An analytical solution for the hyperbolic unsteady thermal behaviour of micro-thermoelectric coolers with a suddenly time-dependent heat generation

The ultrafast thermal behaviour of a micro thermoelectric cooler under the hyperbolic heat conduction model is analysed. An important step forward is taken in that the instantaneous application of the electric current is modelled by means of the Heaviside function. Two terms of internal heat generation derive from this model: the former is time-independent, whereas the latter is time-dependent through Dirac’s delta function. A modified Separation of Variables method is used to solve analytically the governing equations. Also, the initial linear problem is split up into three sub-problems through the principle of superposition. In order to eliminate the numerical oscillations in the temperature profiles at early times in correspondence of the wave fronts, the semi-infinite hyperbolic body model is considered. The performance (COP) of the device is evaluated and then compared with that derived from the parabolic case. An increase of about 27% is observed at early times.