In this study, the internal cooling channel was investigated without any bend. Smooth surfaces and dimpled surfaces were investigated using the different combinations of connecting circular and rectangular holes. The computations were performed using the large eddy simulation (LES) model for Reynolds (Re) numbers from 10,000 to 50,000. A total of six different connecting holes were investigated with a smooth and dimpled surface. A partial spherical dimple with two circular holes showed the highest heat transfer, but it has a higher pressure loss penalty. Even though the leaf dimpled surface with the rectangluar holes indicated a little low heat transfer, it represents the highest efficiency at higher Reynolds numbers because of the low-pressure drops.