A disc assembly for use in, for example, an automatic transmission is disclosed. The disc assembly includes a pair of spaced core members (15-16, 25-26, 36-37, 56-57). A friction facing (17-18, 27-28, 42-43, 62, 77-78) is positioned on the outer side of at least one of said core members. A grooved cooling layer (20, 30, 45, 61) is positioned between the pair of spaced core members and is in fluid communication with a cooling fluid. The disc assembly is used with other disc assemblies and other power elements (12, 48, 65, 83) to form a clutch assembly for the transmission.