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用有限时间热力学方法分析实际热泵循环性能，计入工质与高、低温热源间换热器和回热器的热阻损失及压缩机、膨胀机中的不可逆损失，导出了变温热源不可逆闭式回热式空气热泵的供热率和供热系数与循环压比间的解析式，并给出了详细的数值算例．
The finite element method was used to analyze the actual heat pump cycle performance. The thermal resistance loss of the heat exchanger and the regenerator between the working fluid and the high and low temperature heat sources and the irreversible loss in the compressor and expander were calculated. The irreversible Closed-loop regenerative air-driven heat pump heat supply and heating coefficient and the pressure ratio between the analytical formula, and gives a detailed numerical examples.