Optimization and Entropy Production: Application to Carnot-Like Refrigeration Machines

Abstract

Several optimization models of irreversible reverse cycle machines have been developed based on different optimization criteria in the literature, most of them using linear heat transfer laws at the source and sink. This raises the issue how close to actual operation conditions they are, since the heat transfer law on the phase-change processes is dependent on ΔT3. This paper addresses this issue by proposing a general model for study and optimization of thermal machines with two heat reservoirs applied to a Carnot-like refrigerator, with non-linear heat transfer laws and internal and external irreversibility. The optimization was performed using First and Second Law of Thermodynamics and the Lagrange multipliers method. Thus, several constraints were imposed to the system, also different objective functions were considered, allowing finding the optimum operating conditions, as well as the limited variation ranges of the system parameters. Results show that the nature of the heat transfer laws affects the optimum values of system parameters for obtaining maximum performances and also their magnitude. Sensitivity studies with respect to system several parameters are presented. The results contribute to the understanding of the system limits in operation under different constraints and allow choosing the most convenient variables in given circumstances.

Progress in Carnot and Chambadal Modeling of Thermomechanical Engine by Considering Entropy Production and Heat Transfer Entropy

“…Nevertheless, it does not reflect the exact physical behavior of the endo-irreversible Carnot heat engine that could be different to the linear one. Thus, only (10), which is based on energy and entropy balances, will provide the correct expression of the mechanical work.…”

“…Numerous studies are concerned with the influence of: the form of the heat transfer laws at source and sink [ 6 , 7 , 8 , 9 , 10 ]; the nature of the sources and sinks (thermostats, fluid flows without phase change) [ 11 , 12 ]; various objective functions [ 10 , 13 , 14 , 15 , 16 ]; consideration of added constraints [ 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ]; thermal losses or adiabaticity [ 26 , 27 , 28 ]; various irreversibilities (mainly global approaches by considering Δ S I or I [ 4 ]; or introduced by mechanisms, namely solid or fluid energy dissipation) [ 5 ]. …”

Performance of Universal Reciprocating Heat-Engine Cycle with Variable Specific Heats Ratio of Working Fluid

“…Using finite time thermodynamics (FTT) [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 ] to optimize the performances of practical cycles and processes, a series of achievements were made, including Novikov heat engines [ 17 , 18 , 19 , 20 , 21 ], Curzon–Ahlborn heat engines [ 22 , 23 , 24 ], solar-driven engines [ 25 , 26 ], Maisotaenko cycle [ 27 , 28 , 29 ], OTEC systems [ 30 , 31 , 32 ], Kalina cycle [ 33 ], thermoelectric devices [ 34 , 35 , 36 , 37 , 38 , 39 ], dissipative heat engine [ 40 ], refrigeration cycle [ 41 ], earth [ 42 ], quantum systems [ 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 ], economic systems [ 51 , 52 ], chemical systems [ …”

Effect of Machine Entropy Production on the Optimal Performance of a Refrigerator

“…By examining recently published scientific works regarding reverse cycle machines, one remarks that more papers are devoted to refrigerating machines than to heat pumps [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ], which also corresponds to current applications that are more and more developed; that is, refrigeration freezing and deep-freezing in the food industry, air conditioning, heat pumps, or medical applications.…”