Shroud cooling segment and assembly

A cooling shroud segment for a high pressure turbine that provides improved cooling in the region of the side panels from the midsection thereof forward to the leading edge and particularly in the midsection of the side panel. A shroud subassembly can be formed from a pair of such adjacent shroud segments with opposed adjacent side panels where the spacing of the outlets of the cooling air passages exiting from each of these adjacent side panels are staggered and where the adjacent panels have a spline seal slot with a humped section in at least the midsection of the side panel above and across the outlets of the cooling air passages exiting from the midsection of the side panel, in combination with a spline seal positioned in the gap between the opposed adjacent side panels. This shroud subassembly provides more uniform impingement cooling coverage and localizes more of the cooling air exiting the outlets from these passages in the midsection of the opposed side panels.