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Lekbir et al. Energy Mater. 2025, 5, 500101 https://dx.doi.org/10.20517/energymater.2025.46 Page 7 of 17

EP = CExC × F (9)
p
p
where CExC represents the total exergy consumption equivalent to 36% of the CEC . F is the emission
[47]
p
factor for the element ρ corresponding to the emission factors for electricity production from coal power
[48]
-1
2
-1
plants (i.e., CO = 8.68 × 10 kg/m and GWP = 9.12 × 10 kg.CO .eq) .
2
2
Optimization of the TEG geometry using the PSO method
In the present study, the PSO algorithm is applied to optimize the geometry of TEG legs. PSO is a
metaheuristic optimization technique inspired by the collective behavior of birds flocking and fish
schooling. It is widely used in engineering, artificial intelligence, and other fields to solve complex
optimization problems by iteratively improving candidate solutions based on a population-based search
[49]
approach . In this study, the optimization of TEG geometry using PSO focuses on three main geometric
parameters: the number of legs (n), leg length (l ), and leg cross-sectional area (A ). The optimization of
leg
leg
these parameters directly enhances the performance of the TEG, improving heat transfer, electrical output,
and overall efficiency, while minimizing material usage and ensuring practical feasibility.
The optimization process begins by initializing candidate solutions that include the values for n, l and A .
leg
leg
The search space is constrained within the boundaries 1 < l < 4 mm and 1 < A < 3 mm . The value of n is
2
leg
leg
determined based on the geometric constraints of l and A to ensure feasibility in practical applications.
leg
leg
For this study, the PSO parameters are set with a swarm size of 50 particles and a maximum of 100
iterations, which balances computational efficiency and solution accuracy. The framework of the PSO-based
optimization approach for TEG leg geometry is summarized in Figure 2.
The movement of each particle in the search space is governed by two fundamental update equations:
velocity update and position update. The updating equations for the velocity (V) and position (X) of the
i
i
i-th generation (i = 1, 2, 3 …., N) particles are defined as follows :
[50]
V = ωV + c r (P - X) + c r (G - X) (10)
best,i
best,i
i
2 2
i
1 1
i+1
i
X = X + V (11)
i+1
i+1
i
where ω, c and c , r and r are inertia weight (ω = 0.7), acceleration coefficients (c = c = 2), and the random
1
2
1
2
1
2
number between 0 and 1, respectively. P and G are the best and the global position of the particle,
best,i
best,i
respectively.
RESULT AND DISCUSSION
This analysis mainly focuses on the impact of the different types of materials and system geometry on the
performance of the TEG. This section presents the obtained results of the present study. The obtained
results are based on the type of materials and system geometry. In addition, the result of the different
geometry for commercial TEG modules and optimized geometry is also presented and discussed.
Energy inventory for different TEG materials
The energy inventory of different TEG modules considered in the present study depends on the materials
type contained in the present study. This section presents a comprehensive analysis of the different TEG
modules to determine the total energy consumed over the manufacturing phase of the different TEG
modules. The obtained results are summarized in Table 3.