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The present work illustrates the conceptual design of a new superconducting test facility, ENFASI (Enea FAcility for Superconducting Inserts), which has been mainly conceived to test long length wound conductors. It consists of a background 15 T Nb3Sn solenoid, with a warm bore of 90 cm diameter, divided into three concentric sections corresponding to high field (15 T), medium field (13 T) and low field (8 T), and globally composed of 983 turns. The three different CIC (cable-in-conduit) conductor layouts, one for each section and with rectangular cross-sections, operate at 20 kA and are made of strands with different Cu/nonCu ratios and segregated copper when needed. The facility permits to feed the sample with a current up to 70 kA and to vary the sample temperature in the range [4.5 K-77 K]. The main results of electro-magnetic, structural and thermo-hydraulic analysis which brought to the definition of the main aspects of the design, are presented.