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Based on the thermosize effects of a confined ideal Maxwellian gas, we established a model of micro/nano-scaled heat pump including two isothermal and two isobaric processes, where the Joule-like heating effect was analyzed in detail by using the nonequilibrium thermodynamic theory. Further, in order to improve the performance of a single thermosize device, a model of two-stage micro/nano-scaled heat pump with multiple micro/nano components is for the first time put forward. The general expressions of heating load and coefficient of performance for the single and the two-stage heat pump are derived. The influences of the internal and external irreversibilities of the system, i.e., Fourier heat flow and the Joule-like heating and the finite rate heat transfer with the reservoirs, on the performance characteristic of thermosize devices are studied in detail. Moreover, we also discuss the effect of the allocation the thermosize components on the optimal performance of the two-stage micro/nano-scaled heat pump cycle. It is found that in the presence of the internal and external irreversibilities, the two kinds of the micro/nano-scaled heat pump can achieve specific heating performance. In particular, when the total number M of the thermosize components is fixed, both the maximum of the optimal coefficient of performance Φ opt , max and the maximum of the heating load Π opt , max corresponding to the optimal coefficient of performance appear near n = M / 2 with n being the number of the thermosize elements of the top stage. The results obtained here show several main irreversibility source of the micro/nano-scaled heat pump and have potential applications in the efficient utilization and conversion of energy in the microchannel system using gas.

The new model of a quantum refrigeration cycle composed of two adiabatic and two isomagnetic field processes is established. The working substance in the cycle consists of many non-interacting spin-1/2 systems. The performance of the cycle is investigated, based on the quantum master equation and semi-group approach. The general expressions of several important performance parameters, such as the coefficient of performance, cooling rate and power input, are given. It is found that the coefficient of performance of this cycle is a close analogue of the classical Carnot-cycle. Some performance characteristic curves relating the cooling rate, the coefficient of performance and power input are plotted. Further, for high temperatures, the optimal relations between the cooling rate and the coefficient of performance are analyzed in detail.

The influence of quantum degeneracy on the performance of a Stirling refrigeration cycle is investigated, based on the equation of state of an ideal Fermi gas. The inherent regenerative losses and the coefficient of performance (COP) of the cycle are calculated. It is found that, under the condition of strong gas degeneracy, the COP of the cycle in the first approximation is a function only of the temperatures of the heat reservoirs, while under other conditions, the COPs of the cycle depend on the temperatures of the heat reservoirs and other parameters of the cycle. The results obtained here reveal the general performance characteristics of a Stirling refrigeration cycle having a Fermi gas as its working substance.