A transition nozzle for use with a turbine assembly, said transition nozzle comprising: a liner defining a combustion chamber therein; a wrapper circumscribing said liner such that a cooling duct is defined between said wrapper and said liner; a cooling fluid inlet configured to supply a cooling fluid to the cooling duct; and a first rib, a second rib and a third rib each coupled between said liner and said wrapper such that a plurality of cooling channels are defined in the cooling duct, wherein the first rib is coupled to the second rib, and the second rib is coupled to the third rib and each of said ribs extends circumferentially about the combustion chamber such that the cooling channels are axially spaced, and wherein the axially-spaced cooling channels are arranged in a spiral configuration around the combustion chamber, wherein the plurality of cooling channels comprises a first cooling channel in flow communication with cooling fluid inlet which is separated axially from a second cooling channel by a first rib, said second cooling channel is separated axially from a third cooling channel by a second rib, and third cooling channel is separated axially from a fourth cooling channel by a third rib and wherein fourth cooling channel is in flow communication with the cooling fluid outlet, the first, second, third and fourth cooling channels (234, 236, 240, 244) are in flow communication with one another circumferentially, the first cooling channel is in flow communication with the second cooling channel, the second cooling channel is in flow communication with the third cooling channel, and the third cooling channel is in flow communication with the fourth cooling channel. a liner defining a combustion chamber therein; a wrapper circumscribing said liner such that a cooling duct is defined between said wrapper and said liner; a cooling fluid inlet configured to supply a cooling fluid to the cooling duct; and a first rib, a second rib and a third rib each coupled between said liner and said wrapper such that a plurality of cooling channels are defined in the cooling duct, wherein the first rib is coupled to the second rib, and the second rib is coupled to the third rib and each of said ribs extends circumferentially about the combustion chamber such that the cooling channels are axially spaced, and wherein the axially-spaced cooling channels are arranged in a spiral configuration around the combustion chamber, wherein the plurality of cooling channels comprises a first cooling channel in flow communication with cooling fluid inlet which is separated axially from a second cooling channel by a first rib, said second cooling channel is separated axially from a third cooling channel by a second rib, and third cooling channel is separated axially from a fourth cooling channel by a third rib and wherein fourth cooling channel is in flow communication with the cooling fluid outlet, the first, second, third and fourth cooling channels (234, 236, 240, 244) are in flow communication with one another circumferentially, the first cooling channel is in flow communication with the second cooling channel, the second cooling channel is in flow communication with the third cooling channel, and the third cooling channel is in flow communication with the fourth cooling channel.