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

Abstract

The coefficients of performance (COP) φ 0 and φ for a single thermoelectric (TE) element welded with two metal plates were calculated as functions of temperature difference (Δ T) 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/ φ 0 is enhanced more significantly with an increase of B at larger Δ T and lower ZT, and it reached about 1.20 at Δ T = 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.