The film cooling performance on a convex curved surface subjected to accelerated free-stream flow was investigated. The thermochromic liquid crystals technique was applied to determine adiabatic film cooling effectiveness values and heat transfer coefficients on the test surface. Five different injection geometries, three with cylindrical holes and two with shaped holes were investigated. The experimental results were compared to the results of a previous investigation obtained with constant free-stream velocity to determine the influence of free-stream acceleration. The free-stream acceleration caused decreasing adiabatic film cooling effectiveness values compared to constant free-stream velocity, especially further downstream of the point of injection. For the in-line cylindrical injection configurations, an increase in adiabatic film cooling effectiveness in the near hole region can be obtained for higher blowing rates. It is assumed that this effect is due to the reduced tendency of jet separation in the accelerated free-stream. The influence of the free-stream acceleration on the Stanton number ratio is generally small. (C) 2001 Elsevier Science Ltd. All rights reserved.