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/ϕ0ϕ/ϕ0 for a thermoelectric (TE) element was derived analytically by taking the linear and non-linear components in the temperature (Tz)Tz) 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 TzTz at a position z   along a TE element and the temperature profile along a TE element is linear or non-linear, where ϕϕ and ϕ0ϕ0 are the coefficients of performance (COP) derived from the new and conventional TRE, respectively. The linear and non-linear components in the TzTz-dependences of TE properties were estimated experimentally for Bi–Te alloys. When a TE element has a linear temperature profile, ϕ/ϕ0ϕ/ϕ0 estimated using the linear and/or non-linear components in the TzTz-dependences of their TE properties increases with an increase of ΔTΔT and reached great values of 1.3–1.6 at ZT=1ZT=1 under the condition of T=300K and ΔT=80k. As a result, it was found that the linear component in the electrical resistivity ρρ and the non-linear one in the Seebeck coefficient αα have a significant effect on ϕ/ϕ0ϕ/ϕ0. When ϕ/ϕ0ϕ/ϕ0 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 ϕϕ and ϕ/ϕ0ϕ/ϕ0 are applicable even for the practical TE coolers and refrigerators with a strong non-linearity in the temperature profile.