This paper presents the detailed mathematical modelling and simulation of complex plate heat exchangers under milk fouling, using computational fluid dynamics models. A complex fouling model based on a reaction/mass transfer scheme is described where all the important factors during milk heat treatment are quantified in a formal way. This model is coupled with detailed dynamic models of plate heat exchangers (PHEs). 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 have been compared with available experimental work and a satisfactory agreement has been found. Three different industrial configurations with complex flow arrangement are considered to illustrate aspects of fouling behaviour.