Synthetic jets are a class of jets, characterized by periodic ingestion and expulsion of fluid across the orifice. Most of the experimental and numerical studies available are focused on synthetic jets impinging on flat heat surfaces. The studies conclude that compared to conventional impinging jets, Synthetic jets impinging on flat surfaces are favorable for heat transfer as the periodic suction and ejection creates a series of vortices at the edge of the orifice which penetrates far in to the external field and affect their dynamics favorably for heat transfer. However, the present work conducted two dimensional numerical studies on synthetic jet impinging on surfaces provided with 1) concave dimple 2) convex dimples and 3) a combination of both concave and convex surfaces. Besides, the heat transfer characteristics are also studied by varying the positioning of dimpled contours with respect to the jet axis. The results suggested that synthetic jets over dimpled topologies are actually deteriorating heat transfer compared to flat surfaces. It is concluded that the Concave convex surface in-lined with the jet axis provides the lowest reduction of 25% in the average Nusselt number when compared to other cases.