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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]
ri [W m]
The temperature filed of thermoelectric material is , in which, j is the electric current density defined as  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
Objective 1: calculating the stresses in the PN junction if both ends of them are fixed,
and compare your solutions with Ansys solutions
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.
The electric current I through the TEG can be obtained as
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.
 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.
 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.
 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.
 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.
 Suhir E. An approximate analysis of stresses in multilayered elastic thin films. Journal of Applied Mechanics-Transactions of thee ASME, 1988, 55: 143-148.
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