Elizabeth G. Nabel, director of the National Heart, Lung, and Blood Institute and one of the public faces of its parent, the National Institutes of Health, will be the next president of Brigham and Women's Hospital and Faulkner Hospital in Boston. Nabel, 57, is a cardiologist and clinical researcher who graduated from Cornell University Medical College and trained at Brigham and Women's in the 1980s. She was elected as its president in a unanimous vote by the board of trustees that oversees the hospital and its affiliate, Faulkner Hospital. She will begin her new job Jan. 1.