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• Solar cooling system consisting of a DSSC and a ATEC is established. • The hybrid system is analyzed in terms of energy and exergy. • The hybrid system performance with and without Thomson effect is compared. • The effects of key parameters on the hybrid system performance are revealed. For round shaped cooling space, a dye-sensitized solar cell (DSSC) is used to drive annular thermoelectric cooler (ATEC) to solve the performance deterioration caused by geometric mismatch, in which ATEC considers Seebeck effect, Peltier effect and Thomson effect. Considering all kinds of irreversible losses between DSSC and ATEC, the mathematical formula of performance parameters of hybrid system is derived. The effects of Schottky barrier height, thickness of TiO 2 film, thickness of ATEC, number of thermoelectric elements and annular parameter of the ATEC on the cooling capacity and coefficient of performance (COP) of the coupling system are analyzed theoretically. The theoretical calculation results show that the maximum cooling capacity and COP of the hybrid system are 68.75 W/m2 and 0.071, respectively. In addition, it can be found that the positive Thomson effect had a positive influence on the thermoelectric cooling system. The findings of this work have the potential to provide fresh light of solar-driven annular thermoelectric cooler matching with actual round shaped cooled spaces. [ABSTRACT FROM AUTHOR]

To harvest the waste heat from exothermic reaction processes, a novel hybrid system model mainly incorporating a high-temperature proton exchange membrane fuel cell (HT-PEMFC) and a duplex thermoelectric cooler is conceptualized to theoretically predict the potential performance limit. The duplex thermoelectric cooler is composed of a thermoelectric generator (TEG) and a thermoelectric cooler (TEC), where the TEG harvests the waste heat to generate electricity and the TEC utilizes the generated electricity for cooling production. A mathematical model is established to estimate the proposed system performance from both exergetic and energetic perspectives considering various irreversible effects, from which effectiveness and practicality of the proposed system can be examined. The hybrid system maximal output power density allows 14.1% greater than that of the basic HT-PEMFC, whereas the according destruction rate density of exergy is decreased by 7.7%. The feasibility and effectiveness of the proposed system configuration are verified. Moreover, substantial parametric analyses indicate that the proposed system performance can be improved by elevating the HT-PEMFC operating temperature, inlet relative humidity and doping level while worsened by enhancing the leak current density, electrolyte thickness and Thomson coefficient. The results acquired may be helpful in designing and optimizing such an actual hybrid system. • An HT-PEMFC/duplex thermoelectric cooler hybrid system is put forward. • Models of both HT-PEMFC and duplex thermoelectric cooler are well described. • Key performance indicators for evaluating the hybrid system are formulated. • Performance features and effectiveness of this kind of hybrid system are revealed. • Effects of decisive variables on the hybrid system performance are discussed. [ABSTRACT FROM AUTHOR]

• A broad-spectrum photovoltaic system is achieved. • An integrated system is proposed for power and cooling purposes. • The output power density and efficiency of the hybrid system are improved. • The effect of some parameters on the whole system performance is analyzed. For ample utilization of the inlet sunlight, a novel coupled system composed of a photovoltaic module (PVM), a thermoelectric generator (TEG), and a thermoelectric cooler (TEC) is proposed. Short-wave sunlight is sent to PVM to generate electricity, while long-wave sunlight is converted by SSA into heat for TEG-TEC to provide additional cooling. Considering diverse irreversible losses of the cogeneration system, the current relationship between the PVM and the TEG-TEC is analyzed. Besides, the expressions for the performance indexes of the coupled system are deduced under distinct operating conditions. Numerical calculation results illustrate that the power output density and efficiency of the cogeneration system are 3.98% and 3.97% greater than those of a single PVM system in the working current range of TEG-TEC, respectively. Furthermore, the power output density and efficiency of the coupled system with the Thomson effect are, respectively, reduced by 2.47% and 2.46% compared with the proposed system without the Thomson effect. Finally, the impacts of solar irradiance, PVM operating temperature, thermoelectric elements number, environment temperature, and diode ideality factor on the overall module performance are explored. This study results may supply some new ideas for enhancing PVM performance. [ABSTRACT FROM AUTHOR]

Despite significant attention paid to thermoelectric generators in the energy conversion field, their limited output performance has restricted their large-scale applications. Therefore, there is a pressing need to conceive a novel thermoelectric device concept that can strengthen their competitiveness. In this context, the concept and principle of thermoelectric (TE) transistor with ultrahigh performance is a demand-driven innovation. Built on the foundation of a PNP structure, TE transistor only relies on the Seebeck voltage to operate normally. This work employs P-type Bi 0.5 Sb 1.5 Te 3 and N-type Bi 2 Te 2.97 Se 0.03 as the component materials. By considering the conduction heat, Joule heat, Thomson heat, and temperature-dependent material properties, a one-dimensional heat transfer model was used to obtain the nonlinear temperature profile inside TE transistor. Further, the structure and operation conditions of TE transistor with varying geometric dimensions were determined based on the hole concentration distribution and build-in voltage variation. Finally, the optimal concentrations and geometric dimensions of TE transistor were obtained using a compromise method. The calculation results reveal that TE transistor can achieve an optimal output power of 133.7 mW under a temperature difference of 50 K (T h = 353 K, T c = 303 K) with the corresponding conversion efficiency of 7.73%. This work provides theoretical guidance for future experimental validation of TE transistor. • A feasible and comprehensive theoretical design for thermoelectric (TE) transistor is developed. • The non-linear temperature profile inside TE transistor is determined based on the heat conduction analysis. • Influence of the Thomson effect on TE transistor output performance is analyzed. • Output power of TE transistor is improved greatly by the geometry optimization. [ABSTRACT FROM AUTHOR]

