Performance Analysis And Optimization Of Functionally Graded Thermoelectric Element

The energy crisis and environmental pollution are two urgent problems in today's world.Hence,developing new energies and comprehensive utilizing the existing energies have attracted much more attentions in modern society.Due to the capability of directly converting between heat and electricity,thermoelectric materials have initiated numerous studies in recent years.Because of the absence of working fluid and moving parts such as compression and expansion,thermoelectric devices produce no vibration and noise during working process.Additionally,there is no harmful emissions in the operational process of the thermoelectric device,which is friendly to the environment.However,due to the low energy conversion efficiency of common thermoelectric materials,thermoelectric materials have not realized large-scale application.Functionally graded thermoelectric material is thought as an effective method to improve the efficiency of thermoelectric material and can hopefuly solve some issues about the dilemma of the energy and environment.From this standpoint,performance analysis and optimization of functionally graded thermoelectric element is of great significance for the wide application of thermoelectric materials.Thermoelectric materials are expected to play an important role in energy production and utilization.However,the temperature-dependent material properties including thermal conductivity,electric resistivity and Seebeck coefficient make the theoretical analysis challenging.In this work,the temperature profile is assumed to be close to a linear one.Taking adavantage of perturbation theory,an approximate analytical model is proposed,whereby the distribution of the electric resistivity and Thomson coefficient are evaluated linearly.The temperature profile obtained from the approximate analytical model agrees well with numerical results.More importantly,the temperature gradient,which has great influence on the heat flux distribution and efficiency,also agrees well with the numerical results.Based on the vadility of our proposed model,the performance of a thermoelectric element is researched symmetrically.The results indicate that the temperature-dependent thermal conductivity has significant impact on the performance of thermoelectric materials,i.e.,the energy conversion efficiency.Due to the advantage in static cooling and environmentally friendly properties,thermoelectric cooling is hoped to play a significant role in the electronic industry.In this work,a theoretical model is proposed to predict the performance of a thermoelectric cooler with the consideration of temperature-dependent material properties.The governing thermal equation of the thermoelectric element is derived,whereby the thermal conductivity and Seebeck coefficient are nonlinear functions of temperature T while the electric resistivity adopts the value at mean temperature.The performance of the thermoelectric cooling element,such as temperature field,cooling power,and coefficient of performance(COP),etc.,predicted by the proposed model agrees well with the numerical and finite element result,implying the validation of the theoretical model.And the results suggest that the temperature-dependent thermal conductivity and Seebeck coefficient have obvious influence on the heat flow and COP of the thermoelectric cooling element.In addition,by utilizing the continuum theory of thermoelectric body and composite material theory,the cooling performance of functionally graded thermoelectric element are also investigated.The performance of functionally graded thermoelectric materials(FGTEMs)is studied by numertical method,whereby the material properties are both temperaturally and spatially dependent.The influence of structural distribution of FGTEMs on the performance of a functionally graded thermoelectric element,including the temperature field,heat flux,power output,and energy conversion efficiency is mainly studied.The results suggest that temperature-dependent material properties have important influence on the accurate prediction of the performance of FGTEMs.Meanwhile,the derived data show that a significant increment occurs for the power output and energy conversion efficiency if proper material property gradient distributions are achieved.Additionally,the results indicate that thermal conductivity has considerable influences on temperature field and heat flux distribution while Seebeck coefficient is critical for the power output and energy conversion efficiency.In order to validate the proposed model,it is applied to an experimental device composed by functionally graded bismuth antimony thermoelectric couple which shows a good agreement with the numerical results.Segmented thermoelectric material is a special case of FGTEM.In this work,the performance of equal-volume and variable-section segmented thermoelectric element is researched.The influence of shape factor and segmentation position on energy conversion efficiency and output power is studied through numerical method while the volume of the thermoelectric material keep the same.For the thermoelectric materials presented,the influence of shape factor and segmentation position on the performance of the thermoelectric element is also investigated by numerical method.In addition,the influence of segmentation position and shape factors on the the performance of segmented thermoelectric element under different temperature conditions is studied to optimize the output power and energy conversion efficiency.In order to figure out the influence of temperature-dependent material properties on the performance of annular thermoelectric element,the performance of annular thermoelectric element whose material properties are nonlinear function of temperature is explored.By using the perturbation theory and the equivalent substitution of integrals,a theoretical model is proposed to analyze the annular thermoelectric element with temperature-dependent material properties.The theoretical model is applied to investigate the influence of Thomson effect on the performance of annular thermoelectric element.Additionally,the influences of structural parameters of annular type thermoelectric element and operating conditions on the energy conversion efficiency and output power are also studied.In order to fully utilize the heat source in cylindrical structure,we present a new cylindrical thermoelectric copule model by considering the concept of FGTEM,and the thermodynamic and mechanical performance of this model is studied.The influence of gradient parameters on the radial temperature field and heat flow distribution is analyzed.In addition,the influence of gradient parameters on the output power and energy conversion efficiency of the thermoelectric cylinder is also examined.Based on the obtained temperature field,the mechanical performance of the functionally graded thermoelectric cylinder is further discussed,including the influence of the gradient parameters on the radial stress,cyclic stresses,and the radial displacement of the thermoelectric cylinder.According to the study results,the optimal design of the performance of gradient cylinder can be realized.