Efficient and robust reduced-order prediction of thermal coupling and fluid flow in cross-flow heat exchangers

Cross-flow plate-fin heat exchangers in compact thermal systems require modeling approaches that capture channel-to-channel thermal coupling without incurring prohibitive computational costs during design iterations. To address this, a physics-based reduced-order model (ROM) is formulated from element-wise mass and energy balances. The solid wall and fin domains are represented by a two-dimensional longitudinal-conduction network, with convective terms evaluated using an effective finned surface area to account for finite fin efficiency. The physical interlayer conductance is treated separately from the numerical under-relaxation, which is used solely to stabilize the fixed-point iteration. The formulation accepts independent, prescribed mass-flow rates for individual channels and explicitly couples neighboring elements through the solid matrix. Numerical verification against a conjugate heat-transfer finite-element model gives a maximum wall-temperature deviation of 2.1 K. The selected 100×100 ROM grid requires 2.4597 s, compared with 354 s for the reference model, corresponding to a case-specific speed-up of approximately 144. Furthermore, comparison with published offset-strip-fin experiments yields mean absolute percentage errors of 1.53% for heat duty and 7.55% for pressure drop. The ROM is subsequently applied to assess heat exchanger performance in non-ideal scenarios, specifically focusing on inlet flow maldistributions and non-adiabatic conditions on the end-plates of a three-dimensional prototype. Results indicate that a uniform inlet profile yields 13.8% more heat transfer than the strongest Gaussian profile at a given flow rate, while heat leakage from the end-plates strongly depends on the number of layers and the ambient environment. Ultimately, these results confirm that the ROM is a highly effective tool for the rapid assessment of longitudinal conduction, prescribed channel-flow nonuniformity, and boundary heat leakage.