arXiv:2610.41364v1 Announce Type: new Abstract: Existing low-order models of heat exchangers can lose dynamic accuracy at low flow rates, when fluid residence times become significant. This paper proposes two control-oriented models that improve the low-flow performance. The first extends a finite-volume formulation with the first spatial temperature moment, whereas the second uses Chebyshev--Lobatto collocation. Both capture the coupled heat-transfer and transport dynamics and improve the performance when the system behavior is dominated by the inlet-temperature dynamics. At equal state dimension, comparisons with a high-order reference show more accurate delayed outlet-temperature responses while retaining steady-state accuracy.