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Mathematical Problems in Engineering
Volume 2015, Article ID 697639, 10 pages
Research Article

An Analytical Development of the Hyperbolic Behaviour of Micro Thermoelectric Coolers

1Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, Via Vetoio, Località Coppito, 67100 L’Aquila, Italy
2Department of Industrial and Information Engineering and Economics, University of L’Aquila, Via Giovanni Gronchi 18, 67100 L’Aquila, Italy

Received 9 March 2015; Revised 7 October 2015; Accepted 8 October 2015

Academic Editor: John D. Clayton

Copyright © 2015 Giulia De Aloysio et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The transient behaviour of a micro thermoelectric cooler is described in the present paper through the theory of the thermal wave, involving the relaxation time. The internal heat generation due to the sudden application of the electric current is taken into account by means of the Heaviside function. The governing equations of both the semiconductors are solved by a modified Separation of Variables Method that allows us to have a better description of the device which can be obtained at early times. As regards the performances, the cooling load shows discontinuities due to the contributions of the travelling wave fronts of both the semiconductors. The results show that the coefficient of performance (COP) of the device obtained with the hyperbolic model is lower than that provided by the parabolic model at early times.