Module Design Considerations

It can be seen from previous sections that thermoelectric material properties are critical requirements for the design of better-performing TEMs. However, there are significant parasitic losses when the materials are integrated to form a complete thermoelectric module.

The most notable influences are contact resistance and module geometry. Due to these influences, the module’s performance could be below the values (η_maxor COP_max) predicted on the basis of the ZT of the component materials [54]. Much research has been done to reduce contact resistance and optimize the geometrical parameters of the TEMs, so as to achieve better-performing modules.

2.2.2.1 Contact Resistance

Due to the machining limitations, two solid surfaces will never form a perfect contact when they are pressed together. Even if the surfaces look perfectly smooth, tiny air gaps will always exist between the two contacting surfaces due to roughness. Figure 2.7 presents the locations of thermal and electrical contact resistances [55]. The contact resistances within a TEM include the electrical resistances on both sides of thermoelectric elements, the thermal resistances between the conductive tabs and the ceramic plates and the thermal contact resistance between the thermoelectric elements and the conductive tabs. The influence of contact resistance on the TEMs’ performance can be seen in many experimental TEMs tests [56–60]. Wang et al. [56] found that increasing loading pressure can lead to a decrease in the thermal contact resistance and an increase in both the actual temperature difference across the module and the output power. Sakamoto et al. [57] used CoSi2 as electrodes for the Mg2Si module. 35 % decrease in electrical contact resistance and 27 % increase in output powers were observed.

Based on abundant module test results, both electrical and thermal contact resistances were taken into account when calculating the efficiency of the TEMs. Min and Rowe [61] gave a new expression for the maximum efficiency of a thermoelectric generator modules, in the presence of both an electrical and thermal contact resistance.

ηmax= T_h− Tc where Rc,l, Rc,eare respectively thermal and electrical contact resistance of the TEM. Rl,e

and Rl,T are respectively electrical or thermal resistance of the thermoelectric elements.

Bjφrk et al [62]. also built an analytical model with enough accuracy to calculate the influence of electrical and thermal contact resistance on the efficiency of a TEM. In Bjφrk’s model, the influence of thermal contact resistance was modelled as a factor controlling the temperature span across the thermocouples (T_h.leg and T_c.leg). The electrical contact resistance was modelled as a single external electrical resistance.

Many efforts have also been put into decreasing the magnitude of the contact resistance.

Wang et al. [56] found that increasing loading pressure and application of the thermal grease

Figure 2.8: An example of a TEM design parameters [65]

to the contact interface can lead to a decrease in the thermal contact resistance. Tanji et al. [63] proved that the use of the metallic paste forming bond between thermoelectric mate-rial and electrode is an effective way to achieve low thermal and electric contact resistance.

Nemoto et al. [60] used a Ag-based brazing alloy to join the thermoelectric elements and Ni terminals so as to to reduce the electrical and thermal contact resistance of the module.

Funahashi et al. [64] constructed thermoelectric elements using Ag paste containing p-type and n-type oxide powders for the connection between thermoelectric elements and Ag elec-trodes. The incorporation of oxide powders in Ag paste was showed to be effective to reduce the contact resistance.

2.2.2.2 Module Geometry

Except for the contact resistance, module geometry is another important factor that needs to be considered when designing a TEM. The main geometrical parameters for a TEM include the width, length, and height of the thermoelectric elements and ceramic plates and the occupancy rate of the thermoelectric elements in a module (fill factor). Figure 2.8 shows an example of the geometrical design parameters for a TEM [65].

Investigations found that the geometric structure has remarkable effects on the performance of modules [61, 66–69]. Min and Rowe [66] found that the optimum length of thermoelectric

elements (leg length) to obtain maximum power output differed from that for the maximum conversion efficiency. A compromise had to be made between the requirements for maximum power output and maximum conversion efficiency when optimizing the leg length. Meng et al. [67] adopted a multi-objective and multi-parameter optimization approach to design the optimal structure of a module. Three geometric parameters, number of thermocouples, length thermoelectric element, and occupancy rate of the thermoelectric elements in a mod-ule, were taken as searching variables, which are optimized simultaneously. By setting a weight factor, the power output and efficiency of the module were both improved simulta-neously. Huang et al. [68] built a complete three-dimensional model for a heating-cooling module and used a simplified conjugate-gradient method to optimize geometric structure of the heating-cooling module. The effects of applied current and temperature difference on the optimal geometry had been found out. The optimization results proved that small current and high temperature difference could lead to an increase in the optimum number for the thermocouples. Meydbray et al. [69] investigated the module geometry experimentally by testing modules with different surface area. It found out that the output power showed a significant dependence on module surface area.

Achieving better performance of modules cannot be the only target for module geometrical optimization. The TEMs also need to be cost effective. Thus, there is also a need for module geometrical parameters to be designed based on cost-performance trade-off analyses. Min and Rowe [66] proposed that the module geometry should also be optimized to minimise the cost of the generated electricity. Based on this principle, an optimisation procedure for the module geometry was reported by using an economic factor (£/kWh). Xuan et al. [70]

optimized the design parameters for a heating-cooling module to minimize the total cost, which included both the module and supplied electricity costs. Based on a thermal network model, a general expression for the total cost and an optimization procedure to minimize the total cost were described. Yee et al. [71, 72] developed an analytical framework to quantify the tradeoff between performance and cost in a system level. A new cost-performance metric ($ per W) was developed to optimize the fill factor and leg length to minimizes the ratio of cost to performance.

Figure 2.9: Possible locations for the installation of the TEG in the exhaust system of the vehicles