As urban centers grow and environmental regulations become more stringent, the complexity of integral systems within vehicles, aircraft, and other urban essentials escalates. A pivotal response to this challenge involves achieving enhanced energy efficiency and environmental appeal while maintaining cost-effectiveness. In this context, mathematical modeling, coupled with simulation and optimization techniques, emerges as a pivotal tool. This approach yields favorable outcomes with modest initial investments, contrasting with the resource-intensive nature of purely experimental design. Amongst the fundamental components, heat exchangers find widespread use, facilitating thermal exchange between fluids across diverse applications. Consequently, meticulous design and parametric optimization of these devices to attain peak performance and optimal energy efficiency are imperative, aligning with evolving environmental and energy trends. The simulation of such systems operates within an expansive range of operational and geometric parameters. These encompass mass flow rates, line pressures, pipe diameters, and pipe placements. However, excessive parameter combinations can render optimization computationally infeasible, necessitating judicious simplifications. Striking a balance between precision and computational efficiency, reduced-order models present a valuable intermediary solution. These models, situated between low- and high-order methods, offer robust mathematical representations without significant precision compromises. Thus, reduced-order models, which constitute an intermediate approach when compared to low- and high-order methods, can be used as a mathematical modeling tool without a significant loss of precision in the results. The present work presents an optimization and parametric analysis of a recuperative heat exchanger using a reduced-order approach employing the volume element model (VEM) as a discretization method, which is capable of providing accurate results at low costs. computational. The Laws of Conservation of Mass and Energy are applied to volume elements in combination with empirical correlations in order to quantify the quantities of interest, such as the convection heat transfer coefficient and temperature distribution. A parametric analysis was performed in order to observe the behavior of entropy generation in order to find its minimum points. The mass flow of water varied from 0.001 kg/s to 0.0085 kg/s with the mass flow of hot gases and the mass flow rate of gas was held constant in three stages, namely: 0.14 kg/s; 0.2 kg/s; and 0.3 kg/s. The local minimum was obtained for each of the three gas mass flow rate considerations, 8.53 W/K, 8.78 W/K, and 9.20 W/K respectively.