An analytical development of the hyperbolic behaviour of micro thermoelectric coolers

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.