Self-Driven Reverse Thermal Engines Under Monotonous and Oscillatory Optimal Operation

The complex time-dependent heat and electromagnetic energy transfer in a new type of reverse thermal engine is analyzed. The reverse thermal engine consists of a cold body, a Peltier element and an electric circuit containing an inductor with controllable inductance. This system allows cooling a body below the ambient temperature. The inductor acts as an accumulator of magnetic energy, receiving electrical work from the Peltier element during some time intervals and supplying the Peltier element with electrical work during other time intervals. The system is named self-driven reverse thermal engine since one of its subsystems (the inductor) receives and releases work. The new type of engine has features which make it different from classical reverse thermal engines: it cannot operate in steady state and it operates for a finite time interval. Instead of usual indicators of performance such as the coefficient of performance, other performance indicators should be used, such as the minimum cooled body temperature and the interval of time needed to reach a given cooled body temperature. Significant cooling effects do not necessarily need high inductance values. The operation of the new engine has been optimized by using direct optimal control procedures. The open-source program package BOCOP has been used to transform the optimal control problem into a non-linear dynamic problem. The minimum temperature reached by the cooled body depends on its mass. There exists, however, a global minimum temperature, for a specified optimum mass of the cooled body. The minimum temperature decreases by increasing the value of the Seebeck coefficient and by decreasing the thermal conductance. Thermal damped oscillations may arise under special circumstances. This implies a very small difference between the initial temperatures of the cold and cooled bodies and a specific range of variation for the conductance of the Peltier element.