Turbine nozzle having non-linear cooling conduit

A turbine nozzle (100) having a non-linear cooling conduit (108) is disclosed. In one embodiment, a turbine nozzle (100) includes: an airfoil (102), at least one endwall (104) adjacent the airfoil (102), and a fillet region (106) connecting the airfoil (102) and the at least one endwall (104), the fillet region (106) including an outer surface (110). The turbine nozzle (100) also includes a non-linear cooling conduit (108) located within the fillet region (106) and adjacent the outer surface (110) of the fillet region (106), the non-linear cooling conduit (108) allows fluid flow through the fillet region (106). The non-linear cooling conduit (108) spans substantially along an axial length of the airfoil between a leading edge (113) of the airfoil (102) and a trailing edge (114) of the airfoil (102). Additionally, the non-linear cooling conduit (108) includes an arc profile substantially similar to an arc profile of the airfoil (102).