<![CDATA[General Background Fouling is the dominant cause of the progressive loss of thermal duty in industrial heat exchangers across petrochemical, refining, and power generation sectors. Specific Background The design and monitoring of these units still rely heavily on constant fouling factors that ignore the dependency of deposition on flow rate and surface temperature. Knowledge Gap Conventional lumped methods fail to account for local hydrodynamic and thermal conditions, while existing distributed or data-driven models either impose high computational burdens or lack generalized analytical sensitivity. Aims This study develops a self-contained, simulator-independent mathematical model coupling the steady-flow energy balance, logarithmic-mean-temperature-difference (LMTD) relation, and effectiveness–number-of-transfer-units (epsilon-NTU) formulation to an asymptotic Kern-Seaton-type fouling law. Results At design velocity, the model predicts a 20.3% reduction in overall coefficient, a 10.7% loss of duty, and a 30-day fouling time constant, successfully capturing the inverse-square velocity dependence and Arrhenius film temperature effects. Novelty The framework provides a transparent, computationally trivial analytical model that integrates an explicit velocity- and temperature-dependent fouling law with epsilon-NTU performance prediction and closed-form sensitivity coefficients. Implications The proposed simulator-independent tool is readily embedded in performance-monitoring systems, online soft sensors, and cleaning-schedule optimization routines. Key Findings Highlights The dynamic model successfully couples an asymptotic fouling law with epsilon-NTU relations, demonstrating that a 20.3% drop in overall heat-transfer coefficient results in an attenuated 10.7% loss of thermal duty. Asymptotic fouling resistance and time constants scale predictably with tube velocity and film temperature, confirming that higher flow velocities suppress net deposition while surface temperature accelerates it. Closed-form sensitivity coefficients and uncertainty propagation reveal that duty is most sensitive to inlet temperature differences, and near-pinch operations significantly amplify measurement uncertainties in inferred fouling resistance. Keywords Heat-Exchanger Performance, Fouling Dynamics, Effectiveness-NTU Method, Asymptotic Fouling Resistance, Analytical Sensitivity Analysis]]>
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