Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial
Flight Crew Last 90 Days 150; Flight Crew Total 751; Flight Crew Type 1
Distraction; Situational Awareness; Time Pressure; Communication Breakdown; Confusion
Airspace Violation All Types; Conflict NMAC; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Took Evasive Action
Human Factors; Procedure
We were taking off from ZZZ and on initial climb out from Runway XX. There had been several prior departures before us that had used the same runway.  Approximately 2 miles from the runway we got a traffic alert on our iPads and it was descending into us. The aircraft appeared to be heading into Runway XY and was no making any radio calls.  Our eyes immediately went outside the aircraft trying to make contact with the aircraft.  We continued to climb as he was descending into us and we made a right turn to avoid head on traffic.  Eventually we were able to make visual contact with the airplane and he was approximately 200 feet above us. After we were clear of the aircraft my scan came back inside and I noticed that we were about 100 feet into the ZZZ1 Class Bravo airspace.  Immediately a descent was made out of the airspace and the flight continued.  We did not hear the other aircraft make any calls on the CTAF throughout their flight/approach.Looking back this all happened very fast; and I would have done a couple things differently.  We should have leveled off immediately and made a right hand turn.  However; in the moment we were not sure exactly the location of the aircraft.  Had we done that we would have remained clear of the other aircraft and remained clear of the Bravo airspace.
An instructor pilot departing a non-towered airport reported a NMAC with opposite direction landing traffic which had not been communicating on the CTAF.