A turbine vane (208, 708, 808, 908) for a gas turbine engine, comprising: an airfoil (200, 700, 800) that extends from an inner diameter to an outer diameter, and from a leading edge to a trailing edge; an inner platform (214, 714, 814, 914) coupled to the airfoil at the inner diameter; and a cooling system (202, 702, 802, 902) defined in the airfoil including a first conduit (230, 730, 830, 930) in proximity to the leading edge to cool the leading edge and a second conduit (232, 732, 832) to cool the trailing edge, the first conduit having an inlet at the outer diameter to receive a cooling fluid and an outlet portion (238, 738, 838, 938) that is defined at least partially through the inner platform, and the first conduit includes a plurality of cooling pins (268, 350) that extend between a first surface and a second surface (242, 342) of the first conduit, wherein the first surface of the first conduit is opposite the leading edge; characterised in that each of the plurality of cooling pins includes a first pin end coupled to the first surface and a second pin end coupled to the second surface, each of the plurality of cooling pins includes a top surface opposite a bottom surface, the top surface being upstream from the bottom surface in a direction of cooling fluid flow through the first conduit, the top surface includes a first fillet defined at the first pin end that extends toward the second pin end and the bottom surface includes a second fillet defined at the first pin end that extends toward the second pin end, the first fillet has a first fillet arc that is greater than a second fillet arc of the second fillet. an airfoil (200, 700, 800) that extends from an inner diameter to an outer diameter, and from a leading edge to a trailing edge; an inner platform (214, 714, 814, 914) coupled to the airfoil at the inner diameter; and a cooling system (202, 702, 802, 902) defined in the airfoil including a first conduit (230, 730, 830, 930) in proximity to the leading edge to cool the leading edge and a second conduit (232, 732, 832) to cool the trailing edge, the first conduit having an inlet at the outer diameter to receive a cooling fluid and an outlet portion (238, 738, 838, 938) that is defined at least partially through the inner platform, and the first conduit includes a plurality of cooling pins (268, 350) that extend between a first surface and a second surface (242, 342) of the first conduit, wherein the first surface of the first conduit is opposite the leading edge; characterised in that each of the plurality of cooling pins includes a first pin end coupled to the first surface and a second pin end coupled to the second surface, each of the plurality of cooling pins includes a top surface opposite a bottom surface, the top surface being upstream from the bottom surface in a direction of cooling fluid flow through the first conduit, the top surface includes a first fillet defined at the first pin end that extends toward the second pin end and the bottom surface includes a second fillet defined at the first pin end that extends toward the second pin end, the first fillet has a first fillet arc that is greater than a second fillet arc of the second fillet.