Sensitivity Factors of Thermally Regenerative Electrochemical Cycle Systems Using Fuel Cell’s Waste Heat

Abstract

Recovering waste heat is widely seen as an effective way to improve energy efficiency. Because of its potential to lower both energy costs and greenhouse gas emissions, it has been used for many years in industries with high energy demand. While several technologies are already available for this purpose, most of them require relatively high temperatures to achieve high performance. One approach that can make use of lower temperature heat sources is the thermally regenerative electrochemical cycle (TREC). Systems based on this principle can be a cost-effective option for capturing heat from sources such as fuel cells, although their efficiency depends on several factors. This study applies parameter sensitivity analysis to support more efficient system design. The results show that chemical properties, especially the thermal coefficients of redox pairs, have the strongest effect on performance. Geometric aspects, particularly the size of the active membrane area, also play an important role.

1. Introduction

Recovering waste heat is often one of the most effective energy-saving measures that can be implemented, and due to the substantial cost reductions it offers, it has long been a common practice in more energy-intensive industries [1]. Many forms of utilization of waste heat are widespread, but many of them can operate effectively above a certain limit temperature [1,2]. Low-grade heat sources (under 100 °C) account for over half of global energy waste. Consequently, reusing low-grade waste heat can enhance efficiency and lower CO₂ emissions [3].

One of the simplest and most widely used methods for heat recovery in industry is the use of heat exchangers. Their popularity stems mainly from their simple design and structural flexibility, which allows for easy integration and scaling in existing systems. A common limitation is the need for a low-temperature medium, meaning that in many cases, this is not classic waste heat utilization, but rather the relocation of released heat to another location.

Another common technology is the heat pump, which can overcome negative temperature gradients and efficiently extract heat from low or ultra-low temperature (>40 °C) sources [4]. However, it shares similar drawbacks with heat exchanger systems.

These limitations are partially addressed by the ORC (Organic Rankine Cycle), which converts waste heat into electrical energy. In this technology, a working fluid with a lower boiling point than water is typically used in a steam turbine cycle. For efficient operation, ORCs require a stable heat source of at least 80–90 °C [5], and they also have significant space requirements and high thermal inertia, which limits their suitability for mobile applications.

Unlike ORC systems, the spatial footprint of TEG (Thermoelectric Generator) modules is notably smaller, thanks to their semiconductor materials, which enable low thermal inertia [6,7]—making them potentially promising for mobility applications. Their geometry, however, poses challenges: their narrow design requires the hot and cold sides to be in direct contact, a configuration that is rare in practical applications. While heat pipes can spatially separate the hot and cold sides, the associated losses increase with distance. Furthermore, both TEG modules and heat pipes rely on copper materials, and both have experienced price increases in recent years [8,9]—another important factor to consider in evaluating their use.

Based on the data in Figure 1, industrial waste heat in the EU typically falls within the 40–59 °C range. If we aim to generate electricity directly from this heat, current technologies (e.g., ORC) operate at higher temperature levels. TREC (thermally regenerative electrochemical cycle) systems, however, can operate within this range and directly convert heat into electrical energy, while their shape and size can be easily adapted to the needs of dynamic systems.

The utilization of low-temperature waste heat is a special challenge due to the small temperature difference and the resulting sensitivity (compared to more robust heat utilizers), for which only a few of the classic WHR solutions are suitable. The chemical principal system is one of the large groups of heat recovery systems that function even with a small temperature difference (or low inlet temperature). For example, the PEM cell is considered a low-temperature system. Even though its operating temperature is typically only around 80 °C, nowadays it is increasingly important to make use of its loss, as it is the most common type of cell; currently operating fuel cell cars also use this type. The latter is because the PEM type can handle dynamic load changes well. It follows that the WHR system fitted to it must also be able to withstand the same. Thermally regenerative electrochemical cycles (TREC systems) are theoretically suitable for converting the heat generated by a PEM fuel cell into useful power. TREC modules can be easily adapted to the shape of fuel cells, as their shape and surface are not defined. The hot cell can be placed directly on the heating cell surface, while the cold cell can be placed at any distance on a cooler surface.

On the one hand, because they meet the special temperature requirements described above (they can work even with a small temperature difference), on the other hand, their structure is quite similar to the cell itself, so they also withstand dynamic loads well.

