B747 Flight Engineer experiences fuel migration from the Number 4 fuel tank to the Number 3 tank while in the Inboard Tanks To All Engines configuration. When the Number 4 Tank runs dry the Number 4 engine flames out unexpectedly. After recycling the crossfeed valves the engine is successfully restarted.

Narrative

At top of climb we noticed we had a fuel problem. Initially; we noticed that Number 4 Main tank was losing fuel; while Number 3 Main tank was gaining fuel. We were in the Inboard Tanks to All Engines configuration at the time. We initially assumed that I had a problem with the Number 4 Jettison Transfer valve leaking and we cycled it numerous times; but to no avail. We were still losing fuel from Number 4 Main to Number 3 Main. When the fuel in Number 4 main started going below the standpipe level; we knew we had a different problem. I had cycled Number 3 and Number 4 Crossfeed valves already; so I thought we had a different problem. When cycling the cross feeds; I got the proper in-transit indications that the valves were indeed moving to their proper positions. At no time did I ever have the Number 4 Main tank Boost Pump Low Pressure lights flashing; which would have indicated that there was no fuel pressure behind Number 4 engine and that it was being gravity fed. Obviously; I had a different problem. The fuel got down to 0 in Number 4 Main; which I thought was no problem; since the Number 3 and Number 4 Crossfeed Valves were open. The engine then flamed out. We ran the In Flight Engine Shutdown Checklist. I then recycled the Number 3 and Number 4 Crossfeed Valves one more time; got the proper indications; and suggested we try a restart; and ran the In Flight Engine Start Checklist. We did; and the engine restarted. We then continued on our flight to destination. What had occurred was that it was not a migration problem; but a crossfeed problem; even though I was getting the proper indications for its operation. I reiterate that at no time were the Number 4 Main tank Boost Pump Low Pressure lights flashing; indicating to me that there was no positive fuel pressure reaching Number 4 engine. We wrote up the Number 4 Crossfeed Valve. What we did not write up was the in flight shutdown; which is not required per our Aircraft Operating Manual; and is not in our QRH. The event occurred because with the indications I was receiving; it was a fuel migration problem; and I was told this aircraft has had a history of this problem. I only realized that it was something else after the fuel quantity went below the standpipe level.