This paper presents the development of an iterative analytical model for optimizing the Colburn j factor in full-scale compact heat exchangers, with a specific focus on the geometrical effects of plain and offset fin configurations. The model utilizes a comprehensive set of equations that represent primary and secondary surface areas, flow channel dimensions, and hydraulic diameters of the fins. The j factor, a key parameter in evaluating heat transfer performance, is computed by employing numerical analysis techniques, including the Newton–Raphson f-solve method, which iteratively solves for thermal characteristics based on fin geometry and flow conditions. This work builds on analytical equations for the heat exchanger’s heat transfer and flow characteristics, making it adaptable to a wide range of geometries and conditions. The iterative approach ensures accuracy in predicting the optimized j factor, enabling its use in optimization tasks for design purposes. The results offer insights into the behavior of both plain and offset fins, providing engineers with a valuable tool for designing high-efficiency compact heat exchangers. These findings have potential applications in enhancing thermal performance in aerospace engineering, playing a pivotal role in managing thermal loads in various systems, such as engine cooling, environmental control systems, and electronics cooling. In the aerospace industry, where weight, space, and efficiency are paramount, compact heat exchangers offer significant advantages. Their ability to deliver high heat transfer rates while occupying minimal space makes them ideal for aerospace applications, where every gram and cubic centimeter counts.
