# Heat Transfer in Thermoelectric Generators for Waste Energy Recovery in Piston Engines
## 1 Introduction  
Waste energy through exhaust systems in internal combustion engines is one of the most concerning topics regarding fuel economy, as it is known that approximately a third of the fuel energy input is lost [1]. Thermoelectric generators (TEGs) [2] are devices with the ability to directly convert thermal energy to electrical energy from a temperature gradient using the Seebeck effect. Despite being initially employed almost exclusively in the space industry, thermoelectric generators are currently being investigated as a way of recovering the waste energy from the exhaust gases of ground vehicles, airplanes, industries, etc. [PERSON] et al. [3] studied the potential of harvesting energy from exhaust gases. The influence of the downstream air flow in the lower part of the same vehicle was also studied [4]. In [PERSON] et al. [5], an energy and exergy analysis of thermoelectric recovery from exhaust gases was performed. The baseline waste energy power that can be recovered without heat exchangers or any modifications to the exhaust systems was quantified. In [PERSON] et al. [6], the thermoelectric potential of exhaust gases at different altitudes and with different fuels was analyzed. From the references above, it can be seen that the exhaust gas potential as a waste heat source in internal combustion engines has been studied, but generally, when it comes to heat source assessments, considering the original geometry. However, exhaust gases heat transfer coefficient is far from high [5]. Typically, the adopted solution consists of installing some kind of heat exchanger to increase the heat transfer to the thermoelectric modules. In this way, there are several studies that have dealt with this problem in the literature. [PERSON] et al. [7] analyzed an exhaust heat recovery TEG consisting of 72 Si-Ge TEMs, generating an electric power of up to 35.6 W from a 3 L gasoline engine vehicle. [PERSON] et al. [8] examined the feasibility of waste heat recovery from 24 Bi\({}_{2}\)Te\({}_{3}\)-based thermoelectric modules (TEG), where a maximum power output of 12.41 W was produced. Introducing a heat exchanger means taking several factors into account, given that its final target is optimizing the energetic generation of the TEG: device size, type of exchanger, internal geometry, place where it will be installed, contact surface with TEMs, operating engine conditions, etc. [9]. A cylindrical design with internal folded fins was developed by [PERSON] et al. [10], improving an initial planar design for a BMW's 3 L inline six-cylinder engine. [PERSON] et al. [11] presented a compact and lightweight heat sink that is integrated in the TEG system while being assisted by heat pipe technologies to reinforce heat flux through the thermoelectric generator surface, setting them up in the exhaust stream's radial direction. It is necessary to minimize the impact on engine operation, which means that the backpressure produced by the heat exchanger must be reduced as well [12]. In [PERSON] et al. [9], a design of experiments for a flat-shaped TEG heat exchanger was created, and the influence of internal geometry features was analyzed. A trade-off coefficient between transferred heat and pressure drop losses was defined. [PERSON] et al. [13] designed six exhaust heat exchangers with their respective CFD models to compare both heat transfer and pressure drop values for a 1.2 L gasoline engine. [PERSON] et al. [14] proposed a cylindrical heat exchanger in order to enhance the heat transfer rate as well as the heat transfer area and turbulence intensity. In comparison with other structures, it achieved an improvement in TEG efficiency combined with low backpressure. [PERSON] et al. [15] studied the net thermoelectric generator power output using inner channel geometries with alternating flow impeding panels. An exhaustive analysis of the effect of a thermoelectric generator in an internal combustion engine with a global energy balance including all energy flows can be found in [PERSON] et al. [16]. [PERSON] et al.