Method and system to facilitate enhanced local cooling of turbine engines

A method of assembling a gas turbine engine, said method comprising:

• coupling at least one turbine nozzle segment within the gas turbine engine, wherein the at least one turbine nozzle segment includes at least one airfoil vane extending between an inner band and an outer band that includes an aft flange and a radial inner surface;
• coupling at least one turbine shroud segment downstream from the at least one turbine nozzle segment, wherein the at least one turbine shroud segment includes a leading edge and a radial inner surface;
• coupling a cooling fluid source in flow communication with the at least one turbine nozzle segment such that cooling fluid channeled to each turbine nozzle outer band aft flange is directed at an oblique discharge angle towards the leading edge of the at least one turbine shroud segment;
• and
• channeling the cooling fluid through at least a first group of cooling openings having a first aggregate cross-sectional area and a second group of cooling openings having a second aggregate cross-sectional area, the first aggregate cross-sectional area is larger than the second cross-sectional area, to facilitate preferential cooling of the turbine shroud.