The transient and steady state response of a thermal system with thermoelectric coolers has been studied analytically. The system is comprised of a device with thermal mass inside an insulated enclosure, thermal resistance between the mass and the thermoelectric cooler, insulation thermal resistance, TIM between thermoelectric cooler layers, and a heatsink on the hot side of the thermoelectric cooler. It is assumed that the thermal mass of the thermoelectric cooler is negligible compared to other thermal masses. The analytical transient solution consists of two exponential eigen functions and hence two time scales (i.e. two eigen values). The analytical solution has been validated with a numerical Runge-Kutta solution. A simple method is explained to combine thermoelectric coolers in series and parallel. The time scales are studied for different parameters and the key parameters for time scale minimization are identified. It is found that the thermoelectric module thermal resistance limits the fastest transient response.

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