有限大热电材料非稳态热电传输及热应力问题研究

发布时间：2018-12-08 16:52

【摘要】：热电材料作为一种绿色环保的新型能源材料,近年来受到广泛关注,但是热电材料较低的能量转换效率限制了它的应用和商业推广。由于数学上的困难,目前的研究大部分都是关于热电材料稳态问题的研究,而关于非稳态问题的研究少之又少。本文利用积分变换方法求解了一维和二维的含时非稳态问题,研究了特定尺寸特定边界条件下,电流密度与能量转换效率的关系,并对非稳态问题的电流密度进行了优化。对于一维非稳态问题,本文对比了非稳态和稳态效率的差异,分析了造成非稳态效率低于稳态效率的主要原因,之后求解了一维热电材料中的热应力随时间的变化。对于二维问题,本文研究了含单边裂纹热电材料板在非稳态温度场下的热应力问题,进而还研究了裂纹尖端的应力强度因子在非稳态温度场下随时间的变化。结果表明,通过调节电流的形式可以调节热电材料在非稳态期间各个时刻的能量转换效率,在本文中,得到了一种效果较好的电流密度形式,使得热电材料的能量转换效率得到了提高。一维材料的热应力以及二维材料裂纹尖端的应力强度因子均随着时间变化,直到最后趋于稳定。这些解析解答和结论为提高热电材料在非稳态情况下的可靠性及能量转换效率提供了有力的工具。
[Abstract]:Thermoelectric materials, as a new kind of green energy materials, have been paid more and more attention in recent years. However, the low energy conversion efficiency of thermoelectric materials limits its application and commercial promotion. Due to the difficulty in mathematics, most of the current studies are on the steady state of thermoelectric materials, but there are few researches on the unsteady state problems. In this paper, the integral transformation method is used to solve the time-dependent unsteady problems of one and two dimensions. The relationship between the current density and the energy conversion efficiency is studied under the condition of specific size and specific boundary, and the current density of the unsteady problem is optimized. For one dimensional unsteady state problem, the differences between unsteady and steady state efficiency are compared, and the main reasons for the unsteady efficiency being lower than steady state efficiency are analyzed, and then the variation of thermal stress with time in one dimensional thermoelectric material is solved. For the two-dimensional problem, the thermal stress of a thermoelectric plate with a single crack under the unsteady temperature field is studied, and the variation of the stress intensity factor at the crack tip with time under the unsteady temperature field is also studied. The results show that the energy conversion efficiency of thermoelectric materials can be adjusted by adjusting the current form at various times during the unsteady state. In this paper, a better current density form is obtained. The energy conversion efficiency of thermoelectric materials is improved. The thermal stress of one dimensional material and the stress intensity factor at the crack tip of two dimensional materials all change with time until they tend to stabilize at last. These analytical solutions and conclusions provide a powerful tool for improving the reliability and energy conversion efficiency of thermoelectric materials under unsteady conditions.
【学位授予单位】：南京航空航天大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB34

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