A gas turbine engine assembly includes a combustor configured to combust an air-fuel mixture to produce combustion gases in a first direction; a transition liner coupled to the combustor and adapted to receive the combustion gases from the combustor and to redirect the combustion gases in a second direction; and a turbine coupled to the transition liner and adapted to receive the combustion gases from the transition liner. The transition liner has a plurality of effusion holes that include a first group that extend at least partially in a tangential direction.