Endoreversible Modeling and Optimization of a Multistage Heat Engine System with a Generalized Heat Transfer Law via Hamilton-Jacobi-Bellman Equations and Dynamic Programming

• Authors: S. Xia , L. Chen , F. Sun
• Languages of publication: EN

Abstracts

EN

A multistage endoreversible Carnot heat engine system operating between a finite thermal capacity high-temperature fluid reservoir and an infinite thermal capacity low-temperature environment with a generalized heat transfer law [q ∝ ( Δ (T^{n}))^{m}] is investigated in this paper. Optimal control theory is applied to derive the continuous Hamilton-Jacobi-Bellman equations, which determine the optimal fluid temperature configurations for maximum power output under the conditions of fixed initial time and fixed initial temperature of the driving fluid. Based on the general optimization results, the analytical solution for the case with Newtonian heat transfer law [q ∝ Δ(T)] is further obtained. Since there are no analytical solutions for the other heat transfer laws, the continuous Hamilton-Jacobi-Bellman equations are discretized and the dynamic programming algorithm is adopted to obtain the complete numerical solutions of the optimization problem, and the relationships among the maximum power output of the system, the process period and the fluid temperature are discussed in detail. The results show that the optimal high-temperature fluid reservoir temperature for the maximum power output of the multistage heat engine system with Newtonian and linear phenomenological [q ∝ Δ (T^{-1})] heat transfer laws decrease exponentially and linearly with time, respectively, while those with the Dulong-Petit [q∝(Δ T)^{1.25}], radiative [q∝ Δ (T^4)] and [q∝(Δ(T^4))^{1.25}] heat transfer laws are different from the former two cases significantly.

Keywords

EN

05.70.-a; 05.60.Cd; 05.70.Ln

Discipline

• 05.60.Cd: Classical transport
• 05.70.Ln: Nonequilibrium and irreversible thermodynamics(see also 82.40.Bj Oscillations, chaos, and bifurcations in physical chemistry and chemical physics)
• 05.70.-a: Thermodynamics(see also section 64 Equations of state, phase equilibria, and phase transitions, and section 65 Thermal properties of condensed matter; for chemical thermodynamics, see 82.60.-s; for thermodynamics of plasmas, see 52.25.Kn; for thermodynamic properties of quantum fluids, see 67.25.bd, and 67.30.ef; for thermodynamics of nanoparticles, see 82.60.Qr, and 65.80.-g; for thermodynamic processes in astrophysics, see 95.30.Tg; for thermodynamics in volcanology, see 91.40.Pc)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2011
• Volume: 119
• Issue: 6
• Pages: 747-760

Dates

published

2011-06

received

2011-02-11

Contributors

author

S. Xia

• College of Naval Architecture and Power, Naval University of Engineering, Wuhan 430033, P.R. China

author

L. Chen

• College of Naval Architecture and Power, Naval University of Engineering, Wuhan 430033, P.R. China

author

F. Sun

• College of Naval Architecture and Power, Naval University of Engineering, Wuhan 430033, P.R. China

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Identifiers

DOI

10.12693/APhysPolA.119.747