2. Materials and Methods

2.1. TREC System Electrochemical Model

The thermally regenerative electrochemical cycle (TREC) in the general case consists of two parts: a warm cell, a cell with a lower temperature than the warm cell. The indirect part of the system is a heat source (which determines the temperature of the hot cell) and optionally a cooling or a colder temperature environment for the cold cell. The different temperatures result in a non-zero temperature gradient between the two cells. The intensity of a chemical reaction is affected by the temperature, and since the two cells have different temperatures, the chemical equilibrium constants will also be different [11]. A system that is out of balance, in this case, striving for balance, tries to restore it with material and electron transport. Electron transport corresponds to the electric current, and the material transport is used in the regenerative case to recombine the electrodes depending on the charge and discharge cycles. The list of variables necessary for the interpretation of the following system description is contained in

Table 1. Nomenclature of the used variables.

Nomenclature
Symbol	Description	Unit
A	Contact area	m2
Ac	Electrode active area	m2
α	Signed sum of thermal coefficients of the cells	V/K
BHTH	Activity ratio in hot cell	–
BCTC	Activity ratio in cold cell	–
Ca	Capacitance	F
c	Specific heat	–
cp	Molar heat capacity of electrolyte	J/(mol·K)
d	Width of the contact areas	m
δ	Reaction rate	–
f	Objective function	–
fN	Objective function (indexed)	–
F	Faraday constant	C/mol
Gx	Gibbs energy	–
Hx	Enthalpy	–
i	Current density	A/cm2
I	Current	A
k	Loop variable	–
λ	Thermal conductivity	W/(m·K)
n	Number of electrons transferred	–
η	Concentration-dependent viscosity	Pa·s
ηX	Efficiency	%
ρ	Density of electrolyte	kg/m3
Rx	Inner resistance	Ω
Sx	Entropy	–
σN	Importance value	–
Tx	Hot side temperature	K
θ	Fitting parameter	–
Ux	(Electrochemical) potential, Voltage	V
Vx	Voltage	V
Qx	Heat	J
ΔQHEX	Heat absorbed in heat exchanger	J
γ	Relative sensitivity	–
x0N	Observed values	–
xPN	Modeled values	–

, and the list of omitted indices is contained in

Table 2. Used subscripts and superscripts.

Subscripts and Superscripts
Symbol	Description
C	Cold side
c	Concentration
FC	Fuel cell
H	Hot side
HEX	Heat exchanger
in	Inlet
int.	Internal
L	Lower
N	Parametric index
opt.	Optimal
OUT	Outlet
p	Isobar
ref	Reference
Res	Resistive
TREC	Thermally regenerative electrochemical cycle system
V	Volumetric

. The electrons will choose the path with the least resistance, the wire between the electrodes, and the useful energy of the system is extracted from the interposed consumer.

Figure 2A shows the related T-S diagram. The TREC system has four main steps [12]: The cycle starts at point 1 with the cold cell fully discharged. Heating the warm cell (1 → 2′) (Figure 2B red field) supplies energy Q_in, shifting the redox equilibrium and raising the cell Voltage, charging the system. From 2′ to 2 and along 2 → 3, the warm cell operates at high temperature T_H, delivering electrons to the load and generating electricity.

Next, the system cools (3 → 4′ → 4) (Figure 2B blue field) to T_C, where reverse redox reactions complete the discharge. Material transport between electrodes restores the original redox states, regenerating the electrolytes and enabling continuous cyclic operation. Electron flow occurs through the external circuit, while ions recombine within the electrolytes.

The double redox couples are the basic elements of the system, and they must be chosen so that they respond with the largest possible open-circuit potential difference per unit temperature difference (this is shown in more detail in Appendix A). Essentially, this resulting potential difference causes the output useful power.

In case of continuity, an additional section is installed: the heat and electrolyte exchange section placed between the two cells, with the same assembly (Figure 2B). Here, the physical permeability between anolyte-anolyte and catholyte–catholyte electrolytes allows the material transport to occur due to the difference in concentration. The negative features of this are that the transport is naturally very slow (the sides have a diffusion constant of the order of 9⁻¹⁰–10⁻¹⁰ m²/s); on the other hand, the passage between the cold and hot sides evens out the temperature. Since the performance is proportional to the temperature difference, we also include a heat exchanger (HEX) (Figure 2).

