UPDATE 1-UK's Melrose to sell Nortek Air Management unit for about $3.63 bln

(Adds details on proceeds, quote and background) April 19 (Reuters) - Melrose Industries said on Monday it has agreed to sell its Nortek Air Management business for about 2.62 billion pounds ($3.63 billion) to Chicago-based Madison Industries, and will distribute a portion of the proceeds to shareholders. The British engineering...