Study On The Unsteady Problem Of Electric And Heat Conduction And Thermal Stress In Finite Thermoelectric Materials

As a new environment protecting material,thermoelectric material becomes more and more popular in recent years,but the application and commercial promotion of thermoelectric material are limited by its low energy conversion efficiency.Due to the difficulties in mathematics,most of the researches focus on the steady-state condition in the applications,yet,unsteady problems,even for the one dimensional problem,is rare.In the present work,the problem of time-dependent electric and heat conduction in 1-D and 2-D thermoelectric materials were analyzed by using integral transformation method.The relationship between the electric current density and the energy conversion efficiency was analyzed in detail.The electric current density was optimized for unsteady state problems.In addition,for one-dimensional unsteady state problem,the difference of the energy conversion efficiency between unsteady-state and steady-state was analyzed,and the main reasons for the low energy conversion efficiency of unsteady state were discussed.Then,the thermal stress of one-dimensional thermoelectric material was obtained.For the two-dimensional problem,the thermal stress of the thermoelectric material plate with a side crack under the unsteady state was studied,and the change of the stress intensity factor at the crack tip under unsteady temperature field was studied.The results show that the energy conversion efficiency of the thermoelectric material can be adjusted by adjusting the current in unsteady state,and a better current density was obtained in this paper.the energy conversion efficiency was improved by using this current density.The thermal stress of both the one-dimensional problem and the stress intensity factor at the crack tip of the twodimensional problem change with time.These analytical solutions and results provide a powerful tool for improving the reliability and energy conversion efficiency of thermoelectric materials under unsteady conditions.