The prediction of important control properties is a challenging task for shell and tube heat exchangers design. Dynamic models, which include fouling effects, are still poorly investigated in the recent literature. To study the behavior of variable conditions over time and its influence on the dynamic aspects of the system, a design approach based on TEMA standards has been proposed, aiming to analyze the process in a more realistic equipment. To study the behavior of time-varying conditions and its influence in the system dynamics, the model considered in this work is based on the idea of heat exchanger cells as the basic modeling element. This kind of approach has some advantages over the distributed model, such as continuous variables in time and discrete in space, leading to ordinary differential equations (ODE) and also providing the possibility of controlling the model complexity by adjusting the number of modeling cells. The ratio between output and input signals in each cell generates eight operator transmittances that describe the dynamic of the system. The influence of fouling in the dynamic behavior is evaluated by considering its resistance (R-f) as a function of time. The model was implemented in MATLAB/Simulink and simulations have been carried out for different R-f values with a step change in three input variables. Open loop responses showed that as R-f increases, the quality of response is deteriorated and the system is affected mainly by the inertia and thermal exchange inefficiency.