The universal influence of contact resistance on the efficiency of a thermoelectric generator

The influence of electrical and thermal contact resistance on the efficiency of a segmented thermoelectric generator is investigated. We consider 12 different segmented $p$-legs and 12 different segmented $n$-legs, using 8 different $p$-type and 8 different $n$-type thermoelectric materials. For all systems a universal influence of both the electrical and thermal contact resistance is observed on the leg's efficiency, when the systems are analyzed in terms of the contribution of the contact resistance to the total resistance of the leg. The results are compared with the analytical model of Min and Rowe (1992). In order for the efficiency not to decrease more than 20%, the contact electrical resistance should be less than 30% of the total leg resistance for zero thermal contact resistance, while the thermal contact resistance should be less than 20% for zero electrical contact resistance. The universal behavior also allowed the maximum tolerable contact resistance for a segmented system to be found, i.e. the resistance at which a leg of only the high temperature thermoelectric material has the same efficiency as the segmented leg with a contact resistance at the interface. If e.g. segmentation increases the efficiency by 30% then an electrical contact resistance of 30% or a thermal contact resistance of 20% can be tolerated.Comment: 8 pages, 8 figure

An analytical model for the influence of contact resistance on thermoelectric efficiency

An analytical model is presented that can account for both electrical and hot and cold thermal contact resistances when calculating the efficiency of a thermoelectric generator. The model is compared to a numerical model of a thermoelectric leg, for 16 different thermoelectric materials, as well as the analytical models of Ebling et. al. (2010) and Min \& Rowe (1992). The model presented here is shown to accurately calculate the efficiency for all systems and all contact resistances considered, with an average difference in efficiency between the numerical model and the analytical model of $-0.07\pm0.35$ pp. This makes the model more accurate than previously published models. The maximum absolute difference in efficiency between the analytical model and the numerical model is 1.14 pp for all materials and all contact resistances considered.Comment: 8 pages, 5 figure

The demagnetization factor for randomly packed spheroidal particles

We investigate if the demagnetization factor for a randomly packed powder of magnetic spheroidal particles depend on the shape of the spheroidal particles and what the internal variation in magnetization is within such a powder. A spheroid is an ellipsoid of revolution, i.e. an ellipsoid with two semi-major axis being equal. The demagnetization factor is calculated as function of particle aspect ratio using two independent numerical models for several different packings, and assuming a relative permeability of 2. The calculated demagnetization factor is shown to depend on particle aspect ratio, not because of direct magnetic interaction but because the particle packing depend on the aspect ratio of the particles. The relative standard deviation of the magnetization across the powder was 3\%-8\%, increasing as the particle shape deviates from spherical, while the relative standard deviation within each particle was relatively constant around 5\%.Comment: 7 pages, 9 figure

The performance of a combined solar photovoltaic (PV) and thermoelectric generator (TEG) system

The performance of a combined solar photovoltaic (PV) and thermoelectric generator (TEG) system is examined using an analytical model for four different types of commercial PVs and a commercial bismuth telluride TEG. The TEG is applied directly on the back of the PV, so that the two devices have the same temperature. The PVs considered are crystalline Si (c-Si), amorphous Si (a-Si), copper indium gallium (di)selenide (CIGS) and cadmium telluride (CdTe) cells. The degradation of PV performance with temperature is shown to dominate the increase in power produced by the TEG, due to the low efficiency of the TEG. For c-Si, CIGS and CdTe PV cells the combined system produces a lower power and has a lower efficiency than the PV alone, whereas for an a-Si cell the total system performance may be slightly increased by the TEG.Comment: 10 pages, 6 figure

Topology optimized permanent magnet systems

Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered. First, the Halbach cylinder is topology optimized with iron and an increase of 15% in magnetic efficiency is shown, albeit with an increase of 3.8 pp. in field inhomogeneity - a value compared to the inhomogeneity in a 16 segmented Halbach cylinder. Following this a topology optimized structure to concentrate a homogeneous field is shown to increase the magnitude of the field by 111% for the chosen dimensions. Finally, a permanent magnet with alternating high and low field regions is considered. Here a $\Lambda_\mathrm{cool}$ figure of merit of 0.472 is reached, which is an increase of 100% compared to a previous optimized design.Comment: 10 pages, 10 figure

Modeling the microstructural evolution during constrained sintering

A numerical model able to simulate solid-state constrained sintering is presented. The model couples an existing kinetic Monte Carlo (kMC) model for free sintering with a finite element model (FEM) for calculating stresses on a microstructural level. The microstructural response to the local stress as well as the FEM calculation of the stress field from the microstructural evolution is discussed. The sintering behavior of a sample constrained by a rigid substrate is simulated. The constrained sintering results in a larger number of pores near the substrate, as well as anisotropic sintering shrinkage, with significantly enhanced strain in the central upper part of the sample surface, and minimal strain at the edges near the substrate. All these features have also previously been observed experimentally.Comment: 9 pages, 7 figure

The efficiency and the demagnetization field of a general Halbach cylinder

The maximum magnetic efficiency of a general multipole Halbach cylinder of order $p$ is found as function of $p$. The efficiency is shown to decrease for increasing absolute value of $p$. The optimal ratio between the inner and outer radius, i.e. the ratio resulting in the most efficient design, is also found as function of $p$ and is shown to tend towards smaller and smaller magnet sizes. Finally, the demagnetizing field in a general $p$-Halbach cylinder is calculated, and it is shown that demagnetization is largest either at $\cos 2p\phi=1$ or $\cos 2p\phi=-1$. For the common case of a $p=1$ Halbach cylinder the maximum values of the demagnetizing field is either at $\phi = 0,\pi$ at the outer radius, where the field is always equal to the remanence, or at $\phi = \pm \pi/2$ at the inner radius, where it is the magnitude of the field in the bore. Thus to avoid demagnetization the coercivity of the magnets must be larger than these values.Comment: 5 pages, 5 figure

The lifetime cost of a magnetic refrigerator

The total cost of a 25 W average load magnetic refrigerator using commercial grade Gd is calculated using a numerical model. The price of magnetocaloric material, magnet material and cost of operation are considered, and all influence the total cost. The lowest combined total cost with a device lifetime of 15 years is found to be in the range \$150-\$400 depending on the price of the magnetocaloric and magnet material. The cost of the magnet is largest, followed closely by the cost of operation, while the cost of the magnetocaloric material is almost negligible. For the lowest cost device, the optimal magnetic field is about 1.4 T, the particle size is 0.23 mm, the length of the regenerator is 40-50 mm and the utilization is about 0.2, for all device lifetimes and material and magnet prices, while the operating frequency vary as function of device lifetime. The considered performance characteristics are based on the performance of a conventional A$^{+++}$ refrigeration unit. In a rough life time cost comparison between the magnetic refrigeration device and such a unit we find similar costs, the former being slightly cheaper, assuming the cost of the magnet can be recuperated at end of life.Comment: 17 pages, 17 figure