Effect of temperature dependence of electrical resistivity on the cooling performance of a single thermoelectric element

The coefficients of performance (COP) φ0 and φ for a single thermoelectric (TE) element welded with two metal plates were calculated as functions of temperature difference (ΔT) and thermoelectric figure of merit (ZT) from the conventional thermal rate equations and the new thermal rate ones proposed here, respectively. We made an attempt to take the differences in the Seebeck coefficient α, electrical resistivity ρ and thermal conductivity κ of TE materials at the hot and cold sides of a TE element into the thermal rate equations on the assumption that their TE properties change linearly with temperature. However, the difference in κ was neglected even in the new thermal rate equations because its temperature dependence was too small when φ was applied to the high-performance Bi–Te alloys. The normalized temperature dependences at 300 K of α and ρ were denoted by A and B, respectively. The term of A in the thermal rate equations was canceled out by the Thomson coefficient, but that of B remained. When B > 0 K−1, φ/φ0 is enhanced more significantly with an increase of B at larger ΔT and lower ZT, and it reached about 1.20 at ΔT = 80 K for Bi–Te alloys with B ≈ 5 × 10−3 K−1. It was thus found that the COP of a cooling module is also affected strongly by B as well as ZT.