Intake heat on the hot side (Figure 2B, left side):

$${\dot{Q}}_H=T_H\left|S_H\right|$$

(1)

The usable part of internal energy (according to the Gibbs equation). Here, we see how much energy is extracted from the TREC at the temperature of the system, producing waste heat.

$$G_H={∆H}_H-T_H\left|S_H\right|$$

(2)

Assuming that the specific heat with the temperature change is nearly constant [12], in this case, according to the measurement of [13]. Also, if we are assuming that the heat capacity of the electrolyte is constant, the electrochemical potential (3) (Gibbs–Helmholtz equation):

$$U={\displaystyle \frac{{∆G}_H}{nF}}={\displaystyle \frac{{T_{H}S}_H}{nF}}$$

(3)

Accordingly, the free energy per mole of material (which is heated, for example, by a fuel cell) can also be expressed as potential if we divide it proportionally to the Faraday constant by the number of charges that have flowed through the wire due to this heat (if the free energy of the system comes entirely from the entropy change).

For two anode–cathode pairs of the same material and different temperatures discharged [14] from each other, the potential difference between the hot and cold pairs will appear in the resistance:

$${U_{OUT}}_{opt}=-{\displaystyle \frac{{T_{H}S}_H}{nF}}-{\displaystyle \frac{{T_{L}S}_L}{nF}}=U_H-U_L$$

(4)

In practice, the useful power is also limited by the system’s own internal resistance (5).

We can describe the internal resistance from

$$U_{Res}=I{R}_{int}$$

(5)

Combining Equations (1)–(5), it can be seen that the useful output power of the TREC heat recovery system is given by the potential difference measured between the cold and hot states of the double electrolyte pair, considering that the internal resistance of the system is not included. In this case, the net performance (power output):

$$P_{OUT}=i_c{A}_c\left[\left(-{T_{H}S}_H\right)-\left(-{T_{L}S}_L\right)\right]{\displaystyle \frac{1}{nF}}-2I^2{R}_{int}=I(U_H-U_L-2I{R}_{int})$$

(6)

Equation (6) is precise and correct if the system does not contain a heat exchanger (Figure 2A: 4′-2′ process, Figure 2B: grey ‘HEX’ box), and is called regenerative only by ion transport. If we want to stabilize its operation thermally and install a heat exchanger, this also loses heat, which is returned at the input (in the case of a countercurrent heat exchanger). In the case of regenerative types, the power recovered by the heat exchanger [12]:

$${{\dot{Q}}_{HEX}}_{in}=\left[1-{\eta }_{HEX}\right]c_p\dot{n}∆T=(1-{\eta }_{HEX})c_p{\displaystyle \frac{I}{\rho nF}}(T_H-T_L)$$

(7)

Since the heat exchanger losses in the system used in the experimental setup are negligible, the modified input heat equation in Equation (8) is determined by adding the heat recycled by the heat exchanger to the heat quantity on the hot side (e.g., coming from the fuel cell). Intake heat from the fuel cell (in case of η = 100%):

$${\dot{Q}}_{TREC}={\dot{Q}}_{in}+{{\dot{Q}}_{HEX}}_{in}$$

(8)

where we can calculate ${\dot{Q}}_{in}$ from the material properties and the heat source(s) properties, or by measurement. In case of calculations, we can use the function of conductive heat transfer:

$${\dot{Q}}_{in}={\displaystyle \frac{\lambda ·A·(T_H-T_L)}{d}}$$

(9)

Then, the performance of the TREC system with thermally continuous operation with the heat exchanger is similar to the version without the heat exchanger (6), but with the correct sign; the amount of heat transferred by the heat exchanger must also be taken into account, in addition to the input heat. Useful performance can also be expressed with a calculation of the intake heat from the heat exchanger:

$$P_{TREC}=I\left(U_H-U_L-2I{R}_{int}\right)=I{\displaystyle \frac{(T_H-T_L)({\dot{Q}}_{TREC}-{{\dot{Q}}_{HEX}}_{in}+I^2{R}_{int})}{nF}}$$

(10)

The power of the pump can be omitted from this relation in the case that the ion exchange takes place in the electrolyte without an external force. The efficiency of the whole system (including the regenerative part) is as follows:

$${\eta }_{TREC}={\displaystyle \frac{P_{TREC}}{{\dot{Q}}_{in}}}$$

(11)

The parameters examined in the sensitivity test can be interpreted separately.

