An airfoil and a cooling arrangement for an airfoil platform

An airfoil 40 includes an outer surface 42 having a leading edge 46, a trailing edge 48 downstream from the leading edge, and a convex surface 50 between the leading and trailing edges 46,48. A cavity 58 is inside the outer surface 42, and a platform 44 is connected to the outer surface 42 and defines a top surface 54 around at least a portion of the outer surface 42. A first plurality of trenches 80 is beneath the top surface 54 of the platform 44 upstream from the leading edge 46, wherein each trench 80 in the first plurality of trenches 80 is in fluid communication with the cavity 58 inside the outer surface 42. A first plurality of cooling passages 70 provide fluid communication from the first plurality of trenches 80 through the top surface 54 of the platform 44.