The cold box with heat exchanger plate-fin (PFHE) has been applied in various applications, including air separation units (ASU). Therefore, this cryogenic industry has undergone a lot of development in recent years. Cryogenic technologies are utilized in many industrial procedures where they aid in heat recovery and reduce energy consumption. The multi-stream plate-fin heat exchanger (MSPFHE) is a substantial part of the air separation plant design. In this study, the energy contained in streams resulting from the distillation tower is used to cool the air entering this process to below freezing temperatures (-74 degrees Celsius). In the beginning, to find a suitable model and design, analytical solutions were used to find the heat duty and the optimal heat transfer area, including thermodynamic properties calculations, fin geometry dimensions, heat transfer calculations, and pressure drop calculations. The heat exchanger's design has also been evaluated analytically by calculating the fin efficiency and overall efficiency. A MATLAB code was written to achieve speed, accuracy, and consideration of all possible values. Input data from one of the studies in the literature was used as input for a case study. Finally, the rating of the design of the heat exchanger was done by one of the well-known software programs (EDR), and the results of this work were compared to those of previously published studies and they were found to be good and compatible.