Numerical Design Optimization of a Seebeck Cell for Thermoelectric Sensing

Hadiqa Naaz1, Michał Pawlak2, Jose Ordonez-Miranda3
1Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziądzka 5, 87-100 Toruń, Poland
2Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
3Sorbonne Université, CNRS, Institut des NanoSciences de Paris (INSP), Paris, France
Publié en 2026

Harvesting of waste heat and its conversion into electrical energy using thermo-electrochemical cells is an essential strategy for renewable energy development. Even substantial research has been devoted to these cells; their practical deployment remains limited by the cost of electrode materials and relatively low conversion efficiency. Because the electrical output of these cells scales directly with the internal temperature differential, overcoming these efficiency bottlenecks requires precise control of the thermal gradient (ΔT) at the electrode interfaces. This study presents a 3D finite element analysis (FEA) performed in COMSOL Multiphysics® to compare the thermal response of platinum (Pt) and copper (Cu) rod electrodes, specifically evaluating their ability to localize thermal energy to maximize this critical driving force [1]. The numerical model comprises a hollow alumina (Al2O3) cylinder (diameter: 0.5 mm, length: 10 mm) housing a metallic rod electrode (radius: 0.4 mm, length: 30 mm), where the inner wall of the alumina maintains direct thermal contact with the outer surface of the electrode. The system behavior is governed by the Heat Transfer in Solids interface, which solves the steady-state heat conduction equation: ∇ · (-k ∇T) = Q (1) where k is the material thermal conductivity and Q is the heat source term. A uniform inward heat flux (q0 = 2000 W/m²) was prescribed at the alumina to simulate external heating, which is transferred directly across the solid-solid interface to the embedded metal. Conversely, forced convective cooling was applied at the exposed terminal boundaries of the electrodes, modeled via: qconv = h (Text - T) (2) where qconv is the inward convective heat flux, h is the convective heat transfer coefficient (310 W/(m2.K), Text is the ambient external temperature (298.15 K), and T is the local surface temperature. Point probe diagnostics evaluated along the electrode longitudinal axis (at x = 15 mm) revealed distinct thermal profiles. Under identical boundary conditions, the Pt electrode sustained a wider temperature span (approximately 50 °C to 100 °C) with a probe temperature of 85.052 °C as shown in Figure 1. Due to its lower thermal conductivity inhibiting rapid heat dissipation along the rod, Pt maintained the accumulated thermal energy from the contact zone more effectively than the highly conductive Cu electrode which exhibited a flatter profile (55 °C to 75 °C) and a lower probe temperature of 69.878 °C. Our simulation results demonstrate that selecting an electrode with lower thermal conductivity, such as platinum, yields a significantly elevated spatial temperature distribution and larger magnitudes of ΔT across direct-contact interfaces [2]. This computational framework provides crucial design rules for optimizing thermal profiles to engineer high-sensitivity cells and efficient waste heat harvesting systems.

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