• We studied the influence of Thomson effect on the performance of the Thermoelectric generators (TEGs) with temperature-dependent Seebeck coefficient. • The performance of the TEGs can either be depressed or promoted by the Thomson effect, depending on the temperature difference between the cold- and hot-ends and the Seebeck coefficient of the legs. • The Thomson effect always weakens the improvement of TEG performance induced by increasing the figure of merit (ZT) of the thermoelectric materials. Heat can be converted to electricity by thermoelectric generators (TEGs) directly. In consideration that the thermoelectric properties of the legs depend on the temperature strongly, the Thomson effect affects heat production, heat transfer, and energy conversion. Consequently, the Thomson effect cannot be neglected during evaluating the performance of the TEGs. In this work, we studied the influence of Thomson effect on the performance of the TEGs. Linear and polynomial fitting Seebeck coefficients of the thermoelectric materials are adopted and the three-dimensional thermo-electric coupled equations are solved by the finite-element method to obtain the output power and the conversion efficiency. Our results showed that the performance of the TEGs can either be depressed or promoted by the Thomson effect, depending on the temperature difference between the cold- and hot-ends and the Seebeck coefficient of the legs. Moreover, the Thomson effect always weaken the improvement of TEG performance by the means of increasing the figure of merit (ZT) of the thermoelectric materials. We then applied our model to study the performance of TEGs with Bi 2 Te 3 as the legs and found the difference between the conversion efficiencies with Thomson effect and without Thomson effect increases fast with the temperature difference between the hot- and cold-ends. This study could be useful for guiding the searching for TEG system that are potentially high performance and compatible with environmental-friendly application. [ABSTRACT FROM AUTHOR]

A combined system model consisting of a high-temperature polymer electrolyte membrane fuel cell (HT-PEMFC), a regenerator and a thermoelectric generator (TEG) is proposed, where the TEG is applied to harness the generated waste heat in the HT-PEMFC for extra electricity production. The TEG considers not only the Seebeck effect and Peltier effect but also the Thomson effect. The mathematical expressions of power output, energy efficiency, exergy destruction rate and exergy efficiency for the proposed system are derived. The energetic and exergetic performance characteristics for the whole system are revealed. The optimum operating ranges for some key performance parameters of the combined system are determined using the maximum power density as the objective function. The combined system maximum power density and its corresponding energy efficiency and exergy efficiency allow 19.1%, 12.4% and 12.6% higher than that of a stand-alone HT-PEMFC, while the exergy destruction rate density is only increased by 8.6%. The system performances are compared between the TEG with and without the Thomson effect. Moreover, the impacts of comprehensive parameters on the system performance characteristics are discussed. The obtained results are helpful in developing and designing such an actual combined system for efficient and clean power production. • TEGs are proposed as a waste heat recovery technology for HT-PEMFCs. • Thermal-electrochemical losses within the proposed system are described. • Performance parameters evaluating the proposed system are obtained. • The proposed system is effective for waste heat recovery. • Effects of some design parameter and operating conditions are revealed. [ABSTRACT FROM AUTHOR]

Abstract An original model of directional eutectic growth for lamellar eutectics is presented. This model is based on the analysis of thermodynamic equilibrium at the solidification front. Contrary to previous ones, this model does not use linearization hypothesis on the alloy phase diagram and takes into account variations of densities between phases. Moreover, curvature effects are considered on thermodynamic equilibrium at the solidification front. Its numerical implementation is made possible through a coupling with thermodynamic software based on the CALPHAD approach. This new numerical model is applied to the Al-Al 2 Cu eutectic structure and compared to the Jackson-Hunt theory. Large differences between results of the present model and this theory are observed at high growth rate. In particular, curvature effects on phases concentrations can no more be modeled using a linear approximation, as in the Gibbs-Thomson relation. A good agreement of the numerical model with reported experimental studies is observed for a large range of growth velocities. Graphical abstract Image 1 [ABSTRACT FROM AUTHOR]

To utilize heat from round shaped heat sources or heat sinks effectively, a segmented annular thermoelectric generator was proposed. Each leg is composed of two materials with different optimum operating temperatures jointed in series. Based upon a developed theoretical model, the influences of annular shape parameter, height ratios of high temperature segment to leg in p- and n-type legs, temperature ratio and load ratio on the performance of segmented annular thermoelectric generator were studied. A finite element method was adopted to consider the Thomson effect and temperature-dependence of materials. Performance comparisons with simply non-segmented annular thermoelectric generators were conducted. For application security, the interface temperatures were analyzed. Results show that compared to a simply non-segmented annular thermoelectric generator, the superiority of segmented annular thermoelectric generator becomes visible with rising temperature ratio. As the annular shape parameter increases, the power rises firstly and then declines, and the optimal annular shape parameter is around 1.0, but not strictly equal to 1.0. Besides, the optimal ranges of height ratios in p- and n-type legs for higher performance are identified. The current study demonstrates the potential of segmented annular thermoelectric generator from the perspectives of performance and practicability. [ABSTRACT FROM AUTHOR]

In this paper, the thermodynamics evaluation of an irreversible CPV-TEG cogenerating system, having Siemens SP75 PV module and commercially available Bi 2 Te 3 TE module, has been investigated for wide solar spectrum to encompass the winter and summer solar radiation. Modeling and simulation of the hybrid system has been carried out to understand the feasibility of the system and to determine the irreversibilities present in the hybrid system. The irreversibilities or exergy destruction caused by the irreversible conversion process of solar energy into electricity are calculated using exergy analysis based on second law of thermodynamics. The various exergy losses occurring in the hybrid system have been calculated using exergy analysis. The effects of the incident solar irradiance varying in a wide range from 100 W/m 2 to 1000 W/m 2 , TEG junction temperature ratio, concentration ratio, TEG current, Thomson coefficient, irreversibilities or exergy destruction and the incoming solar radiation exergy have been studied. The results showed that the Thomson effect has adverse effect on the performance of the hybrid system and the irreversibilities increase with increase in concentration ratio, C . Further, the power output of hybrid system increases by 86% as C increases from 1 to optimum value of 3 and the exergy efficiency is higher than the energy efficiency by 8%. The higher values of the irreversibilities make the system less inefficient and therefore, significant improvements are required because the elevated temperature could result in hot spots formation. The results of this analysis may be helpful in designing of practical CPV-TEG hybrid system. [ABSTRACT FROM AUTHOR]

Analytical solutions of transient temperature distributions within semiconductor elements are presented in this study. The performance of a thermoelectric cooler (TEC) under the influences of the Thomson effect, Joule heating, and combined radiation and convection cooling is investigated. The solution of the temperature distributions is obtained by solving the governing heat conduction equation using the superposition technique with the aid of a special transformation function. The closed-form transient temperature profiles for the semiconductor element sizes, applied current, cooling load, heating power, power consumption, and the system coefficient of performance (COP) of a TEC are presented. The interrelationships between the aforementioned effects are examined in detail. The analytical temperature solution presented in this study can be utilized by design engineers in the thermoelectrics industry as a convenient means to demonstrate compliance of the device heating or cooling design specification requirements. [ABSTRACT FROM AUTHOR]

