The universal optimal relations of the allocation and effectiveness of the heat exchangers for power plants with $n$ Carnot-like cycles

Abstract

A model of irreversible Carnot-like power plant with $n$ Carnot-like cycles is optimized. The irreversibilities of each cycle are: finite rate heat transfer between the working fluid and the external heat sources, internal dissipation of the working fluid, and heat leak between reservoirs; is extended to two or more of this combined model. Applying the Bellman' Principle, we find the optimal recurrence relations for the allocation of the heat exchangers for thes power plants. The optimal allocation or effectiveness is determined by two design rules, applied alternatively: internal thermal conductance fixed or areas fixed. The optimal recurrence relations obtained for this combined model are invariant to the power and efficiency and to the heat transfer law.