Analytical study of transient performance of thermoelectric coolers considering the Thomson effect

Analytical solutions of transient temperature distributions within semiconductor elements are presented in this study. The performance of a thermoelectric cooler (TEC) under the influences of the Thomson effect, Joule heating, and combined radiation and convection cooling is investigated. The solution of the temperature distributions is obtained by solving the governing heat conduction equation using the superposition technique with the aid of a special transformation function. The closed-form transient temperature profiles for the semiconductor element sizes, applied current, cooling load, heating power, power consumption, and the system coefficient of performance (COP) of a TEC are presented. The interrelationships between the aforementioned effects are examined in detail. The analytical temperature solution presented in this study can be utilized by design engineers in the thermoelectrics industry as a convenient means to demonstrate compliance of the device heating or cooling design specification requirements.