Effect of thermal coefficient: It is a crucial variable from the point of view of this manuscript, since the formation of the thermogalvanic phenomenon itself is linked to different material reactions to temperature. Typically, results from the entropy difference between the reduced and oxidized particles, we can describe it like [15]

$$\alpha =dU/dt=∆S/nF$$

(12)

If we approach the electrolyte pairs from the point of view of temperature sensitivity, then the useful electrical power is obtained as the difference between the thermoelectric potential (${\alpha }_{cell}∆T)$ and the potential difference due to concentration differences ($R/nFln\left(B_H^{T_h}/B_C^{T_C}\right))$. Here, we already consider that the power outlined in (10) is the constant power of an ideal system; in a non-ideal case, output power depends on the concentrations at every moment. With free ion exchange (Figure 2B, middle tubes) and, if necessary, circulation, Equation (10) can be used; in the absence of these, the change in the concentration difference must be taken into account:

$$P_{max}={\left[{\alpha }_{cell}∆T-R/nFln\left(B_H^{T_h}/B_C^{T_C}\right)\right]}^2/4(R_H-R_C)={OCV}_H-{OCV}_C$$

(13)

Effect of hot side cell temperature: The warm-side temperature has a double effect. On the one hand, the higher temperature means lower resistance in the material, and it generates higher electric performance [16]:

$$R=R_{Ref}/1+\theta (T_H-T_{Ref})$$

(14)

Here we set the $\theta$ fitting parameter 0.06 K-1 according to [17].

This also affects the electrical performance:

$$P_{max}={\left[{\alpha }_{cell}∆T-R/nFln\left(B_H^{T_h}/B_C^{T_C}\right)\right]}^2/4(R_H-R_C)={OCV}_H-{OCV}_C$$

(15)

As with the power, the effect of the heat exchanger must be taken into account when calculating the efficiency. In addition, in asymmetric cases, we must also take into account that the electrical resistance of the high- and low-temperature electrochemical cells is not the same. This is taken into account in Equation (16). The efficiency also changes with the change in resistance:

$${\eta }_{TREC}={\eta }_c\left[{\displaystyle \frac{1-I(R_H-R_L)}{\left|{\alpha }_{cell}\right|∆T}}\right]/\left[{\displaystyle \frac{1+{\eta }_c(1-{\eta }_{HEX)}}{{\alpha }_{cell}\frac{Q_c}{c_p}}}\right]$$

(16)

In addition, the effect seen in Equation (4) also applies, which practically expresses the chemical balance difference due to the temperature difference and the resulting open circuit potential difference.

$$P_{TREC}=I\left[-T_H∆{\dot{S}}_H/nF-T_L∆{\dot{S}}_L/nF\right]=2I^2{R}_{int}$$

(17)

Effect of cooling temperature: The temperature on the cold side is, of course, also necessary for the temperature difference that forms the basis of the phenomenon. Effect of concentration in the electrolyte solution: At higher concentration values, the electrolyte’s resistance decreases [18].

$${R_S}^{-1}={Ca}_S{\displaystyle \frac{c}{{\eta }_c}}$$

(18)

The effects of this on performance are detailed in Equation (14).

Effect of active membrane-electrode area: The intensity of the redox reaction depends on the active electrode surface, which can be calculated separately for the cold and hot sides, according to the charge balance equation [3]:

$$-nF{\delta }_v=i{A}_e$$

(19)

It should be noted that, based on the above equations, an expected optimum in the performance of the TREC system also arises, which we can determine in advance based on the knowledge of the internal resistance:

$$P_{OPT}=i(U_H-U_L-2I^2{R}_{int})$$

(20)

Effect of heat exchanger efficiency: The heat exchanger between the cells prevents the formation of a thermal balance during the ion exchange, as the latter would also equalize the values of the open circuit potential between the cold and hot cells. The amount of heat recovered together with the total heat input can be included in the performance, as shown in Equation (7).

Effect of electrolyte’s specific heat: The specific heat of the circulated medium affects the amount of heat removed by the heat exchanger. We can model this effect with the following expression:

$$∆{{\dot{Q}}_{HEX}}_{in}=c_p\dot{n}(1-{\eta }_{HEXs})(T_H-T_L)$$

(21)

The effect of the heat removed by the heat exchanger is shown in Equation (9), where the factor negatively affects the TREC performance.

When choosing materials, it was an important aspect to work with real electrodes and electrolytes that can be used for the TREC system. Their resistance, but above all their temperature constant, is an important parameter, which is why we paid special attention to this in the literature search. The highest temperature constants from the analyzed experiments or theoretical calculations are shown in Appendix A.

