Effect of linear and non-linear components in the temperature dependences of thermoelectric properties on the cooling performance

The relative cooling of performance of ϕ / ϕ 0 for a thermoelectric (TE) element was derived analytically by taking the linear and non-linear components in the temperature ( T z ) dependences of TE properties into the thermal rate equations (TRE) on the assumption that all of the TE properties are expressed by a quadratic function of T z at a position z along a TE element and the temperature profile along a TE element is linear or non-linear, where ϕ and ϕ 0 are the coefficients of performance (COP) derived from the new and conventional TRE, respectively. The linear and non-linear components in the T z -dependences of TE properties were estimated experimentally for Bi–Te alloys. When a TE element has a linear temperature profile, ϕ / ϕ 0 estimated using the linear and/or non-linear components in the T z -dependences of their TE properties increases with an increase of Δ T and reached great values of 1.3–1.6 at ZT = 1 under the condition of T = 300 K and Δ T = 80 k . As a result, it was found that the linear component in the electrical resistivity ρ and the non-linear one in the Seebeck coefficient α have a significant effect on ϕ / ϕ 0 . When ϕ / ϕ 0 was estimated for a non-linear temperature profile of a module fabricated using these Bi–Te alloys, however, it was slightly lower than that obtained for a linear temperature profile. The formulas obtained for ϕ and ϕ / ϕ 0 are applicable even for the practical TE coolers and refrigerators with a strong non-linearity in the temperature profile.