Abstract. In this article, A Multi-Input Multi-Output system is mathematically modelled using energy balancing differential equations. To model a MIMO system, specifications are very important. The data samples of MIMO are collected from a shell and tube heat exchanger hardware setup. The real time data samples collected are substituted in the predefined differential equation to create a Shell and Tube heat exchanger model. The model output would result as the output obtained from a shell and tube heat exchanger hardware setup. Since shell and tube heat exchanger modelled has two inputs and two outputs, system model is also a TITO system. The System identification method was employed for TITO system modelled to obtain the linear model as the output was highy nonlinear and its transfer function model was determined that had process interaction. The interaction in process doesn‘t allow the system to attain its steady state value faster. Classical controllers were employed for the process to attain steady state faster but the results were not satisfactory. So, Model Predictive controller was used for the designed system to obtain the output responses faster to the desired value by minimizing the error drastically. The nonlinear model response, linearized model response, open loop response and closed loop response with MPC for the designed system were compared and analyzed.