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

The relative cooling of performance of [phi]/[phi]0 for a thermoelectric (TE) element was derived analytically by taking the linear and non-linear components in the temperature (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 Tz at a position z along a TE element and the temperature profile along a TE element is linear or non-linear, where [phi] and [phi]0 are the coefficients of performance (COP) derived from the new and conventional TRE, respectively. The linear and non-linear components in the Tz-dependences of TE properties were estimated experimentally for Bi-Te alloys. When a TE element has a linear temperature profile, [phi]/[phi]0 estimated using the linear and/or non-linear components in the Tz-dependences of their TE properties increases with an increase of [Delta]T and reached great values of 1.3-1.6 at ZT=1 under the condition of and . As a result, it was found that the linear component in the electrical resistivity [rho] and the non-linear one in the Seebeck coefficient [alpha] have a significant effect on [phi]/[phi]0. When [phi]/[phi]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 [phi] and [phi]/[phi]0 are applicable even for the practical TE coolers and refrigerators with a strong non-linearity in the temperature profile.