2.2. Sensitivity Analysis

The presented model is an own-designed thermally regenerative electrochemical cell pair with 0.016 m² active area. The used electrolyte pair was iodine–potassium iodine catholyte with 0.1M/1M concentration and potassium ferricyanide with potassium hexacyanoferrate 0.375M/0.375M (both aqueous soluted) [3]. The parameters (

Table 3. List of variables and fixed values.

Parameter	Name	Unit	Test Range	Value (If Fixed)
Ac	Electrode active area	m2	0.016; 0.036	0.016
α	Signed sum of thermal coefficients of the cells	V/K	0.2 ×1 0−3; 3.2 × 10−3	1.44 × 10−3
cp	Molar heat capacity of electrolyte	J/(mol K)	58.15; 80.77	75.6
F	Faraday constant	C/mol	96.485	96.485
i	Current density	A/cm2	0.0002; 0.006	0.0061
λ	Thermal conductivity	W/mK	237	237
n	Number of electrons transferred	-	2	2
QFC	Heat generated by fuel cell	J	23,750; 50,000	50,000
Qin	Inlet heat to the TREC	J	0; 199,080	50,000
RC	Cold cell resistance	Ω	5.14; 24.25	24.5
RH	Hot cell resistance	Ω	5.14; 24.25	24.5
Rint	Inner resistance	Ω	5.14; 24.25	24.5
TC	Cold side temperature	K	297.15	297.15
TH	Hot side temperature	K	297.15; 360.15	357.15
ηHEX	Efficiency of heat exchanger	-	0.6; 0.8	0.7

) were typically chosen in such a way that the variables take values available within the size range of the prepared TREC system. The temperature of the cold side was taken from the installation environment as cooling, so that no external energy source was needed. The hot side temperature is maximized at the maximum temperature of the PEM fuel cells.

The list of parameters differs from the nomenclature; this is because not all parameters were examined in terms of sensitivity. For a given commercial carbon felt electrode, the electrode area (A) is proportional to the tested contact area. Similarly, the electrode thickness is a fixed, given geometric parameter, and its effect on the amount of electrolyte that can be accommodated was indirectly taken into account when examining the capacity. For a given electrode, the current density and the current strength also show analogous behavior; therefore, it is sufficient to examine only the current density. Since the molar heat capacity and the cell heat capacity (C_a) are analogous concepts, I considered only the molar specific heat capacity. The degree of reaction and the degree of activity are instantaneous values, and for the reasons discussed in Equation (13), there are no or negligible effects in the concentration-balanced system outlined in Figure 2. The free energy and entropy terms are among the parameters examined, so examining them as complex terms is difficult to use in practice. The heat absorbed by the heat exchanger was also not examined in terms of sensitivity, since the efficiency of the heat exchanger is more easily selected or modified by the user in practice, and this value is also given for a given input heat quantity.

During the sensitivity tests, we examined two groups, heat-sensitive and current-sensitive members, and we examined these two variables in terms of sensitivity.

Heat and current are two parameters in relation to which all of the necessary parameters can be examined, thus aiding comparability. In each case of the study, we selected a primary trend, which, according to the MPSA approach, represents the series of observed values (Figure 3). We want to check the relative importance of each parameter. This is important because, in the experimental phase, we adjust the parameters that have a significant effect on performance to achieve higher performance. For this, the Multi-Parametric Analysis (MPSA) was used [19].

The process of conducting MPSA calculations (Figure 3) can be summarized in the following steps. First, the parameters to be tested are selected. Next, the range for each parameter is defined. Within these ranges, a series of independent, random numbers is generated for each parameter, following a uniform distribution. The model is then executed using the generated parameter series, and the objective function is calculated for each cell’s current value according to Equation (22).

$$f_N=\sum _{k=1}^j{\left[{x_0}_N-{x_P}_N\left(k\right)\right]}^2$$

(22)

Subsequently, the relative importance of each parameter is determined for each current value using Equation (23).

$${\sigma }_N={\displaystyle \frac{f_N}{{x_0}_N}}$$

(23)

Finally, parametric sensitivity is evaluated to identify sensitive and insensitive parameters, as described by Equation (24).

$$\gamma =\sum _{T_H=297.15}^{j_{max}}{\sigma }_H$$

(24)

According to the method shown in Figure 3, the program assigns a value to each independent variable according to the MPSA model, which expresses the degree of sensitivity of the given physical parameter.

