Small Aircraft; Low Wing; 1 Eng; Fixed Gear
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 169; Flight Crew Total 591; Flight Crew Type 216
Communication Breakdown
Conflict NMAC
Flight Crew Took Evasive Action
Environment - Non Weather Related; Aircraft
Event occurred while I (instructor) was conducting flight training at ZZZ; flying left closed traffic for Runway XX. My student was flying the aircraft and making position reports on the radio while I was monitoring performance and looking for traffic. We were established on the left downwind for Runway XX when I first saw the potential traffic conflict on ADS-B. My student made a second left downwind position report. The conflicting aircraft was Aircraft Y; who was apparently making a 45 degree entry to the left downwind; continued to directly converge with our aircraft; Aircraft X.  I attempted to make radio contact with the aircraft; who was now confirmed to not be communicating on the CTAF. At this point; I made visual contact with the other aircraft who was now on a direct collision course with our aircraft and I proceeded to take evasive action. My student and I departed the area and flew back to our home airport (ZZZ1). In the future if I spot any potential traffic conflict on ADS-B; and they are not communicating; I will maneuver for adequate spacing well before it becomes a potential conflict.
Instructor pilot reported an NMAC at a non-towered airport with an aircraft that was not on CTAF.