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Analytical and numerical estimates of efficiency for an irreversible heat engine with distributed working fluid.

Previous work on estimating power output from heat engines is extended to estimating efficiency under finite-time constraints. A numerical method for estimating efficiencies for a class of finite-time thermodynamic models with variable-temperature reservoirs and arbitrary heat-exchange laws is proposed. The method is based on energy and entropy balances, and on the use of optimal control, Lagrange multipliers, and convex optimization. It is applicable both to lumped-parameter and distributed-parameter models. An analytical expression for the upper bound of the efficiency is obtained for constant-temperature reservoirs and Newtonian heat-exchange laws. Results of computations for two efficiency definitions are presented.