On July 7, 1998, about 0640 central daylight time, a Boeing 737-7H4, N701GS, registered to and operated by Southwest Airlines Company as flight 1565, a Title 14 CFR Part 121 scheduled domestic passenger flight from Tampa, Florida, to Birmingham, Alabama, had a failure of the No. 2 engine during descent for landing at Birmingham. Visual meteorological conditions prevailed at the time and an instrument flight rules flight plan was filed. The aircraft received minor damage. The airline transport-rated pilot, first officer, 3 flight attendants, and 91 passengers were not injured. The flight originated from Tampa, Florida, the same day, about 0549. The pilots reported to an FAA inspector and the operator that they were at 3,000 feet msl, about 20 miles from Birmingham, while in descent for landing, when they observed an indication that the No. 2 generator was off line and observed a rise in the No. 2 engine exhaust gas temperature. Flight attendants reported to them that flame was visible coming from the No. 2 engine tailpipe and extending aft toward the tail of the aircraft. They did not receive a fire warning for the No. 2 engine and did not activate the fire extinguishing system. They shut down the No. 2 engine and made an uneventful landing at Birmingham. After landing, they stopped on the taxiway and shut down the remaining engine. After fire department personnel on the ground examined the aircraft for fire and deemed it safe, the aircraft was towed to the gate, where the passengers were deplaned via the jetway. Examination of the digital flight data recorder, removed from N701GS after the incident, showed the aircraft was level at 2,875 feet pressure altitude, at an airspeed of 239 knots, on a heading of 310 degrees. The N1 speed for the Nos. 1 and 2 engines was 25.8 and 25.6 percent respectively. The fuel flow for the Nos. 1 and 2 engines was 656 pounds per hour. TheNo. 2 engine fuel flow then increased from a value of 656 pounds per hour to a high of 3,920 pounds per hour over a 74 second period, and then began to decrease. The No. 2 engine exhaust gas temperature (EGT) increased from 430 degrees centigrade to a high of 973 degrees centigrade over a 52 second period and then began to decrease. The No. 2 engine cutoff occurred about 74 seconds after the EGT began to rise. The N1 speed for the No. 2 engine decreased from 25.6 percent to 12.8 percent at the time of engine cutoff. (See attached Flight Data Recorder Specialist's Factual Report) Postcrash examination of the aircraft by an FAA inspector showed the tailpipe of the No. 2 engine contained metal debris. The aircraft structure had no fire damage. Examination of the No. 2 engine was performed at General Electric Aircraft Engines, Strother, Kansas, following removal from N701GS at Birmingham, Alabama. Examination showed that the melted metal debris found in the tailpipe was from the low pressure turbine and that the N1 rotor was locked. All chip detectors were clean and there was no evidence of fuel in the engine oil. Diagnostic interrogation of the engine's electronic control unit (ECU) revealed the hydromechanical unit (HMU) had a fuel metering valve (FMV) feedback disagree fault on Channel A and B and an FMV feedback out of range fault on Channel B. The HMU was removed from the engine for testing. Testing of the HMU showed the resolver module's Channel B sine output voltage became unstable when the HMU was tested on a flow bench with the test fluid heated to 180 degrees Fahrenheit. The resolver module was removed from the HMU and tested separately. The tests confirmed that when the resolver module was heated above 160 degrees Fahrenheit, the Channel B sine output voltage became unstable. Disassembly of the resolver unit revealed a broken wire to the sine magnet stator. The ECU computer software logic allowed the unit to lock on the unstable Channel B and lock out Channel A. The unstable sine out voltage of Channel B resulted in the ECU commanding the FMV to a full open position. With the sudden increase in fuel flow while the engine was at idle speed, the core of the engine stalled. Examination of the broken wire by the NTSB Materials Laboratory showed the wire had fracture features typical of ductile overstress separation and that the fracture surface was covered with lead-tin deposits. (See attached NTSB Materials Laboratory Factual Report) Changes were made in the resolver unit design and manufacture processes, the ECU computer software to improve handling of resolver failures, and a dispatch prohibition if a single Channel resolver fault is indicated in the cockpit. (See attached Powerplants Group Chairman Report and CFM report-CFM56-7B Uncommanded Fuel Flow Increase Events) An additional party to the NTSB investigation was John H. Middleton, Kearfott Guidance and Navigation, Black Mountain, North Carolina.