Analysis of a polymer-based textile-embroidered thermoelectric generator for harvesting electrical power from the human body

Warm and lightweight clothing is indispensable in cold climates, and textile thermoelectric generators embroidered into fabrics provide a practical solution for harnessing body heat to generate electricity. This study performed analytical and numerical analyses for a textile thermoelectric generator with p-type legs composed of polymer:polyelectrolyte-coated threads and n-type legs made of silver-plated threads sewn on a thick wool fabric. The one-dimensional thermoelectric equations, derived from energy balance on small thermoelectric elements, were analytically solved for a constant Seebeck coefficient under three boundary conditions: (a) fixed temperatures at both sides, (b) fixed temperature at the hot side with convection at the cold side, and (c) convection at both sides. These conditions effectively simulate the thermal contact resistance encountered in wearable thermoelectric generators. Subsequently, a semi-analytical approach was applied to the one-dimensional thermoelectric equation for a p-type leg with linearly temperature-dependent Seebeck coefficient and thermal conductivity under ideal thermal contact with the heat sources. The analysis yielded the temperature and electric potential distributions along the textile thermoelectric legs, as well as the maximum achievable power, peak power current, and optimal load resistance. A higher temperature gradient significantly enhanced maximum power output and associated electric current. As the convective heat transfer coefficient increased, the maximum power and corresponding electric current initially rose sharply before stabilizing at higher values, influenced by the temperature gradient. With convective heat transfer on both sides and a temperature gradient of 50 K, a maximum power of 46.65 nW per thermocouple unit was achieved at a textile thickness of 15.9 mm. Interestingly, the analytical analysis revealed that the optimal load resistance for maximum power generation was unaffected by the boundary conditions and was consistently equal to the thermoelectric generator’s internal resistance. The thermoelectric generator-embroidered fabric reached a steady state power generation after 17 min, with the open-circuit voltage increasing linearly as more thermoelectric pairs were added. This study presents a comprehensive mathematical framework for analyzing and optimizing thermoelectric generator designs for industrial applications.