Approximate Model of Thermoeconomic Optimization for Printed‐Circuit Heat Exchangers in Sodium–Nitrogen Dispatchable Nuclear Power Systems

Dispatchable power systems, adjusting power in response to energy demand variations, are essential to address renewable intermittency. In this study, a thermoeconomic optimization framework for printed‐circuit heat exchangers (PCHEs) is proposed, focusing on sodium–nitrogen dispatchable systems. To enhance the framework, approximate models were developed to predict the optimal Reynolds (Re) numbers for thermoeconomic design without discretizations or iterations. These models are derived from the dominant thermal resistance characteristics of each exchanger type: gas‐side convective resistance rather than liquid metal resistance in intermediate heat exchangers (IHXs) and symmetric convective resistance in recuperators that use nitrogen on both sides. The approximate models for the IHX and recuperator closely matched the optimal design results from a validated one‐dimensional (1‐D) PCHE code, with deviations below 10% across a wide range of operating and design conditions. The models successfully predicted how the optimal design trends shifted in response to variations in thermoeconomic parameters. The optimal Re number increased with larger hydraulic diameters and higher material costs and decreased as the electricity cost increased. The channel shapes (straight, zigzag, and airfoil) significantly influenced the optimal design: the straight channel exhibited the highest optimal Re number, the zigzag channel the lowest, and the airfoil channel an intermediate value, with enhanced geometries yielding lower total costs and flow requirements. These findings demonstrate that the approximate models are effective analysis tools for identifying cost‐performance tradeoffs and trend variations. The approximate models are highly usable for early‐stage design, technoeconomic screening, and rapid optimization of advanced energy systems under diverse design constraints.