Effect of heat leak on cascaded heat engines

The effect of heat leak on the performance of cascaded heat engines is investigated. Two heat leak models are suggested. In the first model, the heat leak occurs across consecutive engines. In the second model, the heat leak takes place between the first engine and all other engines. Analytical expressions for the overall efficiency and overall output power of N cascaded engines in terms of the individual efficiencies of the engines, leakage fractions and heat input are derived for both models. The effect of cascading is found to increase the overall efficiency and power output, while the effect of heat leak is to diminish this rate of increase. Optimization of performance is possible for the first model only. Analytical expressions for the intermediate temperatures that maximize power and efficiency in addition to formulae for maximum power and efficiency, for the case of equal heat leak conductances, are developed.

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