瞬态热冲击下热电材料梁的温度场及热应力分析

基于热电材料特性,通过热电平衡方程和本构方程,得出热电材料梁瞬态模型的控制方程.采用分离变量法结合模型的初始条件和边界条件求出热电材料梁的非线性瞬态温度场,根据热应力理论分析求出瞬态热应力场,利用数学软件MATLAB给出了热电材料梁的呈抛物线分布的瞬态温度场和瞬态热应力场的特性曲线,研究了热冲击载荷下的热电材料梁在热电耦合环境中的热应力分析.讨论了不同时刻温度场和应力场随厚度的变化,以及对比p型和n型Bi₂Te₃热电材料梁热应力特性曲线.结果表明:瞬态温度场受其瞬态项的影响随厚度增加有增有减;瞬态温度场和瞬态热应力场随时间的增加最终趋于稳态不再随时间变化;趋于稳态后的Bi₂Te₃热电材料梁的热应力最值大于瞬态下的热应力最值;p型Bi₂Te₃热电材料梁的热应力总是大于n型Bi₂Te₃热电材料梁的热应力.

Analysis of temperature field and thermal stresses of thermoelectric material beams under transient thermal shock

Based on the characteristics of thermoelectric materials, the governing equations of the transient model of thermoelectric materials are obtained by the thermoelectric equilibrium equation and constitutive equation. The nonlinear transient temperature field of the thermoelectric material beam is obtained by using the separated variable method combined with the initial and boundary conditions of the model, and the transient thermal stress field is obtained according to the thermal stress theory analysis. Then the characteristic curves of the transient temperature field and transient thermal stress field of the thermoelectric material beam with parabolic distribution are given by using the mathematical software MATLAB. The thermal stress analysis of thermoelectric material beam under thermal shock load in thermoelectric coupling environment is studied. The changes of temperature field and stress field with thickness at different times are discussed, and the thermal stress characteristic curves of p-type and n-type Bi₂Te₃ thermoelectric material beams are compared. The results show that the transient temperature field increases and decreases with the increase of thickness under the influence of transient term, and the transient temperature field and transient thermal stress field finally tend to steady state and no longer change with time; the thermal stress of Bi₂Te₃ thermoelectric material beam after steady state is greater than that of transient state; the thermal stress of p-type Bi₂Te₃ thermoelectric material beam is always greater than that of n-type Bi₂Te₃ thermoelectric material beam.