The study of annular thermoelectric generators (ATEG) has attracted more attention in recent years due to their ability to cover round shaped surfaces. Moreover, transient and pulsed inputs have been introduced as some of the effective methods to enhance the performance of thermoelectric devices. Hence, in the present study, a three-dimensional transient simulation of ATEG including the influence of Thomson effect is carried out based on finite element method. The effect of pulsed heat inputs on the performance of ATEG is studied considering rectangular, triangular, sinusoidal and two types of the sawtooth input functions for modeling the transient heat load. Electric current, voltage, output power and conversion efficiency of ATEG under pulsed and steady-state heating are compared. The effects of two critical parameters, the ratio of maximum heat flux to minimum heat flux ( b / a ) and duty cycle ( t 0 / τ ) values on the performance of ATEG are studied. Results indicate that transient pulsed heating enhances the efficiency of ATEG for all types of heat input functions. In addition, it is found that rectangular input function leads to better results compared to other functions. Also, it is shown that for a constant amount of duty cycle, the increment of ( b / a ) increases the performance of ATEG unit. For duty cycle value of 0.1 and ( b / a = 48 ) a maximum efficiency enhancement of 249.36% is achieved when the rectangular input function is employed. It is found that in the range of the studied values of ( b / a ) , the duty cycle of 0.4 leads to better results. A comparison of results with and without Thomson effect proves that the Thomson effect decreases the performance of ATEG. Additionally, it is observed that for sawtooth input functions, the implementation of heat load gradient plays an important role determining the performance. [ABSTRACT FROM AUTHOR]

Modeling thermoelectric generator (TEG) performances plays an important role in guiding the design of TEGs to achieve better efficiency. However, a rigorous 1-D TEG modeling performance has not yet been conducted, which prevents reliable prediction of TEG performance. In this work, a detailed 1-D model has been developed to take into account temperature-dependent thermoelectric material properties, heat loss due to radiation and conduction, and Thomson effect. A Lead Telluride (PbTe) TEG was chosen as a sample module and the modeling results agree very well with the experimental results, which proves how powerful the presented detailed 1-D model can be used to predict and validate TEG experimental results. TEG power and efficiency were found to have a respective decrease of 10% and 31% from the simplified model at a temperature gradient of 570 K. While heat loss attributable to conduction and radiation were found to be small, the Thomson effect, which is often neglected, was found to significantly reduce TEG performances. The deep analysis enabled by the new model provides useful guidelines to improve the performance of TEGs. [ABSTRACT FROM AUTHOR]

A solar thermoelectric generation system characterized by Fresnel lens, cavity receiver and heat pipe, i.e., FCH-STGS, was proposed. To analyze the performance of FCH-STGS accurately, a comprehensive theoretical model was built, where a finite element method was employed to consider the Thomson effect and temperature-dependence of thermoelectric materials. With this model, the influences of emissivity of ceramic plate and environment factors such as solar irradiation, optical concentration ratio, wind speed, wind incident angle, system tilt angle and ambient temperature were discussed. Results show that the FCH-STGS has the potential to reach the output power and efficiency of 45.73 W and 3.289%. Both output power and efficiency of FCH-STGS can be improved by decreasing the emissivity of ceramic plate or ambient temperature, or increasing the total solar irradiation (product of solar irradiation and optical concentration ratio). However, the efficiency reduces slightly when the total solar irradiation exceeds a certain value. As the wind speed increases, both output power and efficiency rise firstly and then fall. Due to the high thermal efficiency of cavity (exceeding 85%), the effects of wind incident angle and system tilt angle are approximately negligible. Compared with the previous STGSs, the FCH-STGS is excellent in the perspectives of performance, economy and practicability. [ABSTRACT FROM AUTHOR]

Key concepts like waste heat recycling or waste heat recovery are the basic ideas in thermoelectricity so as to the design the newest solid state sources of energy for a stable supply of electricity and environmental protection. According to several theoretical predictions; at device level, the geometry and configuration of the thermoelectric legs are crucial in the thermoelectric performance of the thermoelectric modules. Unlike to conventional geometry thermoelectric legs, asymmetrical (pyramidal) legs could help by lowering the overall thermal conductance of the device so as to increase the temperature gradient in the legs, as well as by harnessing the Thomson effect, which is generally neglected in conventional symmetrical (rectangular) thermoelectric legs. Curiously, experimental studies confirming the previous predictions have not been carried out so far, perhaps because of the existing constraints to fabricate thermoelectric legs with complex geometrical shapes. In this work, based on the promising enhancement of the thermoelectric performance in thermoelectric modules via legs with non-constant cross sections, it has been developed a novel design of a thermoelectric module having asymmetrical legs with truncated square pyramid shape, and by first time it has been validated experimentally its thermoelectric performance by realizing a proof-of concept device which shows to have almost twofold the thermoelectric figure of merit as compared to conventional one with a constant square cross section. Besides, the variables required to engineer enhanced performance thermoelectric devices are properly identified for use as power sources especially in low consumption portable devices. Therefore, the present results prove that geometrical configuration of the device legs can improve significantly the thermoelectric performance of the device. [ABSTRACT FROM AUTHOR]

An analytical model for growth in a semi-infinite matrix with cross-diffusion between species is presented. Application is given for precipitation of the γ′-phase in the γ-matrix during isothermal holding at 600 °C in the Ni - 7.56 at.% Al - 8.56 at.% Cr alloy. The exact time-dependent solutions for the solute profiles and the growth kinetics are validated with a numerical front-tracking simulation. The simulation of cross diffusion terms in a multicomponent alloy is thus demonstrated. Extension of the analytical solution is given for growth in a matrix of finite size. The driving force is then based on a mathematical estimation of the far-field composition. The Gibbs-Thomson effect is also accounted for to consider the effect of curvature on the equilibrium tie-lines. Comparison of analytical solution with the numerical front-tracking simulation shows excellent agreement. Results also point out the detrimental approximation of using the average composition of the matrix for computing the driving force as well as the limitation of the solution proposed by Chen et al. [Acta Mater. 56 (2008) 1890]. A detailed discussion is finally given on the origin of oscillations observed for the time evolution of the precipitate radius which alternates between growth and dissolution regimes, pointing out the combined role of solute fluxes and tie-lines compositions at the precipitate/matrix interface. [ABSTRACT FROM AUTHOR]

