The Thomson effect and the ideal equation on thermoelectric coolers

•The formulation of the ideal equations for a thermoelectric device from the Thomson relations using the Onsager's relations.•The Thomson effect is small for typical commercial thermoelectric coolers.•The Ideal Equation effectively predicts the performance.

The formulation of the classical basic equations for a thermoelectric cooler from the Thomson relations to the non-linear differential equation with Onsager's reciprocal relations was performed to basically study the Thomson effect in conjunction with the ideal equation. The ideal equation is obtained when the Thomson coefficient is assumed to be zero. The exact solutions derived for a commercial thermoelectric cooler module provided the temperature distributions including the Thomson effect. The positive Thomson coefficient led to a slight improvement on the performance of the thermoelectric device while the negative Thomson coefficient led to a slight declination of the performance. The comparison between the exact solutions and the ideal equation on the cooling power and the coefficient of performance over a wide range of temperature differences showed close agreement. In conclusion, the Thomson effect is small for typical commercial thermoelectric coolers and the ideal equation effectively predicts the performance.