Proposing wavy-shaped legs for performance improvement of thermoelectric generators: energy, exergy, environmental, and mechanical analysis using a CFD-trained machine learning method

Abstract

The innovative wavy-shaped leg proposed in this research enables a longer thermoelectric leg without increasing the total height of the thermoelectric module (see the graphical abstract). A greater leg height enhances TEG’s performance while maintaining the same overall module height. The proposed idea is investigated from energy, exergy, environmental, and mechanical performance perspectives using machine learning trained with data coming from a 3D validated numerical simulations based on the Finite Element Method (FEM) for a segmented thermoelectric generator. The wavy-shaped leg is designed with varying wave amplitude (A_w), number of cycles (N), leg thickness (t_l), and height ratio between segments (h_r), all of which are evaluated based on their impact on voltage, generated power, efficiency, exergy-based efficiency, CO₂ savings, and von Mises stress. The FEM simulations are then used to develop a highly accurate predictive model employing Deep Neural Networks (DNN), enabling rapid and efficient optimization and extrapolation across parameter values. Comprehensive results are identified and reported in this study. According to the results, the wavy structure generates more power while the higher number of cycles the higher generated voltage. Outcomes also confirm that larger A_w, N, h_r, and $q_{\mathrm{in}}$ values yield considerable improvements in terms of thermoelectric performance. For instance, at$q_{\mathrm{in}}$ = 35,000  W/m² and h_r = 0.8, output power reaches 0.0178 W, with respective CO₂ savings of 0.03045 kg. Slim legs (t_l = 0.1) in combination with larger A_w values maximize output and efficiency but drive von Mises stress over 400 MPa. The DNN model accurately forecasts such trends, with high agreement with FEM (e.g., for A_w = 0.1  mm and t_l = 0.1  mm) DNN forecasts CO₂ savings of 0.01893 kg, in contrast with 0.01888 kg for FEM). It also yields continuous and smooth extrapolation for intermediate values, such as h_r = 0.24032 (voltage = 0.076676 V) and t_l = 0.1201 mm (stress = 270.02 MPa). Integration between FEM simulations and prediction with DNN brings computational accuracy and efficiency together, allowing for rapid and efficient optimization of robust and high-performance TEGs.