A mathematical model for single shell and tube heat exchangers under milk fouling is presented. A fouling model based on a reaction/mass-transfer scheme is detailed in which the main factors during milk heat treatment are quantified in a formal way. This model is coupled with a detailed dynamic model of a shell-and-tube heat exchanger where both radial and axial domains are taken into account. An analytical procedure for the calculation of key parameters provides the means to achieve more accuracy. The simulation results agree well with available experimental work. Four different heat exchanger arrangements are then considered to illustrate their impact on the fouling behavior. The results are encouraging enough to validate current operating industrial techniques for fouling mitigation. For a given thermal duty, short heat exchangers are more prone to fouling due to high-temperature requirements and milk should be heated 11s gradually as possible to minimize fouling. The results show that there are main tradeoffs between design and operation issues.