Optimization of the power output of Carnot and closed Brayton cycles is considered for both finite and infinite thermal capacitance rates of the external fluid streams. The method of Lagrange multipliers is used to solve for working fluid temperatures that yield maximum power. Analytical expressions for the maximum power and the cycle efficiency at maximum power are obtained. A comparison of the maximum power from the two cycles for the same boundary conditions, i.e., the same heat source/sink inlet temperatures, thermal capacitance rates, and heat exchanger conductances, shows that the Brayton cycle can produce more power than the Carnot cycle. This comparison illustrates that cycles exist that can produce more power than the Carnot cycle. The optimum heat power cycle, which will provide the upper limit of power obtained from any thermodynamic cycle for specified boundary conditions and heat exchanger conductances is considered. The optimum heat power cycle is identified by optimizing the sum of the power output from a sequence of Carnot cycles. The shape of the optimum heat power cycle, the power output, and corresponding efficiency are presented. The efficiency at maximum power of all cycles investigated in this study is found to be equal to (or well approximated by) η=1−TL,in/φTH,in where φ is a factor relating the entropy changes during heat rejection and heat addition.
Previous investigators have shown that an internally reversible Carnot cycle, operating with heat transfer limitations between the heat source and heat sink at temperatures TH and TL, achieves maximum power at an efficiency equal to 1−TL/TH independent of the heat exchanger transfer coefficients. In this paper, optimization of the power output of an internally irreversible heat engine is considered for finite capacitance rates of the external fluid streams. The method of Lagrange multipliers is used to solve for working fluid temperatures which yield maximum power. Analytical expressions for the maximum power and the cycle efficiency at maximum power are obtained. The effects of irreversibility and economics on the performance of a heat engine are investigated. A relationship between the maximum power point and economically optimum design is identified. It is demonstrated that, with certain reasonable economic assumptions, the maximum power point of a heat engine corresponds to a point of minimum life-cycle costs.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.