Scaling Laws and Thermodynamic Limits of Modular Thermoelastic Energy Harvesting from Low-Grade Heat

Low-grade thermal energy is widely available in industrial waste-heat streams and natural temperature fluctuations, yet its utilization remains limited because of weak thermodynamic driving forces and the complexity of conventional heat-engine technologies. This study presents a physics-based framework for modular thermoelastic energy harvesting using the reversible thermal expansion and contraction of structural materials. Analytical models are established to quantify thermoelastic work, structural constraints, thermodynamic and exergy efficiencies, and long-term energy production. Material selection and thermo-mechanical limitations are evaluated through parametric analysis and finite-element verification. The results indicate that extractable work is fundamentally constrained by yield strength, buckling resistance, temperature swing, and the limited exergy content of low-grade heat. Scaling laws show that annual energy generation scales approximately linearly with active structural mass while remaining strongly dependent on column diameter, thermal-cycle frequency, and material performance indices. Thermodynamic and exergy efficiencies remain well below the Carnot limit, highlighting the inherent limitations of solid-state thermoelastic conversion. A techno-economic assessment further indicates that economic viability depends primarily on multi-cycle operation and low-cost implementation. Although the achievable energy density remains modest compared with conventional renewable technologies, the proposed framework provides quantitative performance limits and practical design guidelines for evaluating thermoelastic energy harvesting from low-grade heat.