Model of a total momentum filtered energy selective electron heat pump affected by heat leakage and its performance characteristics

A total momentum filtered energy selective electron (ESE) heat pump model with heat leakage is established in this paper. The analytical expressions of heating load and coefficient of performance (COP) for both the total momentum filtered (k_r-filtered) ESE heat pump and the conventionally filtered (k_x-filtered) ESE heat pump in which the electrons are transmitted according to the momentum in the direction of transport only are derived, respectively. The optimal performance of the k_r-filtered ESE heat pump is analyzed by using the theory of finite time thermodynamics (FTT). The optimal regions of COP and heating load for the k_r-filtered heat pump are obtained. By comparing the performance of the k_r-filtered device with that of the k_x-filtered device, it is found that the heating load performance and the COP versus heating load characteristic curves of the k_r-filtered heat pump are totally different from those of the k_x-filtered device; and the maximum COP and maximum heating load of the k_r-filtered device are generally higher than those of the k_x-filtered device. The influences of heat leakage, resonance width, hot reservoir temperature and chemical potential on the performance of the total momentum filtered ESE heat pump are further analyzed by numerical calculations. The obtained results can provide some theoretical guidelines for the design of practical electron systems such as solid-state thermionic heat pump devices.