Physics-informed neural control of heat flow rate in a counter-flow heat exchanger: modeling, identification and experimental validation

The advanced operation of heat exchangers plays a critical role in the development of efficient and sustainable multivector energy systems. This paper proposes a hybrid physics-informed and data-driven framework for the analysis, identification, and regulation of transient heat transfer in counter-flow heat exchangers. A parameterized physical model combines classical heat-transfer relations with transport equations to capture convective propagation, transport-induced delays, and nonlinear effects associated with flow-rate variations. The heat-transfer coefficient is identified from experimental data, enabling the characterization of flow-dependent heat-transfer dynamics over a broad operating range. The identified model is then used to develop a hierarchical real-time control strategy. An inner loop regulates the volumetric flow rate using a high-order data-driven linear model, while an outer loop regulates the exchanged heat power using a machine-learning controller initially trained on the physical model and subsequently refined with experimental data. Experimental results demonstrate accurate reproduction of transient heat-transfer dynamics and effective heat-flow-rate regulation under varying thermal boundary conditions (identification fit above 94% in normalized root-mean-square error and total variation of the flow rate reduced by half compared to a proportional-integral controller). The proposed framework combines physical interpretability with data-driven adaptation for the analysis and real-time operation of dynamic heat-transfer systems.