Transient interlaminar thermal stress in multi-layered thermoelectric materials

This paper studies the transient interlaminar stress in a multilayered thermoelectric material (TEM), which consists of a N-type and a P-type thermocouple, separated by an insulating layer. Analytical solution for one-dimensional temperature and the associated interlaminar stresses at the steady-state and the transient state are obtained. The influence of insulating layer’s thickness and material properties on the peeling stress, which is the key reason for delamination, has also been investigated. Distribution of the temperature and interlaminar stress are presented graphically. The interlaminar stress at the free ends of the TEM shows significant stress concentration. A thinner insulating layer results in a smaller interlaminar stress. The interlaminar stress also reduces if the insulting layer has a smaller Young’s modulus. The value of the transient interlaminar stress is found to be very different from that of the steady-state. Overall, the interlaminar stress level at the transient-state is higher than that at the steady-state

Thermally induced vibration and strength failure analysis of thermoelectric generators

Thermal vibration and the strength failure of a thermoelectric generator (TEG) subjected to the time-dependent heat flux is discussed in this paper. The heat flux is considered as varying along the circumference of the circular cross section of the TEG, which consists a series of n-type and p-type thermoelectric elements. Vibrations that are parallel and perpendicular to the gravity direction are analyzed, respectively. Analytical and simplified solutions of the vibration deflections of the TEG are given. The maximum principal stress in the TEG is derived analytically. Based on the criterion of maximum principal stress, the envelop curve of heat flux and electric current density corresponding to failure strength of the TEG is obtained. It is found that the vibration deflection is proportional to the heat flux and the value of square electric current. The thermal vibration reduces the output power of the TEG but it only has effect on the output power in a very short time. A bigger damping ration results in a smaller maximum principal stress. The maximum principal stress does not vary with the damping ratio if the length of TEG is small. The critical heat flux and electric current density increase and finally trend to constants with damping ratio

Analysis of thermally induced delamination and buckling of thin-film thermoelectric generators made up of pn-junctions

This paper investigates the problem of delamination and buckling of thermoelectric pn-junctions, which have many potential civil and military applications including thermal protection systems in space industry. Based on the compatibility equations of deformation, equilibrium equations of axial force and the strain compatibility equation at the interface of the bonding part are derived. Analytical solution of the delamination energy release rate is obtained. It is noted that there is no energy release rate when the magnitude of the temperature difference between the right end and the left end of the pn-junction is zero. The energy release rate can decrease or increase with the coefficient of thermal expansion. Distributions of the critical temperature differences for the delamination propagation and buckling are presented graphically. The critical temperature differences decrease continually with delamination and buckling lengths. Either a higher temperature difference or a higher electric current density can result in a bigger delamination energy release rate, a larger buckling deflection and a strong axial force. The buckling deflection increases but the axial force decreases with the increase of buckling length

Effective thermoelectric conversion properties of thermoelectric composites containing a crack/hole

Despite the wide applications in engineering of thermoelectric materials, effective thermoelectric conversion behavior of cracked thermoelectric composites has never been investigated so far. To establish the effective properties of a thermoelectric composite, we revisit the general model of a bi-layered thermoelectric composite system with an interfacial crack and study the effect of interfacial cracking on the thermoelectric properties. Through an equivalent principle, the effective thermoelectric properties are given and the influence of applied temperature, crack boundary, crack size, and crack shape are discussed in detail. Generally, a higher effective figure of merit (thermoelectric conversion efficiency) can be obtained in a cracked thermoelectric composite. A significant increase of the effective figure of merit can be observed as the crack size getting larger. In practical engineering, the results in this paper will have a good approximation for cracked thermoelectric composites and can be directly used for design and optimization of thermoelectric devices

Effect of buckling on the cooling performance of free-standing planar thermoelectric coolers

This article investigates the effect of buckling on the cooling performance of planar thermoelectric (TE) coolers (TECs). The TEC is made up of n-type and p-type TE elements with large length-to-thickness ratio. Each TE element is modeled as a fixed–fixed thin plate. Theoretical model for the solutions of temperature and electric potential fields of the TE element after buckling is established. The corresponding coefficient of performance (COP) that indicates the cooling performance of TEC is also given. Influence of Seebeck coefficient, thermal conductivity, temperature difference, and the ratio of length-to-thickness on the cooling performance are discussed. It is found that buckling of TEC will reduce its cooling performance. A bigger Seebeck coefficient and smaller thermal conductivity can both improve the value of COP. It is also found that there is no maximum COP when the temperature difference across the TEC is zero. However, the effect of buckling on the cooling performance of TEC can be ignored if the TEC achieves the maximum COP. The peak value of COP is independent of the ratio of length-to-thickness of the TEC. An optimized value of the electric current corresponding to the maximum COP of the TEC is obtained

Modeling of thermoelectric generators with effects of side surface heat convection and temperature dependence of material properties