To improve the power output and efficiency of the thermoelectric generator system, the variation in the thermoelectric leg configuration is another option. In this paper, the thermodynamic analysis of exoreversible thermoelectric generator including influence of Thomson effect as well as influence of leg geometry on the power output and efficiency of the device has been carried out. The modified expressions for dimensionless figure of merit, power output, irreversibilities, energy and exergy efficiency considering Thomson effect have been derived analytically. The effects of various parameters such as dimensionless temperature ratio ( θ ), shape parameter ( R A ), Thomson effect and load resistance ratio ( R L / R 0 ) on the power output, energy and exergy efficiency have been studied. The operating range for shape parameter has been found which improves the power output, energy and exergy efficiency of the device, however, the optimum operating point corresponding to maximum power output is different from that of the maximum energy and exergy efficiency. The results of this study shows that when the shape parameter is increased from 1 (flat plate TEG) to 2 (trapezoidal TEG), then the energy and exergy efficiency improve by 2.32% and 2.31% respectively with a 1.3% decrease in power output at R L / R 0 = 10 and θ = 0.5. This study will help in designing of the improved thermoelectric generator systems for different leg geometries. [ABSTRACT FROM AUTHOR]

A thermodynamic model of thermoelectric (TE) generator (TEG) driven TE heat pump (TEH) combined-device (TEG-TEH) with Thomson effect and external heat transfer loss is built by using non-equilibrium thermodynamics and finite-time thermodynamics. Heating load, COP and exergetic efficiency are derived and optimized by optimizing distributions of heat conductances among four heat exchangers (HEXs) and TE element numbers between TEG and TEH, respectively, with fixed total number of TE element and fixed HEX inventory. Influences of heat source temperature of TEG, heating space temperature of TEH and Thomson effect on general performances and optimal performances are analyzed. The results show that Thomson effect makes general performances and optimal performances of combined device decrease. Thomson effect makes the maximum COP, maximum heating load and maximum exergetic efficiency decrease from 15.68 × 10 − 2 , 28.44 W and 3.651% to 10.27 × 10 − 2 , 21.68 W and 2.404%, respectively, makes the optimal performance ranges narrow down, makes the optimal distribution range of TE element numbers between TEH and TEG, optimal distribution range of heat conductances between TEH and TEG, and optimal distribution range of heat conductances between hot- and cold HEXs in TEG narrow down, and makes the optimal distribution range of heat conductances between hot- and cold-side HEXs in TEH broaden. [Display omitted] • Thermodynamic model of thermoelectric generator driven thermoelectric heat pump is built. Thomson effect is considered. [ABSTRACT FROM AUTHOR]

In the Floating Silicon Method (FSM), a single-crystal Si ribbon is grown while floating on the surface of a Si melt. In this paper, we describe the phenomenology of FSM, including the observation of approximately regularly spaced “facet lines” on the ribbon surface whose orientation aligns with (111) crystal planes. Sb demarcation experiments sectioned through the thickness of the ribbon reveal that the solid/melt interface consists of dual (111) planes and that the leading edge facet growth is saccadic in nature, rather than steady-state. To explain this behavior, we propose a heuristic solidification limit cycle theory, using a continuum level of description with anisotropic kinetics as developed by others, and generalizing the interface kinetics to include a roughening transition as well as a re-faceting mechanism that involves curvature and the Gibbs–Thomson effect. [ABSTRACT FROM AUTHOR]

In this paper, the energy and exergy analysis of the solar annular thermoelectric generator (SATEG) considering Thomson effect in conjunction with Peltier, Joule and Fourier heat conduction have been introduced. Unlike the flat plate thermoelectric generator, the cross section area of an annular thermoelectric generator increase along the radial direction. Therefore, the annular thermoelectric generator possess higher total heat transfer area when compared with flat plate thermoelectric generator. The solar radiation absorbed by the solar heat pipe is given as the energy input to the SATEG. This system has the advantage of providing electrical power output and hot water output. The results of this study show that the power output and overall exergy efficiency of the SATEG are 1.92 W and 5.02% respectively and are 0.52% and 0.40% higher than that of solar flat plate thermoelectric generator (SFTEG). SATEG system has advantage of better thermal insulation, improved heat transfer characteristics, easy installation and maintenance when compared with the solar flat plate thermoelectric generator because of its cylindrical structure. This study will be helpful in designing of actual solar annular thermoelectric generation systems. [ABSTRACT FROM AUTHOR]

In this study, a thermodynamic model for analysing the performance of a concentrated photovoltaic–thermoelectric generator (CPV–TEG) hybrid system including Thomson effect in conjunction with Seebeck, Joule and Fourier heat conduction effects has been developed and simulated in MATALB environment. The expressions for calculating the temperature of photovoltaic (PV) module, hot and cold sides of thermoelectric (TE) module are derived analytically as well. The effect of concentration ratio, number of thermocouples in TE module, solar irradiance, PV module current and TE module current on power output and efficiency of the PV, TEG and hybrid PV–TEG system have been studied. The optimum concentration ratio corresponding to maximum power output of the hybrid system has been found out. It has been observed that by considering Thomson effect in TEG module, the power output of the PV, TE and hybrid PV–TEG systems decreases and at C = 1 and 5, it reduces the power output of hybrid system by 0.7% and 4.78% respectively. The results of this study may provide basis for performance optimization of a practical irreversible CPV–TEG hybrid system. [ABSTRACT FROM AUTHOR]

In this paper, the exoreversible and irreversible thermodynamic models of a TTEG (two stage thermoelectric Generator) considering Thomson effect combined with Peltier, Joule and Fourier heat conduction have been investigated using exergy analysis. The expressions for interstage temperature, optimum current for the maximum power output condition and energy/exergy efficiency of a TTEG are derived. The number of thermocouples in the first and second stages of a TTEG for the maximum power output and energy/exergy efficiency conditions are optimized as well. The results show that the exergy efficiency of TTEG is greater than the energy efficiency. In an irreversible TTEG with 30 thermocouples, and with heat source temperature ( T H ) of 450 K and heat sink temperature ( T C ) of 300 K, the obtained maximum power output, maximum energy and exergy efficiency are 0.2996 W, 4.35% and 13.05% respectively. It has also been proved that the optimum number of thermocouples obtained in the first and second stages of a TTEG are different from the previous studies because of the influence of Thomson effect. This study will help in the designing of the actual multistage thermoelectric generator systems. [ABSTRACT FROM AUTHOR]

