A turbine blade assembly is provided. The turbine blade assembly comprises a turbine blade comprising a cavity, and a blade platform supporting the turbine blade, the cavity extending into the blade platform. The blade platform comprises an upper surface adjacent the turbine blade and a lower surface comprising a first rib, the cavity extending into the first rib, the first rib coupled to the lower surface, tapering as it extends away from the turbine blade, and comprising a first port extending from the cavity to the upper surface.