This work presents the mathematical modelling and simulation of complex plate heat exchanger arrangements under milk fouling, using detailed dynamic models. A complex fouling model based on a reaction/mass transfer scheme is coupled with a general thermal dynamic model of plate heat exchangers. All the important factors affecting milk heat treatment are formally quantified. The final model comprises a set of partial differential, integral and algebraic equations. Parameter estimation analysis is performed based on the solution of a dynamic optimization problem. The simulation results are in a good agreement with available experimental work. Three different configurations with complex flow arrangements are considered to illustrate aspects of fouling behaviour. The simulation results provide significant insight into the key factors affecting milk fouling.