u }_{\rm D0}\), \(T_{\rm f0}\)) and the different conditions of heat extraction \((h, h')\), for air and steam, respectively.

Fig. 4
figure 4

Voltage obtained for air

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Fig. 5
figure 5

Voltage obtained for steam

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The electric potential is determined by solving the coupled equations of electric charge conservation and thermal energy balance within the thermoelectric elements domain, see Sect. 3.1. At one end of the electrical circuit, it is imposed ground voltage condition, while at the other end, it is imposed an estimation of the electric current by Eq. 25. Under the initial heat extraction conditions, it was found that the values of \(\varDelta \psi\) increase with the fluid thermal load, reaching values within [34.11–105.02] (mV) and [33.93–104.38] (mV) for air and steam, respectively. The electric potential values obtained are of similar magnitude due to the similar thermal conductivity values of both fluids within the temperature range studied. The similarity in the values of this transport property generates equivalent heat transfer rates at the fluid–solid interface, which cause a homogeneous temperature distribution in the thermoelectric devices, as shown in Fig. 6. This temperature distribution between the ends of the thermoelements results in a generation of an electric potential due to the Seebeck effect which can be seen from Fig. 7. Considering the heat transfer coefficient \(h'\), the new values of \(\varDelta \psi '\) are within [164.25–510.28] (mV) and [159.52–488.87] (mV) for air and steam, respectively. The increase in these values lies within the range of [4.68–4.85] times the determined values when the heat transfer coefficient was h. From these results, it can be stated that the thermoelectric generation under the system considered for study is favored with the increase in the working fluid thermal load, being further accentuated with the increase in the heat extraction rate at the ceramic material upper boundary.

Fig. 6
figure 6

Temperature contours in (K) obtained for \(\mathbf{u }_{\rm D0} = 1\) (m/s) and \(T_{\rm f0} = 400\) (K) with steam as waste heat carrier fluid

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Fig. 7
figure 7

Voltage contours \(\varDelta \psi '\) in (mV) obtained for \(\mathbf{u }_{\rm D0} = 3\) (m/s) and \(T_{\rm f0} = 600\) (K) with steam as waste heat carrier fluid

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Overall efficiency is directly proportional to the product of the square of the electrical current and the electrical resistance and inversely proportional to the energy delivered by the waste heat carrier fluid, as expressed in Eq. 27. The efficiency values increase with the fluid temperature, together with a thermal resistance decrease for the energy flow to the environment, because higher thermal gradients favor thermogeneration and conversion efficiency, as shown in Figs. 8 and 9. For the initial conditions of heat extraction, it was found that the values of \(\eta\) are within [0.25–5.12] (%) and [0.11–4.28] (%) for air and steam, respectively, while with the heat transfer coefficient \(h'\), values of \(\eta '\) fall within [1.55–9.22] (%) and [1.22–7.68] (%), for air and steam, respectively. It is noted that the overall efficiency values decrease with the increase in the fluid thermal load. With reference to Eq. 27, the electric current increase is not proportional to the energy input increase. Consequently, the overall energy efficiency decreases with higher thermal loads of the residual energy carrier fluid. Under equivalent operating conditions, the efficiency was higher when air was used as the carrier fluid. This response is due to the specific heat values computed from Eqs. 11 and 12. Using the average temperature of each fluid, for the set of cases studied, it was found that the value of the specific heat of the steam doubles the air one, thus promoting lower values of global efficiency. Temperature drop values were found in the range [0.31–15.75] (K) and [0.13–15.14] (K), for air and steam, respectively, with the higher values obtained with the decrease in the heat resistance and the gas velocity.

Fig. 8
figure 8

Overall efficiency values for air

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Fig. 9
figure 9

Overall efficiency values for steam

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Power was calculated from the product between the square of the current intensity and the total electrical resistance of thermogenerator system. Figures 10 and 11 present the total power obtained from the computational predictions. The values of \({\text {P}}\) under the initial conditions of heat extraction increase slightly as the thermal load of the fluids also increases, reaching values of [0.03–0.31] (W) and [0.03–0.30] (W) for air and steam, respectively, while, when the heat extraction conditions were modified the \({\text {P}}'\) values reached [0.74–7.16] (W) and [0.70–6.57] (W). The increase in these values is within the range of [14.2–29.6] times the values determined when the coefficient implemented was h. The calculated values of \({\text {P}}\) and \({\text {P}}'\) are consistent with the evolution of \(\varDelta \psi\) presented in Figs. 4 and 5, since Ohm’s Law establishes a direct proportionality of the power with the square of the voltage, which is reflected in the high peak of \({\text {P}}'\) with the increase of \(\varDelta \psi\).

Fig. 10
figure 10

Power obtained for air

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Fig. 11
figure 11

Power obtained for steam

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6 Conclusions

A numerical study on waste heat recovery system and energy conversion by thermoelectric generator was performed.

Under the range of variables tested, the highest values of electrical potential were reached when the thermal load of the working fluids was increased. It was observed that lower heat transfer resistance values to the environment produce higher temperature gradients in the thermoelectric devices and consequently increase the electrical potential due to the Seebeck effect.

The overall efficiency increased with the inlet temperature of the fluids and decreased with their thermal load. The highest efficiency values were reached when the thermal resistance was decreased and the residual energy carrier fluid was air. This was due to the fact that the value of the specific heat of the gas was approximately half of the value of the same intensive property of the steam within the operational conditions considered.

As presented, the external coupling of the TEG system is an alternative method for residual energy harvesting without the need of complex internal structures which may cause perturbations in the flow field. In operational terms, the temperature drop generated by the heat extraction is not enough to generate steam or air condensation up to a \(\approx 80\) (%) of relative humidity.