Thermoelectric devices (TE) are solid state energy converter devices operating either as power generators (TEG) by means of the Seebeck effect or as coolers, using the Peltier effect (TEC). Due to increasing interest in micro and nanotechnology, many attempts have been made in order to improve the performance of micro thermoelectric devices (in particular of microcoolers) as they provide an effective cooling in microelectronics or microscale machinery. Many papers model the thermal behaviour of these systems under steady-state conditions. However, the transient behaviour of TE systems also plays an important role in the actual devices, in particular during the start up and the shut down phase, or when changing the operational parameters. Aim of this paper is to provide a complete characterization of the transient thermal behaviour of thermoelectric microcoolers (including the Thomson effect), by solving the parabolic heat diffusion equations, through two different analytical methods, the Laplace Transform (LT) and the Separation of Variables (SOV). Once the temperature distribution is known in both the semiconductors of the p-n junction, the heat fluxes and the efficiency (COP) of the cooler may be obtained when the steady state is reached. Both the presence and the absence of the Thomson effect are analysed.
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