Police identified her as Fatima Kama, 28, believed to be Lebanese with a Canadian passport, who had been renting a flat in Marble Arch, central London for several weeks. She was last seen alive by friends on Saturday afternoon, less than nine hours before she was killed.
Police investigating the murder said the woman's family in Canada, including her mother and sister, alerted relatives in Britain when she failed to arrive at the weekend. The British relatives in turn contacted Scotland Yard yesterday after reading about the discovery of the unidentified body at Heathrow.
"They put two and two together and got four. They feared the worst," a police spokesman said.
Ms Kama, who was single, had been due to fly to Montreal with Air Canada, possibly on Sunday, police said.
Her body was found by security staff at Heathrow after members of the public reported the unattended 3ft black suitcase, which had had its wheels removed, near the stairs on the third level car park of terminal 3.
Police were last night interviewing Ms Kama's relatives to piece together her last movements. Investigators believe the killer may have caught a flight out of Britain immediately after abandoning her body. They are examining hours of closed circuit television footage and checking passenger lists to try to identify the murderer from among thousands of travellers who boarded 200 flights leaving terminal 3 on Saturday.
Police believe the killer was in the car park for minutes to dump the suitcase before catching a flight.
They do not know whether the suitcase was brought into the car park by car or foot, and have not ruled out the possibility it was taken to Heathrow by Tube. They are appealing to anyone who may have seen someone struggling with a heavy suitcase on Saturday to come forward. "One of the theories we are working on at the moment is that whoever murdered this woman left the suitcase at the car park, then caught a flight out," Chief Inspector Richard Taber said.
"We know that she wasn't killed at the location. We're working on the theory that she was brought into the car park."
Flights from the terminal go to the Far East, the Middle East, the US and Australasia, and police are checking passenger lists. They also plan to trace 1,500 drivers caught on camera entering or leaving the car park that day. There were no surveillance cameras in the car park.
Chief Inspector Tabar said the victim was 5ft tall and weighed 10 stone, but the killer must have struggled with the case and may have been bloodstained.
"It was an extremely violent attack," Chief Inspector Tabar said.
"This woman has been subjected to multiple stab wounds and has died as a result of them.
To have your loved one bundled ignominiously into the suitcase and callously abandoned in a car park, I think, is awful."
Anyone with information can contact detectives on 0181 247 4567 or 0800 555111.