The exoreversible and irreversible thermodynamic models of a two stage thermoelectric cooler (TTEC) considering Thomson effect in conjunction with Peltier, Joule and Fourier heat conduction effects have been investigated using exergy analysis. New expressions for the interstage temperature, optimum current for the maximum cooling power, energy and exergy efficiency conditions, energy efficiency and exergy efficiency of a TTEC are derived as well. The number of thermocouples in the first and second stages of a TTEC for the maximum cooling power, energy and exergy efficiency conditions are optimized. The results show that the exergy efficiency is lower than the energy efficiency e.g., in an irreversible TTEC with total 30 thermocouples, heat sink temperature ( T H ) of 300 K and heat source temperature ( T C ) of 280 K, the obtained maximum cooling power, maximum energy and exergy efficiency are 20.37 W, 0.7147 and 5.10% respectively. It has been found that the Thomson effect increases the cooling power and energy efficiency of the TTEC system e.g., in the exoreversible TTEC the cooling power and energy efficiency increased from 14.87 W to 16.36 W and from 0.4079 to 0.4998 respectively for Δ T C of 40 K when Thomson effect is considered. It has also been found that the heat transfer area at the hot side of an irreversible TTEC should be higher than the cold side for maximum performance operation. This study will help in the designing of the actual multistage thermoelectric cooling systems. [ABSTRACT FROM AUTHOR]

In this paper the concept of annular thermoelectric cooler (ATEC) has been introduced. An exoreversible thermodynamic model of the annular thermoelectric cooler considering Thomson effect in conjunction with Peltier, Joule and Fourier heat conduction has been investigated using exergy analysis. New expressions for optimum current at the maximum energy/exergy efficiency, maximum cooling power conditions and dimensionless irreversibilities in the ATEC are derived. The modified expression for figure of merit of a thermoelectric cooler considering the Thomson effect has also been obtained. The results show that the cooling power, energy and exergy efficiency of the ATEC is lower than the flat plate thermoelectric cooler. The effects of annular shape parameter ( S r = r 2 / r 1 ), dimensionless temperature ratio ( θ = T h / T c ) and the electrical contact resistances on cooling power, energy/exergy efficiency of an ATEC have been studied. It has also been proved that because of the influence of Thomson effect, the cooling power and energy/exergy efficiency of the ATEC is increased. This study will help in the designing of the actual annular thermoelectric cooling systems. [ABSTRACT FROM AUTHOR]

The exoreversible thermodynamic model of an annular thermoelectric generator (ATEG) considering Thomson effect in conjunction with Peltier, Joule and Fourier heat conduction has been investigated using exergy analysis. New expressions for optimum current at the maximum power output and maximum energy, exergy efficiency conditions, and dimensionless irreversibilities in the ATEG are derived. The modified expression for figure of merit of a thermoelectric generator considering the Thomson effect has also been obtained. The results show that the power output, energy and exergy efficiency of the ATEG is lower than the flat plate thermoelectric generator. The effects of annular shape parameter ( S r = r 2 /r 1 ), load resistance ( R L ), dimensionless temperature ratio ( θ = T h /T c ) and the thermal and electrical contact resistances in power output, energy/exergy efficiency of the ATEG have been studied. It has also been proved that because of the influence of Thomson effect, the power output and energy/exergy efficiency of the ATEG is reduced. This study will help in the designing of the actual annular thermoelectric generation systems. [ABSTRACT FROM AUTHOR]

The I − Δ V characteristic curve of a well type ionization chamber irradiated with 192 Ir sources (0.75 Ci–120 Ci) was fitted using the exact solution of the Thomson problem. The recombination coefficient and saturation current were estimated using this new approach. The saturation current was compared with the results of the conventional method based on Boag–Wilson formula. It was verified that differences larger than 1% between both methods only occurred at activities higher than 55 Ci. We concluded that this new approach is recommended for a more accurate estimate of the saturation current when it is not possible to measure currents satisfying the condition I / I sat > 0.95 . From the calibration curve the average value of pairs of carriers created per unit volume was estimated to be equal to η = 8.1 × 10 − 3 cm − 3 s − 1 Bq −1 and from that value it was estimated that ~ 17 pairs were created on average per second for each decay of the source. [ABSTRACT FROM AUTHOR]

Modelling of (solid-state) precipitation kinetics in terms of particle nucleation and particle growth requires evaluation of the thermodynamic relations pertaining to these mechanisms, i.e. evaluation of the nucleation barrier and of the Gibbs–Thomson effect. In the present work, frequently occurring problems and misconceptions of the thermodynamic evaluation are identified and a practical approach with regard to kinetic modelling is proposed for combined and unified analysis of the thermodynamics of nucleation and growth, based on the fundamental thermodynamic equilibrium consideration in a particle–matrix system. A computationally efficient method for numerical determination of the thermodynamic relations is presented which allows an easy and flexible implementation into kinetic modelling. [ABSTRACT FROM AUTHOR]

A comprehensive study of the mechanisms of the thermal electromotive force, heating and cooling originated by a temperature gradient and an electric current in semiconductor devices is reported. The Seebeck, Peltier, Joule and Thomson phenomena are studied self-consistently under the approximation of weak electric current and temperature gradient. Analytical calculations show that the contributions of each effect to the temperature distribution are commensurable. A new formulation and interpretation of the Thomson effect are given. Additionally, attention is paid to some questions of nonequilibrium thermodynamics of thermoelectric and electrothermic phenomena, that demand some clarification. [ABSTRACT FROM AUTHOR]

Abstract: With the help of Domenicali's equation and the heat flux equation, a finite difference method is directly used to determine the temperature and heat flux distribution profiles in one dimension of a thermoelectric generator simultaneously including the Peltier, Fourier, Joule, and Thomson effects. This calculative method is also used to evaluate the performance of a thermoelectric generator, based on experimental data of thermoelectric materials PbTe1−yIy and PbTe: Na/Ag2Te. The efficiency of the thermoelectric generator as a function of the electric current is calculated and the effects of structure parameters on the performance of the thermoelectric generator are revealed. The method proposed here offers a simple way to properly choose n-type and p-type thermoelectric materials of a thermoelectric generator. [Copyright &y& Elsevier]

Highlights: [•] Quasi-equilibrium condensation of ionized fluxes results in surface self-assembly. [•] Surface self-assembly corresponds to selective formation of developed morphology. [•] Electric field and local surface curvature are key competing factors in self-assembly. [Copyright &y& Elsevier]