For a given parameter, the higher the value of the index ‘γ’, the greater the sensitivity of the fuel cell model to that parameter. Using the index ‘γ’, the following criteria were applied to define the relative sensitivity of the fuel cell model to a specific parameter [20]. The values assigned to the parameters strength:

$\gamma \le 500\to$ The parameter is intensive

$500<\gamma \le \mathrm{1,000}\to$ The parameter is semi-intensive

$\mathrm{10,000}<\gamma \to$ The parameter is sensitive

The model assumptions in summarized are summarized in a version provided on the

Table A1. Assumptions and justifications of the calculation.

Assumption	Justification	Fixed Value(s)
Constant specific and molar heat capacity	Variation in the studied temperature range is small	cp = 75.6 J/(mol·K) (test: 58.15–80.77)
Free energy fully derived from entropy change	Applied Gibbs–Helmholtz approximation	–
Heat transfer only by conduction	Based on aluminum plate conduction	λ = 237 W/mK; thickness = 2 mm; area = 0.16 m2
Neglected pump power	Ion exchange occurs by diffusion, no external driving	Diffusion constant, around 10−9; 10−10 m2/s
Constant, symmetric internal resistance	Assumed identical in both cells	Rint = RH = RC = 24.5 Ω (test: 5.14–24.25)
Fixed cold-side temperature, fixed humidity	Taken from environment, no external cooling	TC = 297.15 K (24 °C)
Hot-side temperature limited by PEM cell	Limited by PEM fuel cell maximum operating temperature	TH = 357.15 K (84 °C); test: 297.15–360.15 K
Fixed electrolyte pair	Iodine–KI and ferricyanide–hexacyanoferrate aqueous solutions	0.1/1 M (I2–KI); 0.375/0.375 M (Fe(CN)63−/Fe(CN)64−)
Heat generated by fuel cell is fix and constant	Represents the external heat source	QFC = 50,000 J (test: 23,750–50,000 J)

in Appendix A.3.

3. Results

Based on the insights gained from the results (

Table 4. Result of sensitivity analysis. (Red: Sensitive parameters, Green: Highly sensitive parameters, Blue: Intensive parameters).

Dependency	Variable	Sensitivity Factor	Sensitivity Category
Current	Hot side temperature	1454.7	Sensitive
	Resistance of electrodes	35,035.1	Highly sensitive
Temperature	Current	30,287.3	Highly sensitive
	Active membrane area	552.1	Sensitive
	Thermal coefficient	737,799.5	Highly sensitive
	Molar capacity	28.5	Intensive
	Efficiency of HEX	7.64 × 10−8	Intensive

), enhancing the performance of TREC systems requires prioritizing the material properties of the selected substances, particularly their thermal constant and internal resistance. The latter is a construction parameter and a material property. If the material is given, the magnitude of the operating current is the most important. If this is limited due to the input heat or other electrotechnical properties, it is worth increasing either the input heat itself (heat side temperature) or the active membrane surface. It is also instructive that the variables related to the heat exchanger affect the performance of the TREC itself with little intensity; their effect is not in the field of performance but in the field of efficiency.

Examining the effect of the temperature on the hot side, we considered the input heat on the heating surface in such a way that it changes linearly with the current strength (Figure 4A). As an example, we chose a 2 mm-thick, 0.16 m² aluminum sheet with a thermal conductivity of 237 W/mK, which in a real installation environment is close to a fuel cell in a car. The reason for the choice was that this system generates a small heat output (usually a maximum temperature of 80 °C); therefore, it represents a special challenge for a heat utilization task.

During the evaluation, the parameter was classified as ‘sensitive’. In practice, however, it is not advisable to increase this value, as it would also mean a decrease in the efficiency of the primary equipment. However, the contact surface and the amount of heat flowing through it can be increased by design, e.g., with a larger paved surface, or by connecting modules placed on several heated parts in series.

We also examined the effect of internal resistance on performance (Figure 4B). In the tested range, the system is sensitive to this parameter, especially in the case of higher loads, we can expect a significant change when changing the internal resistance. As expected, the current density (Figure 5A), i.e., the magnitude of the electric current falling on a unit of reactive surface, also fell into the same sensitivity category. However, this test can also be considered theoretical; in practice, this value follows the external parameters, and the user and the designer cannot influence it. It affects the active surface, which falls into the ‘Sensitive’ category (Figure 5B). Here, we used traditional solid electrodes, but based on the results, felt electrodes, which are more expensive but have an order of magnitude larger surface area, can be considered.

