A turbine nozzle , comprising: an airfoil that extends in span from an inner band to an outer band , the airfoil comprising a leading edge portion , a trailing edge portion , a suction side wall , and a pressure side wall , wherein the inner band and the outer band define inner and outer flow boundaries of the turbine nozzle ; wherein the inner band defines: at least one inlet passage for receiving a cooling fluid; a plurality of cooling channels in fluid communication with, and downstream of, the inlet passage , the cooling channels being configured to provide convection cooling to a gas side surface of the inner band ; a coolant discharge plenum in fluid communication with, and downstream of, the cooling channels , wherein the plurality of cooling channels and the coolant discharge plenum are formed beneath a gas side surface of the inner band ; and at least one coolant discharge port in fluid communication with, and downstream from, the coolant discharge plenum ; characterised in that the cooling channels are arranged to follow a curvature of one or more of the leading edge portion , the trailing edge portion , the suction side wall , and the pressure side wall of the airfoil . an airfoil that extends in span from an inner band to an outer band , the airfoil comprising a leading edge portion , a trailing edge portion , a suction side wall , and a pressure side wall , wherein the inner band and the outer band define inner and outer flow boundaries of the turbine nozzle ; wherein the inner band defines: at least one inlet passage for receiving a cooling fluid; a plurality of cooling channels in fluid communication with, and downstream of, the inlet passage , the cooling channels being configured to provide convection cooling to a gas side surface of the inner band ; a coolant discharge plenum in fluid communication with, and downstream of, the cooling channels , wherein the plurality of cooling channels and the coolant discharge plenum are formed beneath a gas side surface of the inner band ; and at least one coolant discharge port in fluid communication with, and downstream from, the coolant discharge plenum ; characterised in that the cooling channels are arranged to follow a curvature of one or more of the leading edge portion , the trailing edge portion , the suction side wall , and the pressure side wall of the airfoil . at least one inlet passage for receiving a cooling fluid; a plurality of cooling channels in fluid communication with, and downstream of, the inlet passage , the cooling channels being configured to provide convection cooling to a gas side surface of the inner band ; a coolant discharge plenum in fluid communication with, and downstream of, the cooling channels , wherein the plurality of cooling channels and the coolant discharge plenum are formed beneath a gas side surface of the inner band ; and at least one coolant discharge port in fluid communication with, and downstream from, the coolant discharge plenum ; characterised in that the cooling channels are arranged to follow a curvature of one or more of the leading edge portion , the trailing edge portion , the suction side wall , and the pressure side wall of the airfoil . <EOS>