The present invention relates to a turbine assembly having an aerofoil and/or an end wall each having an outer surface with a structure for directing a flow of a cooling medium at the outer surface. The structure at the outer surface has at least a first groove and a second groove extending in the outer surface from a leading to a trailing edge and being oriented in at least two different directions with a deflection angle (α) towards each other, with the deflection angle (α) having a component in a span wise direction of the aerofoil. The structure at the outer surface of the end wall has at least a first groove and a second groove extending in an axial direction of the turbine assembly, matching an outer profile of the aerofoil and oriented in at least two different directions with a deflection angle (α) towards each other.