An engine is has a cylinder block defining a cylinder and a block cooling jacket having an open passage along a block deck face, and a cylinder head having an exhaust bridge conduit. A head gasket is placed between the block and the head and defines first and second apertures connecting the open passage of the block cooling jacket to the exhaust bridge conduit. A cylinder head has a deck face, and a cooling jacket. The cooling jacket has a passage formed by an inlet channel with a conduit at one end and extending into an exhaust bridge between adjacent exhaust ports. The inlet channel intersects the deck face and is elongated along a longitudinal axis of the cylinder head. The inlet channel has a convex surface positioned between opposed ends of the channel and extending away from the deck face.