Abstract: Correspondences between the Thomson problem and atomic electron shell-filling patterns are observed as systematic non-uniformities in the distribution of potential energy necessary to change configurations of N ≤ 100 electrons into discrete geometries of neighboring N − 1 systems. These non-uniformities yield electron energy pairs, intra-subshell pattern similarities with empirical ionization energy, and a salient pattern that coincides with size-normalized empirical ionization energies. Spatial symmetry limitations on discrete charges constrained to a spherical volume are conjectured as underlying physical mechanisms responsible for shell-filling patterns in atomic electronic structure and the Periodic Law. [Copyright &y& Elsevier]

Abstract: The formulation of the classical basic equations for a thermoelectric cooler from the Thomson relations to the non-linear differential equation with Onsager's reciprocal relations was performed to basically study the Thomson effect in conjunction with the ideal equation. The ideal equation is obtained when the Thomson coefficient is assumed to be zero. The exact solutions derived for a commercial thermoelectric cooler module provided the temperature distributions including the Thomson effect. The positive Thomson coefficient led to a slight improvement on the performance of the thermoelectric device while the negative Thomson coefficient led to a slight declination of the performance. The comparison between the exact solutions and the ideal equation on the cooling power and the coefficient of performance over a wide range of temperature differences showed close agreement. In conclusion, the Thomson effect is small for typical commercial thermoelectric coolers and the ideal equation effectively predicts the performance. [Copyright &y& Elsevier]

Abstract: Thermoelectric self-cooling systems hold good prospects for the future, since they improve the cooling of any heat-generating device without electricity consumption. The potential number of applications seems to be enormous, hence the necessity of a specific model to simulate this type of thermoelectric application. This paper presents a computational model for thermoelectric self-cooling applications, capable of simulating both the steady and the transient state of the whole system. Supported by fluid-dynamics software and based on the implicit finite differences, the model solves the system of equations composed of the Fourier's law and the thermoelectric effects Seebeck, Peltier, Joule and Thomson, including temperature-dependant properties. Furthermore, the model architecture allows the inclusion of new analytical expressions and/or procedures in order to simulate any component with higher accuracy or include more complex ones. Statistical studies indicate ±12% of maximum deviation between experimental and simulated values of the main outputs. Furthermore, the model simulates the performance of the system under abruptly changing conditions. In conclusion, the computational model turns out to be a powerful tool that will play a key role in the design and development of thermoelectric self-cooling applications. [Copyright &y& Elsevier]

Abstract: LILIA is an experiment of light ions acceleration trough laser interaction with thin metal targets to be done at the FLAME facility, which is now running in INFN-LNF of Frascati (Rome). In the framework of LILIA, the LNS is involved in the design and construction of a spectrometer based on the Thomson's configuration in order to diagnostic the ion ejection from the laser-generated plasma. The main goal is to realize a compact system which is both very practical and optimized with regard to the mass and energy resolution of particles obtained by laser–plasma interactions. The preliminary design has to be able to analyze and resolve beams of protons and ions up the total energy of 10MeV. However, the technical choices adopted in this prototype have to be applied for the final device concerning a challenging spectrograph able to analyze beams of 150MeVof total energy. The magnetic and the electric part have been built and these have been assembled. The vacuum and the high voltage test have been accomplished out and also the magnetic measurements. The results will be presented and discussed. [Copyright &y& Elsevier]

Abstract: Most thermoelectric device modeling neglects the non-linear Thomson effect in order to develop a closed-form solution to the governing heat equation. This simplified solution is beneficial for system modeling and optimization when more intensive numerical techniques are prohibitive. An averaged Seebeck coefficient is often used in conjunction with the closed-form solution to incorporate approximately the effect of this neglected term (termed the “standard model”). While the standard model has been accepted in the past for materials under small temperature gradients and relatively constant Seebeck coefficient, there has not been a systematic assessment of validity of this modeling approach, especially for emerging materials and large temperature gradients. This work rigorously demonstrates the accuracy and limitations of the standard model through analytical derivation and comparison with an efficient numerical solution. It is proven that the standard model produces the exact module output power if an integral-averaged Seebeck coefficient is used, and also that the standard model provides a reasonably-accurate estimation of module efficiency, despite its limiting assumptions. These findings prove that the standard model in fact incorporates the Thomson effect with sufficient accuracy that it may be used to simulate and optimize thermoelectric systems as an alternative to computationally expensive numerical simulations. [Copyright &y& Elsevier]

Abstract: Conventional hollow fiber models in process simulators usually assume constant membrane permeance i.e., independent of pressure and temperature. In this work, hollow fiber membrane model has been proposed to cater the effects of temperature and pressure on membrane permeance. The proposed model is incorporated with Aspen HYSYS as a user defined unit operation in order to study the performance of gas separation system. The simulated model is validated by experimental and published data. The temperature drop due to Joule Thomson effect and its contribution to the change in membrane permeance has also been investigated. Similarly, the effect of pressure on membrane permeance has been studied. The influence of these effects on the separation performance and process economics has been investigated for the separation of CO2 from natural gas. The proposed hollow fiber membrane model has potential to be applied for design, optimization and scale up of wide range of gas separation systems. [Copyright &y& Elsevier]

Abstract: Crystal-melt interfacial free energies of fcc metals were calculated by molecular dynamics simulation. Spherical crystal nucleus was embedded in the undercooled melt to create an ideal model of homogeneous nucleation. Growth and melting behaviors of the nucleus were examined. There was a critical temperature dividing growth and melting of the nucleus. The critical undercooling, as the difference between the critical temperature and the bulk melting point, was proportional to the inverse of the nucleus radius, which is regarded as the Gibbs–Thomson effect. The Gibbs–Thomson coefficient was determined from the relation between the critical undercooling and the nucleus radius. The crystal-melt interfacial free energies, which were estimated from the Gibbs–Thomson coefficients, were consistent with the experimental results of Turnbull. [Copyright &y& Elsevier]

Abstract: Simplified models are usually used to describe the behavior of thermoelectric elements due to their low computational effort needed for solving the physical behavior in a wide number of situations (e.g., in both heating/cooling mode – TEH or TEC – and in power generation mode – TEG). The accuracy of these models depends on different assumptions like: (i) the Thomson effect is assumed to be negligible and (ii) the thermoelectric properties are assumed to be constant in the thermoelectric leg and are estimated from the mean temperature of its two sides. This paper attempts to analyze simplified models’ accuracy, with regards to the performance (COP, efficiency), the voltage–current characteristics and the thermal/electrical power. The simplified models are compared to more accurate models, such as models based on an electrical analogy and on the finite element method (FEM). The benefits and drawbacks of each kind of model are discussed in order to help select the appropriate approach depending of the goal aimed. The improved simplified model using two different Seebeck coefficients with a constant Thomson coefficient greatly increases the accuracy of the results, particularly in TEG mode with large temperature differences between the two sides. The model based on the electrical analogy gives an intermediate approach between simplified models and FEM models. For one-dimensional modeling, the analogical model gives strictly the same results as those obtained with ANSYS (FEM-based software). In all the cases, we show that the key point is to use a null Thomson coefficient when a constant Seebeck coefficient is defined. [Copyright &y& Elsevier]

