Physics-Informed Neural Networks for Estimating Convective Heat Transfer in Jet Impingement Cooling: A Comparison with Conjugate Heat Transfer Simulations

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Abstract
Efficient cooling is vital for the performance and reliability of modern systems such as electronics, nuclear reactors, and industrial equipment. Jet impingement cooling is widely used for its high local heat transfer rates. Accurate estimation of convective heat transfer coefficient (CHTC) is essential for design, simulation, and control of thermal systems. However, estimating spatially varying CHTCs from limited and noisy temperature data poses a challenging inverse problem. This study presents a physics-informed neural network (PINN) framework to estimate both averaged and spatially varying CHTCs at the fluid-solid interface in a jet impingement setup at Reynolds number 5000. The model uses sparse and noisy temperature data from within the solid and embeds the transient heat conduction equation along with boundary and initial conditions into its loss function. This enables inference of unknown boundary parameters without explicit modeling of the fluid domain. Validation is performed using synthetic temperature data from high-fidelity conjugate heat transfer (CHT) simulations. The framework is tested under various additive Gaussian noise levels (up to 30 percent) and sampling rates 0.25 to 4.0 per second. For noise levels up to 10% and sampling rates of 0.5 per second or higher, estimated CHTCs match CHT-derived benchmarks with relative errors below 8 percent. Even under high-noise scenarios, the framework maintains predictive accuracy when time resolution is sufficient. These results highlight the method's robustness to noise and sparse data, offering a scalable alternative to traditional inverse methods, experimental measurements, or full CHT modeling for estimating boundary thermal parameters in real-world cooling applications.
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