The temperature coefficient was clearly the most important parameter for the system’s performance (Figure 6). This value is characteristic of electrolyte-electrode assemblies. This is the only term whose importance increases not linearly, but exponentially with temperature. Since it is such an extremely influential factor, we performed a separate investigation to see which of the currently published materials have which temperature coefficient (Appendix A.1).

Although it has to be considered mathematically, in practice, the molar percentage of the electrolyte (Figure A2a in Appendix A.2) and the efficiency of the heat exchanger (Figure A2b in Appendix A.2) have little influence on the performance of the TREC in the investigation range, that is the reason why we can see just the individual value changing on the Figure A2a in Appendix A.2 and Figure A2b in Appendix A.2. These devices were included in the performance-focused model due to the need for completeness; in fact, they are not crucial in performance, but for continuous operation.

4. Discussion

The aim of this study is to identify the key parameters influencing the performance of thermally regenerative electrochemical cycle (TREC) systems, with a particular emphasis on the utilization of low-temperature waste heat from fuel cells. The authors conducted a sensitivity analysis based on a self-developed TREC model, employing the Multi-Parametric Sensitivity Analysis (MPSA) method. The impact of various physical and chemical parameters on system performance and efficiency was investigated using electrolyte properties and actual cell geometry.

Based primarily on the results of the sensitivity analysis:

• The thermal coefficient of the redox couples was found to be the most critical factor affecting system performance (γ ≈ 737,800).
• Internal resistance and current density also emerged as highly sensitive parameters, with a considerable influence on performance (γ ≈ 35,035 and γ ≈ 30,287, respectively).
• The hot-side temperature and the size of the active membrane area were identified as sensitive parameters that play a significant role in energy conversion.
• The efficiency of the heat exchanger and the specific heat capacity of the electrolyte have a lesser effect on performance, though they do influence overall system efficiency.
• During the study, literature data for 81 redox couples were reviewed and compared, providing a foundation for future material selection.

Based on the sensitivity studies, we can distinguish three categories: the construction parameters include the resistance of the electrodes and the active membrane surface. These are highly sensitive values in themselves and indicate that they are worth considering geometrically in the design. If we only have the option of one, we increase the active surface when working with a current collector, including the contact surface. This means that the contact resistance is a critical parameter between the electrode surface and the current collection point, which must be minimized. The construction parameters include the heat exchanger, whose impact on performance is small, but we would like to emphasize that its importance in terms of efficiency and service life should not be neglected.

Chemical variables such as thermal coefficient and molar capacity yielded mixed results, which led to the conclusion that it is definitely worth pairing multiple electrolytes so that their combined thermal coefficient is as high as possible, even if their molar heat capacity is not as favorable.

The more difficult to influence parameters, which result from the instantaneous behavior of the external system (hot side temperature, current), are extremely sensitive or sensitive. We have little influence on these when designing. The lesson to be learned is that these are such influential variables that we will not be able to compensate for them with e.g., chemical parameters with low sensitivity (e.g., more expensive electrolyte).

The results were classified into construction and material categories, which helps us predict the extent of deviations from the basic model in similar calculations of significantly different but identically functioning constructions. The model’s verifiable scalability enables its application to systems of various sizes and capacities, including both automotive and industrial contexts. Future research directions include extending the model to account for dynamic operating conditions—for instance, to explore heat generation in vehicles under variable loads. Experimental validation of selected redox couples could enhance practical applicability and support material development efforts. The system may also be integrated into hybrid energy storage or heat recovery solutions, such as heat pumps or supercapacitors. Furthermore, the methodology is adaptable to other low-temperature heat sources, including waste heat from data centers or industrial cooling water.

5. Patents

This research was funded by Project no. RRF-2.3.1-21-2022-00009, titled the National Laboratory for Renewable Energy, and has been implemented with the support provided by the Recovery and Resilience Facility of the European Union within the framework of Program Széchenyi Plan Plus.

Prepared With the Professional Support of the Co-operative Doctoral Program of the University Research Scholarship Program of The Ministry of Culture and Innovation, financed from the National Research, Development and Innovation Fund.