Abstract: GaN nanowires were grown using chemical vapor deposition with controlled aspect ratio. The catalyst and catalyst-diameter dependent growth kinetics is investigated in detail. We first discuss gold catalyst diameter dependent growth kinetics and subsequently compare with nickel and palladium catalyst. For different diameters of gold catalyst there was hardly any variation in the length of the nanowires but for other catalysts with different diameter a strong length variation of the nanowires was observed. We calculated the critical diameter dependence on adatoms pressure inside the reactor and inside the catalytic particle. This gives an increasing trend in critical diameter as per the order gold, nickel and palladium for the current set of experimental conditions. Based on the critical diameter, with gold and nickel catalyst the nanowire growth was understood to be governed by limited surface diffusion of adatoms and by Gibbs–Thomson effect for the palladium catalyst. [Copyright &y& Elsevier]

Abstract: Miniature thermoelectric cooler (TEC) has been considered as a promising device to achieve effective cooling in microprocessors and other small-scale equipments. To understand the performances of miniature thermoelectric coolers, three different thermoelectric cooling modules are analyzed through a three-dimensional numerical simulation. Particular attention is paid to the influence of scaling effect and Thomson effect on the cooling performance. Two different temperature differences of 0 and 10K between the top and the bottom copper interconnectors are taken into account. In addition, three different modules of TEC, consisting of 8, 20 and 40 pairs of TEC, are investigated where a single TEC length decreases from 500 to 100μm with the condition of fixed ratio of cross-sectional area to length. It is observed that when the number of pairs of TEC in a module is increased from 8 to 40, the cooling power of the module grows drastically, revealing that the miniature TEC is a desirable route to achieve thermoelectric cooling with high performance. The obtained results also suggest that the cooling power of a thermoelectric cooling module with Thomson effect can be improved by a factor of 5–7%, and the higher the number of pairs of TEC, the better the improvement of the Thomson effect on the cooling power. [Copyright &y& Elsevier]

Abstract: This study conducts experimental investigation and numerical analysis for one-stage thermoelectric cooler (TEC) considering Thomson effect. Three Seebeck coefficient models are applied to numerically and experimentally study the Thomson effect on TEC. Results show that higher current, higher hot side temperature, or lower heat load can increase the temperature difference between the cold and hot sides. Opposite trends are found for COP. Specific current should be chosen as the upper threshold in thermoelectric cooler design. The cooling performance can improve when the Thomson heat maintains positive. [Copyright &y& Elsevier]

Abstract: A novel approach to estimate energy conversion efficiency for a power-generating thermoelectric element, whose material properties possess both linear (first order) and nonlinear (second order) dependence on temperature, is developed by solving the differential equation governing its temperature distribution, which includes both the Joule heat and the Thomson effect. In order to obtain analytic expressions for power output and energy conversion efficiency, several steps of simplification are taken. Most notably, the material properties are evaluated with a linear temperature profile between the hot and cold ends. The model is further applied to a high-performance n-type half-Heusler alloy, matching the results of direct numerical analysis. The close correspondence between the proposed model and the numerical solution indeed proves that the approximations we have made are valid. The effect of linear and nonlinear components in the temperature dependence of material properties on the energy conversion efficiency is analyzed both qualitatively and quantitatively with the model. The results suggest that the accurate inclusion of the Thomson effect is essential to understand even the qualitative behavior of thermoelectric energy conversion. [Copyright &y& Elsevier]

Abstract: Photovoltaic cells convert most of the absorbed photon energy to heat. Removal of the heat by thermal conduction creates a temperature gradient that is significant in concentrating photovoltaic (CPV) cells subject to high incident radiation flux. The Thomson effect interaction between this temperature gradient and the electrical current in the cell can either increase or decrease the electrical power output of the cell. Here we show that the Thomson effect has a non-negligible impact on the conversion efficiency of Ge-based CPV cells, which is comparable to the impact of typical series resistance, and therefore this effect should be considered in cell modeling. The effect may also have a significant impact on the performance of other high power optoelectronic devices. [Copyright &y& Elsevier]

Abstract: This paper proposes an approach to calculate the efficiency of throttling in which the exergy (available energy) is used to evaluate the energy conversion processes. In the exergy calculation for real gases, a difficult part of integration can be removed by judiciously advised thermodynamic paths; the compressibility factor is calculated by using Peng–Robinson (P–R) equation. It is found that the largest deviation between the exergies calculated by the real gas equation and ideal gas assumption is about 1%. Because the exergy is a function of the pressure and temperature, the Joule–Thomson coefficients are used to calculate the temperature changes of throttling, based on the compressibility factors of the Soave–Redlich–Kwong (S–R–K) and P–R equations, and the temperature decreases are compared with those calculated by empirical formula. The result shows that the heat exergy contributes very little in throttling. The simple equation of ideal gas is suggested to calculate the efficiency of throttling for air at atmospheric temperatures. [Copyright &y& Elsevier]

Kelvin's relations may be considered as cornerstones in the theory of thermoelectricity. Indeed, they gather together the three thermoelectric effects, associated respectively with Seebeck, Peltier and Thomson, to get a unique and consistent description of thermoelectric phenomena. However, their physical status in literature are quite different. On the one hand, the second Kelvin's relation is associated with the microscopic reversibility, considered as a fundamental thermodynamical property. On the other hand, the first Kelvin's relation is traditionally introduced only as a convenient mathematical relation between Seebeck and Thomson coefficients. In the present article, we stress that, contrary to common believes, this relation may demonstrates deeper insights than a bold mathematical expression between thermoelectric coefficients. It actually reflects the coexistence of two different mechanisms taking place inside thermoelectric systems: Energy conversion and reorganization of heat flow when Seebeck coefficient varies. [ABSTRACT FROM AUTHOR]

