y x M M Tc Th N-type P-type H H L RL I Fig. 1 Schematic diagram of thermoelectric generator Thermoelectric generators (TEG) made up of N-type and P-type thermoelectric material can directly convert heat energy into electricity. For the convenience of fabrication, the N-type and P-type thermoelectric materials have the same length, thickness and width (along z-axis), denoted as L, H and W. The bending moment applying at the TEG is M. Temperatures at the hot side (y = 0) and cold side (y = L) of TEGs are Th = 520 K and Tc = 300 K. The external electric resistance is RL, and electric current in the closed circuit is I, where I=jA. The thermal conductivity, electrical resistivity, coefficient of thermal expansion, seebeck coefficient, Young’s modulus and Poisson’s ratio of thermoelectric material is denoted as ki, ri, ai, Si, Ei and ui (i =N, P). Here, thermoelectric materials are modeled as bismuth telluride (Bi2Te3) whose material properties and geometric dimensions are listed in Table I [1-3]. Table I material properties and dimensions of Bi2Te3 [1-3] ki [W/(mK)]ri [W m]ai [10-5/K]Si [mV/K]Ei [GPa]uiL [mm]H [mm]W [mm]N-type2.21.19´10-51.68-200470.411.92.611.9P-type0.911.16´10-51.2120062.350.2311.92.611.9 The temperature filed of thermoelectric material is , in which, j is the electric current density defined as [4] j = (SP–SN)(Th–Tc) / [AP(RI + RL)], RI represents electric resistance of thermoelectric generator, . Under the hypotheses RL = RI and there is only temperature loadings, what are axial forces in thermoelectric generator and interlaminar shear stress at the interface between N-type and P-type thermoelectric material. For this problem, the temperature distribution is obtained from the solution of and is (6) Objective 1: calculating the stresses in the PN junction if both ends of them are fixed, and compare your solutions with Ansys solutions Hint: Calculate the temperature and stresses in the beam for the following geometry and environmental parameters: L is between 11.9 mm and 26.0 mm, j0 is between and , Th=310 K (this is approximately the human body temperature), Tc is between 273 K and 305 K. Plot the distribution of temperature along x for different values of L, j0 and Tc. Plot the distribution of stress vs j0 for different values of L and Tc. Study the effects of beam thickness L, the applied electric flux j0 and the environment temperature Tc. Objective 2: Study the output power of the PN junction and compare the results with Ansys solution. Hint: The electric current I through the TEG can be obtained as (3) where Th and Tc are the temperatures at the end of thermoelectric legs, RI is the total electric resistance of p- and n-type legs. The power out P can be calculated by . Study the effects of beam thickness L and the environment temperature Tc. References [1] Gao JL, Du QG, Zhang XD, et al.. Thermal stress analysis and structure parameter selection for a Bi2Te3-based thermoelectric module. Journal of Electronic Materials, 2011, 40: 884-888. [2] Al-Merbati AS, Yilbas BS, Sahin AZ. Thermodynamics and thermal stress analysis of thermoelectric power generator: influence of pin geometry on device performance. Applied Thermal Engineering, 2013, 50: 683-692. [3] Chavez R, Angst S, Hall J, et al.. High temperature thermoelectric device concept using large area PN junctions. Journal of Electronic Materials, 2014, 43: 2376-2383. [4] Ahmet ZS, Bekir SY. The thermoelement as thermoelectric power generator: Effect of leg geometry on the efficiency and power generation. Energy Conversion and Management, 2013, 65: 26-32. [5] Suhir E. An approximate analysis of stresses in multilayered elastic thin films. Journal of Applied Mechanics-Transactions of thee ASME, 1988, 55: 143-148.
