Numerical investigation of thermoelectric generator leg length optimization for building wall integration under low temperature Gradients: A COMSOL Multiphysics study

• Longer TEG legs (100–200 mm) maximize power output, contrary to high-temperature industrial design principles. • 200 mm configuration produces 9 × higher voltage than 2 mm baseline at ΔT = 20°C. • Voltage-dominated power optimization, not current-balanced. • Maximum power density: ∼3,000 µW/m 2 at winter conditions. • Annual generation: 0.8–1.2 kWh/m 2 in temperate climates, winter-concentrated. Building envelopes represent a significant source of waste thermal energy, dissipated to the environment through heat loss in winter and heat gain in summer. Thermoelectric generators (TEGs) embedded in walls can exploit temperature gradients across building assemblies to generate electricity, yet systematic design guidelines for geometric optimization remain absent. This study addresses this gap through comprehensive numerical modelling using COMSOL Multiphysics to investigate how TEG leg length variations influence electrical performance under realistic building temperature conditions. Five distinct leg length configurations (2, 10, 20, 100, and 200 mm) were parametrically evaluated across temperature differences of 0–20°C, representing seasonal building envelope gradients. Results demonstrate that voltage generation scales monotonically with leg length, with the 200 mm configuration producing approximately 0.008 V per unit at ΔT = 20°C—nine times higher than the 2 mm baseline. Conversely, current generation exhibits inverse dependence on leg length due to increased electrical resistance. Power output is overwhelmingly voltage-dominated, with 200 mm and 100 mm configurations yielding maximum output (∼0.006–0.008 µW per unit). When scaled to integrated wall modules (approximately 500 units per m 2 ), maximum power density reaches ∼ 3,000 µW/m 2 at winter conditions. This represents a paradigm shift from conventional thermoelectric design principles developed for high-temperature industrial waste heat recovery: building walls, constrained to low temperature differences (5–25°C), require longer leg geometries to maximize Seebeck voltage accumulation rather than current flow. The study provides quantitative design guidelines for optimizing TEG geometry in building-integrated applications and establishes that performance remains practical yet economically challenged without hybridization or material advances (ZT > 2). These findings form the foundation for informed design decisions in sustainable building envelope systems.