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.
Highlights
The second half of the last century saw the emergence of a new branch of Thermodynamics, called Thermodynamics in Finite Time, due to the process duration that was considered by the heat transfer rate [1,2]
The optimization method described above leads to a system of non-linear equations that is numerically solved in Matlab by applying Newton-Raphson method
The above results contribute to the understanding of the system limits in operation under different constraints and allow the engineer to choose the most convenient variables in certain circumstances
Summary
The second half of the last century saw the emergence of a new branch of Thermodynamics, called Thermodynamics in Finite Time, due to the process duration that was considered by the heat transfer rate [1,2]. The corresponding approach emphasized a maximum power regime [3] for an endo-reversible, but exo-irreversible engine. The engine efficiency at maximum power regime is less than the Carnot cycle one, and it introduced the particular form of the “nice radical”. Quite a lot of works analyzing the exo-irreversible engines have been developed [4,5]. They have considered only the external irreversibility of the thermal machine, which is due to the heat transfer at finite temperature difference between the sources and the working fluid. Mainly the linear form of the heat transfer law was used
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