Predicting performance of fiber thermoelectric generator arrays in wearable electronic applications

Highlights

• Models of three-dimensional array generator with a low temperature difference under conductive and radiative heat transfer.

• Quantified influences of materials, device structure and application conditions on output performance of the device.

• Theoretical upper limits of performance of the device worn on human back at various ambient temperatures.

Abstract

Emerging fiber-based thermoelectric generators have shown great potentials to power wearable electronics by harvesting thermal energy from human body and environment. However, the lack of quantitative analytical tools has hindered the research progress, particularly related to their design and evaluation, covering selection and optimization of thermoelectric, electric and structural materials, device structure, fabrication processes and application conditions. Here, we report a quantitative approach to predict the performance of three-dimensional fiber-based thermoelectric generators composed of one-dimensional fiber generator array, working under conductive and radiative heat transfer conditions with a low temperature difference. We first present an experimentally verified model of single fiber generator unit, consisting of core/sheath fiber leg and electrodes, to quantify the effects of the material properties and structural parameters on the output power and energy conversion efficiency of the fiber unit. Then we propose a second model of three-dimensional fiber-based thermoelectric array generator to predict its output performance in terms of fiber unit packing density and surface emissivity. Finally, the theoretical upper limits of output power and conversion efficiency are given for the fiber-based thermoelectric array generators worn on a human torso back under a range of ambient temperature.

Introduction

Fiber-based thermoelectric generators (FTEGs) are flexible, conformable and light-weight devices, which can directly convert heat into electricity without any moving parts or working fluids [1]. At present, the output performance of such devices is generally lower, in the range of ~1 μW/cm², close to body temperature with a small temperature difference, say ~15 K [2,3]. These devices are great candidates to provide energy to the wearable electronics. To this end, high output power and energy conversion efficient are essential for FTEGs in wearable applications. However, up to date, there is no quantitative analytical tool that can guide the engineering design of FTEGs, including selection of thermoelectric (TE), electric and structural materials, the device structure and fabrication processes with particular application conditions.

To achieve high energy conversion efficiency of rigid thermoelectric generators (TEGs), significant progress has been made to explore TE materials of high figure of merit, $ZT=\sigma {\alpha }^{2}T/\kappa$, where $\sigma$ is the electrical conductivity; $\alpha$ is the Seebeck coefficient; $T$ is the temperature; $\kappa$ is the thermal conductivity [[4], [5], [6], [7], [8], [9]]. For the power generation application, these materials include Bi₂Te₃ and its alloy [10], silicides [11], PbTe [[12], [13], [14]], half-Heusler [15], poly(3,4-ethylenedioxythiophene): poly(styrenesulfonate) (PEDOT: PSS) [16], and graphene and composites [17]. The theoretical studies of traditional TEGs have been conducted for solid cuboid structure, usually with a large temperature difference and under conditions of conductive heat transfer [[18], [19], [20]]. These models have provided important engineering design guidelines in traditional rigid TEGs by changing the cross-sectional area, length and segment of solid p- and n-type TE legs for the high output performance [[21], [22], [23], [24]]. However, these models cannot be applied in the wearable applications where the temperature at one end is fixed but at the other end is free. For example, the surface temperature of human torso can be regarded as a constant. Under this condition, the temperature at the other end is the result of the heat transfer.

Three-dimensional (3D) spacer fabric structure may offer high specific output power from the FTEGs because of the light weight and the large temperature difference between the face and back sides connected by numerous one-dimensional (1D) FTEG units¹. The output performance of the 3D FTEGs is determined by those of 1D FTEGs. Compared with the thick TE columns in traditional rigid TEG arrays, the 1D FTEG units have much higher aspect ratio, which results in the large deformability and flexibility. A recent work reported 3D space fabric FTEGs comprising 1D FTEG units where the core was a carbon nanotube yarn (CNTY) acting as a continuous electrode³. The sheath was coated with p-type PEDOT: PSS and n-type polyethyleneimine (PEI). It is not desirable that in the FTEGs much thermal energy was conducted from the hot to cold end through the CNTY of high thermal conductivity. Therefore, higher performance of the FTEG can be achieved with a more appropriate consideration of materials and device structure, ideally guided by a quantitative analytical tool.

Hence, this paper presents a quantitative approach to predict the performance of 3D FTEG composed of 1D FTEG array in simulated wearable conditions, that is, under conductive and radiative heat transfer with low temperature differences. The single 1D FTEG unit, consisting of core/sheath fiber TEG leg and electrodes, is dealt with under conduction and radiation heat transfer. The influences of the radius and the length of filament, the thickness of TE coating layer, the distance between the adjacent surfaces of 1D FTEGs and the surface emissivity are quantified. Finally, the upper limits of output power and conversion efficiency of the FTEG array device with various TE materials are given if worn on a human torso back under a range of ambient temperature.