This Thesis is conducted in the framework of a cooperation between DIAEE (Department of Astronautic, Electrical and Energy Engineering) of University of Rome and the Experimental Engineering Division (FSN-ING) of ENEA C.R. Brasimone, under the coordination of the European project Horizon2020 EUROfusion. Its aim is the development of a conceptual design for the Primary Heat Transfer System of the nuclear reactor DEMO, also demonstrating the compatibility with the main engineering requirements. The activity focuses on the thermal-hydraulic design, the sizing and analyses of the main components of the Primary Heat Transfer System and Energy Storage System. This is pursued through engineering approaches and the application of RELAP 5-MOD3.3, the main numerical tool between the thermal-hydraulic system codes.