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

Area of Science:

• Thermodynamics
• Thermal Engineering
• Refrigeration Cycles

Background:

• Existing optimization models for irreversible reverse cycle machines often use linear heat transfer laws.
• Linear models may not accurately represent actual operating conditions, especially during phase-change processes where heat transfer is non-linear (dependent on ΔT³).

Purpose of the Study:

• To propose a general model for the study and optimization of thermal machines with two heat reservoirs.
• To apply this model to a Carnot-like refrigerator considering non-linear heat transfer laws and irreversibilities.
• To determine optimum operating conditions and parameter ranges under various constraints.

Main Methods:

• Development of a general thermodynamic model for reverse cycle machines with non-linear heat transfer.
• Application of First and Second Laws of Thermodynamics for analysis.
• Utilizing the Lagrange multipliers method for optimization under defined constraints.
• Consideration of internal and external irreversibilities.

Main Results:

• The nature of heat transfer laws significantly affects the optimal values and magnitude of system parameters for maximum performance.
• Identified optimum operating conditions and limited variation ranges for system parameters.
• Sensitivity analyses were performed to understand parameter influence.

Conclusions:

• The proposed model provides a more realistic approach to optimizing refrigerators by incorporating non-linear heat transfer.
• Understanding the impact of heat transfer laws is crucial for achieving maximum system performance.
• The findings aid in selecting optimal operating variables under specific constraints for enhanced efficiency.