Abstract: We examine binary substitutional diffusion in cylindrical diffusion couples in which free surfaces are considered explicit vacancy sources and sinks. The central region of the cylinder is initially occupied by an atomic species with a larger hop frequency, while the outer region is occupied by another atomic species with a smaller hop frequency. Equilibrium vacancy concentration is maintained at free surfaces that serve as vacancy sources and sinks. In the crystal, diffusion is governed by the standard diffusion equations with analytically evaluated diffusion coefficients. The void growth dynamics and hollow cylinder formation stemming from the Kirkendall effect are simulated. Our results show that the Kirkendall void growth involves two competing factors. One is the net inward vacancy flux that favors void growth. The other is the Gibbs–Thomson effect that favors void shrinkage. We compute the critical initial radius for void growth above which the Kirkendall effect dominates over the Gibbs–Thomson effect. The fully grown void radius and the elapsed time to the fully grown size are also predicted for different fast-diffuser volume fractions and fast-to-slow diffuser atomic hop frequency ratios. [Copyright &y& Elsevier]

Abstract: The resultant Seebeck coefficient αR (Tz ) of a thermoelectric (TE) element was derived analytically from the temperature dependence of the intrinsic Seebeck coefficient αI (Tz ) by taking into account the Thomson effect, where Tz is a temperature at z along a TE element. The analysis was performed by expanding αI (Tz ) in a power series in (Tz − T), where T is a mean temperature. As a result, when αI (Tz ) has a convex curve exhibiting a local maximum at Tz = T, αR (Tz ) is increased at the interfaces of a TE element, while when it has a concave curve giving a local minimum at Tz = T, αR (Tz ) deteriorates there. If the p-type (Bi0.4Sb0.6)2Te3 with a local maximum of αI (Tz ) at T =390K is employed for a TE element, αR (Tz )/αI (T) at both interfaces is increased up to 1.53 under the condition of T =390K and ΔT =200K. A similar enhancement in αR (Tz )/αI (T) appeared even in the n-type (Zr–Hf)NiSn half-Heusler. When αI (Tz ) varies nonlinearly with changes in Tz , therefore, the TE figure of merit ZR (Tz )Tz is found to be affected dramatically at the interfaces. The average resultants ZAR (T) estimated for the p-type Bi–Te and n-type half-Heusler compound reach great values of 1.46 and 1.26 times as large as their intrinsic Z(T), respectively. The experimental method to confirm such a phenomenon is also proposed here. The performance of a TE element is thus expected to be enhanced significantly not only by improving the intrinsic Z(Tz )Tz but also by optimizing the Tz -dependence of αI (Tz ). [Copyright &y& Elsevier]

This paper presents a comprehensive analysis of novel, unileg cascade thermoelectric systems. Unileg systems offer the flexibility of selecting a single (p- or n-) thermoelectric material in a thermoelectric system compared to two (n- and p-) materials. Finite element analysis simulations were performed to design and analyze two and three stages of cascade systems. Simulation results show that unileg cascade systems perform significantly (∼75%) better than their unicouple counterparts in both two and three stage configurations due to the elimination of the poorly performing thermoelectric leg. In addition to the enhanced thermoelectric power generation, thermal stress is lowered in unileg systems since the mismatch of the thermal expansion coefficient originating between different TE legs material can be minimized. Overall, the presented unileg systems show their promise for the future thermoelectric energy generation or cooling applications for electronics. • Comparison between unicouple and unileg cascade TEG systems is introduced. • Thermal reliability and TE performance are investigated for cascade TEG systems. • Unileg cascade TEG generates higher TE power and displays lower Von Mises stresses. • Unicouple cascade TEG shows higher heat losses compared to unileg cascade TEG. • Thomson effect is higher in Unileg TEG compared to unicouple TEG. [ABSTRACT FROM AUTHOR]

Abstract: Finite time thermodynamics, a subfield of irreversible thermodynamics, is employed to model a cascaded thermoelectric generator, which incorporates all the essential features of a real heat engine. Control volume formulation of a cascaded thermoelectric element was carried out over a small but finite temperature gap to comply with the principles of irreversible thermodynamics. Three important dimensionless parameters are identified to designate poor Thomson effect; low thermal conductivity and low electrical resistivity of a good semiconductor or semimetal. For ideal values of these parameters it has been demonstrated that exactly half of the Joulean heat arrives at both hot and cold junction when temperature maximum passes through the longitudinal center of the thermoelectric element. In general when Thomson heat cannot be neglected, the maximum and the minimum permissible length of any individual module of a cascaded thermoelectric device is predicted involving thermoelectric properties of the materials and passing current. It is observed that maximum permissible length is devoid of dependence on applied temperature gradient whereas the minimum allowable length is not. When half the Joulean heat affects hot end and half the cold side, thermal conductance inventory is allocated equally between the high and low temperature side for best possible device performance. Finally, it has been argued that the choice of constancy of total conductance is not only a natural constraint but also a purely realistic design criterion for heat engines or refrigerators. Such design prescriptions those lead to the prediction of shape and structure in any flowing system is reported in open literature as constructal principle. [Copyright &y& Elsevier]

Abstract: This work has two parts. The first part details the thermal analysis of a thin-film thermoelectric cooler under the influence of the Thomson heating, the Joule heating, and the Fourier''s heat conduction. A constant Thomson coefficient, instead of traditionally a constant Seebeck coefficient, is assumed. The influence of the Thomson effect on the cooling power, the achievable temperature difference and the optimum operating current density is then explored. It is found that the Joule''s heat and the conduction heat flowing to the cold junction can be significantly reduced if thermoelectric materials with properly designed Thomson coefficients are employed. A modified thermal conductance and a modified electric resistance are resulted. The second part of this paper details the analysis of the thermal stresses existing in the layered structure and induced by the temperature difference via a non-coupled thermal elastic theory. The results provide a preliminary knowledge to judge whether the thin-film structure is destroyed by the thermal stresses or not, especially by the shear stresses between adjacent layers. [Copyright &y& Elsevier]

Abstract: The temperature distribution of a thermoelectric cooler under the influence of the Thomson effect, the Joule heating, the Fourier’s heat conduction, and the radiation and convection heat transfer is derived. The influence of the Thomson effect on the temperature profiles, on the fraction of the Joule’s heat that flows back to the low-temperature side, and consequently on the maximum attainable temperature difference and the maximum allowable heat load are emphasized and explored. The results suggest that the cooling efficiency of a thermoelectric cooler can be improved not only by increasing the figure-of-merit of the thermoelectric materials but also by taking advantage of the Thomson effect. A possible development direction for the thermoelectric materials is thus given. [Copyright &y& Elsevier]