A SIMULATOR INDEPENDENT DYNAMIC EFFECTIVENESS-NTU MODEL FOR HEAT-EXCHANGER PERFORMANCE PREDICTION UNDER FLOW, TEMPERATURE, AND FOULING DEPENDENT OPERATION
DOI:
https://doi.org/10.51699/bcapab05Keywords:
Heat-exchanger performance, Fouling dynamics, Effectiveness–NTU method, Logarithmic mean temperature difference, Asymptotic fouling resistance, Analytical sensitivity analysis, Thermal degradation, Cleaning-schedule optimizationAbstract
Fouling is the dominant cause of the progressive loss of thermal duty in industrial heat exchangers, yet the design and monitoring of these units still rely largely on constant fouling factors that ignore the dependence of deposition on flow rate and surface temperature. This work develops a self-contained, simulator-independent mathematical model that couples the steady-flow energy balance, the logarithmic-mean-temperature-difference (LMTD) relation and the effectiveness–number-of-transfer-units (ε–NTU) formulation to an asymptotic, Kern–Seaton-type fouling law whose deposition and removal terms are written as explicit functions of tube velocity and film temperature. The overall heat-transfer coefficient, the effectiveness and the duty are advanced in time by integrating a single ordinary differential equation for the fouling resistance, with the thermal field solved quasi-steadily at each instant. Closed-form normalized sensitivity coefficients are derived for the effectiveness, the duty and the overall coefficient with respect to NTU, mass flow rate, inlet temperature difference and fouling resistance, and a dimensionless fouling-degradation number Θ = Uc Rf* is introduced to collapse the asymptotic performance loss onto a single group. The framework is verified against the exact ε–NTU/LMTD duty identity and against the analytical solution of the fouling law, and is then exercised on a thermodynamically consistent counterflow shell-and-tube case study. At the design velocity the model predicts a 20% reduction in the overall coefficient, a 10.7% loss of duty and a 30-day fouling time constant, and it reproduces the experimentally reported inverse-square dependence of that time constant on velocity. An uncertainty analysis quantifies the amplification of measurement error near a close temperature approach. The resulting model is transparent, computationally trivial and readily embedded in performance-monitoring and cleaning-schedule tools.
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