This work presents the implementation of a dual-extended Kalman filter (DEKF) in a double pipe counter-current heat exchanger. The DEKF aims to estimate online the heat transfer coefficient (HTC) to monitor the process. Some investigations estimate parameters in heat exchangers to detect fouling. However, there is limited research on online estimation using DEKF. The tests were performed at two operating conditions: in the first condition, the inlet temperatures were without perturbation; meanwhile, in the second operating condition, the cold-water inlet temperature was perturbed by the environmental heat. The experimental tests were carried out at different cold mass flow rates, which impact the temperatures and vary the heat transfer coefficient of the heat exchanger. The results showed adequate agreement between the estimated values of the heat transfer coefficients and those calculated with algebraic equations. This adequate agreement indicates that the DEKF method is conducive to detecting some problems in heat exchanger applications, such as poor heat transfer performance caused by fouling.

This article presents the implementation of an adaptive observer to validate a falling film evaporator mathematical model. The evaporator consists of four coils, and each coil has four tubes. The heating flow in the first and third coils flows from bottom to top. Meanwhile, the heating flow in the second and fourth coils flows from top to bottom. The mathematical model of the evaporator is parameterized with the geometry data of the experimental device. Since the mathematical model depends on the film breakdown onset Reynolds number ($R{e}_{Onset}$) to estimate the evaporator temperatures, an adaptive observer is applied to estimate this unknown parameter ($R{e}_{Onset}$). The observer design is developed through the evaporator mathematical model. The research aims to estimate the $R{e}_{Onset}$ at different operating conditions to accurately estimate the evaporator temperatures since there is no general correlation for estimating it or a sensor to measure this parameter. Once the $R{e}_{Onset}$ is estimated at different operating conditions, the $R{e}_{Onset}$ results are injected into the model for validation. The results of implementing the observer showed that the temperature estimation errors are between 0.00003% and 0.02815%. Moreover, the temperatures simulated with the model using the $R{e}_{Onset}$ estimated with the observers had errors between 0.04012% and 0.14160%.