Thermal characterization of micro thermoelectric coolers: an analytical study

Aim of this paper is to provide a complete characterization of the transient thermal behaviour of thermoelectric (TE) micro-coolers by solving the parabolic heat diffusion equation, through two different analytical methods, the Laplace Transform (LT) and the Separation of Variables (SOV). The results of the performed analysis show that a numerical inversion of the Laplace Transform is necessary, because the analytical-based Riemann-sum approximation does not yield temperature values at very early times. Once the temperature distribution is known in both the semiconductors of the p-n junction, the heat fluxes and the coefficient of performance (COP) of the cooler may be obtained. Then, by applying the proposed procedure to an existing micro-TE cooler, it is observed that the cooling load and the COP reach their maximum values, 2.9 W and 2, respectively, at different times, 3.4 ms vs. 1.7 ms. When a steady-state is reached, the micro-system is characterized by a cooling load of about 1.9 W with an efficiency of nearly 0.5, both in agreement with experimental and numerical data.