Study on heat recovery of a methane-fueled solid oxide fuel cell through two thermoelectric generators and modified absorption refrigeration cycle: Comprehensive 4E analysis with genetic-based optimization

• Utilizing a TEG unit and a TEG-aided branched GAX cycle to increase SOFC efficiency. • Evaluate system performance by conducting a comprehensive parametric study. • Performing a bi-objective optimization to maximize exergy efficiency while minimizing carbon dioxide emission. • Based on optimized settings, exergy efficiency and carbon dioxide emission rate improved by 2.7% and 14.22%, respectively. • The system economic results yielded an 8.82-year payback period. This study presents a novel tri-generation system for combined cooling, heating, and power (CCHP) by integrating a methane-fueled solid oxide fuel cell (SOFC), dual thermoelectric generators (TEGs), and a modified branched generator-absorber heat exchanger (GAX) absorption refrigeration cycle. Comprehensive energy, exergy, economic, and environmental (4E) analyses are performed, followed by multi-objective genetic-based optimization to determine the optimal operating conditions. The effects of SOFC temperature, current density, generator temperature, and degassing range are systematically investigated. Increasing SOFC temperature and current density enhances electricity output and exergy efficiency, although higher current density results in increased emissions and operating costs. Under optimal conditions (SOFC temperature of 900 K, current density of 5000 A/m 2 , generator temperature of 417.5 K, and degassing range of 0.345), the system produces 378.2 kW of electricity and achieves a maximum exergy efficiency of 55.49%. The total input exergy rate is 703.52 kW, of which 390.40 kW (55.48%) is converted into useful products, including 354.80 kW (50.42%) of electricity, 21.58 kW (3.07%) of heating, and 14.00 kW (1.99%) of cooling. The overall exergy destruction rate is 290.82 kW (41.33%), mainly attributed to the SOFC, the first heat exchanger, and the first throttle valve. Carbon dioxide emissions are reduced to 110.4 kg/MWh, representing a 14.22% decrease compared to the base case. Moreover, cooling and heating capacities increase by 16.12 and 4.22%, respectively, the sustainability index improves by 11.01%, and the payback period decreases from over 20 years to 8.82 years under optimized product selling prices.