This paper develops a general model to analyze the performance of thermoelectric generators (TEGs) with consideration of their side surface heat convection (SSHC) and temperature-dependent material properties. The closed-form solutions of temperature field and energy conversion efficiency are derived, and the analytical results agree well with numerical results as well. These explicit expressions can be used to evaluate the performance of TEGs under various boundary conditions directly. Based on the derived expressions of temperature and efficiency, we find that the optimization of a TEG module can be attributed to only three parameters. Through an example, we give some useful suggestions for the design of high-performance thermoelectric modules

Power output evaluation of a porous annular thermoelectric generator for waste heat harvesting

Comparing with traditional thermoelectric generators (TEGs) heating a solid body and extracting heat indirectly, porous TEGs can directly extract heat from gaseous/liquid medias and convert them into electric power. This paper considers the electrical and thermal contact resistances between the heat source/heat sink and TEG, and evaluates the power output of a porous annular TEG for waste heat harvesting. A theoretical model for the effects of gas velocity, the external resistance, porosity and the electrical/thermal contact resistances on power output is proposed. Analytical and simplified expressions of power output are derived. The analysis demonstrates that the porous structure can significantly enhance the performance of TEG comparing to the bulk TEG. It is found that power output is proportional to the temperature difference across the TEG and inversely proportional to the cross-sectional area of the TEG. Effect of gas velocity on the power output is relatively insignificant. The power output increases to a peak value and then decreases with porosity, external electrical resistance and cross section area of TEG. The optimized area of cross section and porosity of TEG for maximum power output are given. With the increase of external electrical resistance, porosity should be enhanced to obtain the maximum power output. Relation between the optimized porosity and pore diameter of sample is presented

Analysis of thermally induced delamination of thermoelectric thin film/substrate system

Thermoelectric thin film/substrate structures have many practical applications such as in heat recovery systems. The general problem of thermally induced delamination between a thermoelectric thin film and a substrate is investigated. The temperature varies along the length direction but is constant along the thickness direction of the film. Analytical solutions of the temperature field in the film and the stress intensity factors (SIFs) at the delamination crack tips are obtained. The combined heat convection and heat radiation between the film surfaces and the surrounding medium (i.e., the air) are taken into account. Numerical results show that the SIFs sharply increase as the tips of the delamination crack approach the ends of the film. The combined heat convection and heat radiation can increase or decrease the SIFs. The mechanism for the delamination propagation in the thermoelectric film/substrate system is examined. The critical (permissible) temperature difference across the film governing the delamination propagation is identified

Analysis of inclusion in thermoelectric materials : the thermal stress field and the effect of inclusion on thermoelectric properties

This paper analyses a two-dimensional problem in thermoelectric materials with an inclined elliptic inclusion. We have obtained the closed-form solutions of electric current density and temperature considering the inclusion's electrical and thermal permeability. Based on the derived thermoelectric field, the thermal stresses are given in the explicit form and the effect of inclusion on effective thermoelectric properties is investigated. The electrically impermeable and thermally impermeable inclusions will respectively cause maximum electric current concentration and heat concentration. The thermally impermeable and rigid inclusion will cause maximum stress concentration around the inclusion. Furthermore, we find that the effective electric conductivity (effective thermal conductivity) of the matrix-inclusion system is increased when the inclusion have higher electric conductivity (thermal conductivity) than the matrix. It is possible to enhance the effective figure of merit by inserting inclusions with specific electric conductivity and heat conductivity. It predicts a new way for the design of high-performance thermoelectric devices. The results in this paper can be directly used for reliability consideration in design and optimization of thermoelectric devices in engineering

Time-dependent power output and elastic/plastic fracture analyses of porous thermoelectric ceramics for generators

If made in porous foam, thermoelectric ceramics for power generation can enhance the power output by directly extracting thermal energy from heat sources. This paper discusses the time-dependent power output and elastic/plastic fracture of the porous thermoelectric generator (TEG) with a small oblique-through crack. Analytical solutions of temperature and thermal stress of the TEG are derived based on an effective model of porous foam. The finite element numerical model is created to validate the analytical solutions and to explore more thermomechanical properties and constitutive behaviors of the porous materials. Comparing to the traditional bulk TEG, porous TEG can greatly improve the power output however the thermal stress is enhanced therefore the strength is substantially reduced. The power output gradually increases to a peak value and then decreases with the length of the TEG. Based on the criterion of fracture mechanics, a simplified and useful expression of the critical heat flux for crack propagation is identified. The critical heat flux for crack growth is inversely proportional to the porosity and the crack length. A more rigid contact between the TEG and the elastic boundary results in a larger thermal stress and a smaller critical heat flux. The velocity of crack propagation is mostly determined by the porosity and the ratio of the initial crack length to the arbitrary crack length. Also observed is that the length of plastic zone at the crack tips increases with the increasing porosity