Numerical and Statistical Thermal-Electric Analysis of Metal Rods

Abstract

This study presents a numerical and statistical investigation of the thermoelectric behavior of metal rods made of bronze (CuSn3Zn1), structural steel, and magnesium alloy under different electric currents. Numerical simulations were performed using ANSYS Workbench, while statistical optimization was conducted using the Taguchi method with an L9 orthogonal array. Material type and electric current were selected as influencing factors, whereas temperature and heat flux were considered the response parameters. Signal-to-noise (S/N) analysis was employed to evaluate the effects of the selected factors and determine their optimal levels. Analysis of variance (ANOVA) was performed to quantify the contribution of each factor to the thermal responses. The results revealed that the electrical resistivity of the materials significantly influences temperature and heat flux. Material type and electric current contributed 75.64% and 18.95% to temperature, respectively, while their corresponding contributions to heat flux were 85.99% and 7.86%, respectively, highlighting the dominant influence of material properties.

Keywords

• Electric current
• Finite element method
• Heat flux
• Temperature

References

1. [1]. Majed, MF, Mgohimi, M, 2025. Numerical investigation of the thermosiphon-thermoelectric generator by different parameters. Journal of Techniques; 7(2): 46-59. https://doi.org/10.51173/jt.v7i2.2666
2. [2]. Özlem Esen, D, Yacoub A Shabaneh, SA, Tural H, 2025. Optimizing thermoelectric energy recovery from gasoline engine exhaust: A computational approach using ansys. Case Studies in Thermal Engineering; 73: 106435. https://doi.org/10.1016/j.csite.2025.106435
3. [3]. Aljaghtham, M, Nawafleh, N, 2025. Multi-parameter design optimization of segmented annular thermoelectric generators: enhanced machine learning. Applied Thermal Engineering; 281: 128749. https://doi.org/10.1016/j.applthermaleng.2025.128749
4. [4]. Kim, SH, Lee, KW, 2015. Numerical approach to joule heating analysis for electrical parts using MSC Marc. Journal of Mechanical Science and Technology; 29(5): 2081-2087. https://doi.org/10.1007/s12206-015-0429-y
5. [5]. Spinelli, G, Guarini, R, Vertuccio, L, Guadagno, L, Romano, V, 2024. Simulation and Experimental Comparison of Joule‐Heating Effect in Carbon‐Based Epoxy Resin. Macromolecular Symposia; 413(4): 2400034. https://doi.org/10.1002/masy.202400034
6. [6]. Tomse, AD, Molnar, CO, 2025. Multi-physics Simulation of Electrical Contacts: Coupled Mechanical and Thermal Analysis Using ANSYS. Journal of Electrical and Electronics Engineering; 18(2): 93-96.
7. [7]. Zhang, YF, Ge, Q, 2019. A numerical framework for the design of Joule-heating circuits to thermally activate smart materials. Smart Materials and Structures; 28(11): 115026. https://doi.org/10.1088/1361-665X/ab47e4
8. [8]. Kenzhegulov, BZ, Kenzhegulova, SB, Alibiyev, DB, Kazhikenova, ASh, 2022. Finite element modeling of heat propagation of a complete rod of constant cross-section. Bulletin of the University of Karaganda-Physics, 108(4): 94-105. https://doi.org/10.31489/2022PH4/94-105

9. [9]. Prajwal, KT, Bhat, P, 2021. Thermal analysis of a Thermoelectric Generator (TEG) using FEM technique. IOP Conference Series: Materials Science and Engineering; 1045(1): 012018. https://doi.org/10.1088/1757-899X/1045/1/012018
10. [10]. Aswin, MR, Pavithran, A, Mangrole, Y, Shivaraman, S, Kulaye, CS, Balaji, R, 2023. Material selection based on joule heating simulation for resistojet thruster. Materials Today: Proceedings; 2023. https://doi.org/10.1016/j.matpr.2023.07.274
11. [11]. Afzal, MJ, Ashrf, MW, Tayyaba, S, Javaid, F, 2025. Thermoelectric ANSYS Simulation for Current Generation and Current Density Analysis. Scientific Inquiry and Review; 9(2): 09-23. https://doi.org/10.32350/sir.92.02
12. [12]. Wielgosz, SE, Clifford, CE, Yu, Kevin, Barry, MM, 2023. Fully–coupled thermal–electric modeling of thermoelectric generators. Energy; 266: 126324. https://doi.org/10.1016/j.energy.2022.126324
13. [13]. ANSYS, Engineering Data Sources, Canonsburg, PA: ANSYS Inc. 2021.
14. [14]. Antonova, EE, Looman, DC, 2005. Finite elements for thermoelectric device analysis in ANSYS. ICT Proceedings; 2005. https://doi.org/10.1109/ICT.2005.1519922
15. [15]. Filippis, S.de, Košel, V, Dibra, D, Decker, S, Köck, H, Irace, A, 2011. ANSYS based 3D electro-thermal simulations for the evaluation of power MOSFETs robustness, Microelectronics Reliability; 51(9-11): 1954-1958. https://doi.org/10.1016/j.microrel.2011.06.047
16. [16]. Målqvist, A, Stillfjord, T, 2017. Finite element convergence analysis for the thermoviscoelastic Joule heating problem, BIT Numerical Mathematics; 57(3): 787-810. https://doi.org/10.1007/s10543-017-0653-1
17. [17]. Bollati, J, Briozzo, AC, Kharin, SN, Nauryz, TA, 2024. Mathematical model of thermal phenomena of closure electrical contact with Joule heat source and nonlinear thermal coefficients, International Journal of Non Linear Mechanics 158: 104568. https://doi.org/10.1016/j.ijnonlinmec.2023.104568
18. [18]. Ross, PJ, Taguchi Techniques for Quality Engineering. McGraw-Hill International Editions, 2nd Edition, New York, USA, 1996.