Measurements were made to determine quasi-local heat transfer coefficients at the smooth principal wall of a flat rectangular duct whose other principal wall is covered by an array of blocklike elements (to be termed modules). The hydraulic-diameter Reynolds number ranged from about 3000 to 18,000. The fully developed Nusselt numbers agreed well with those for smooth-walled ducts when the hydraulic diameter was based on the rectangular cross-section between the tops of the modules and the smooth wall. Heating at both the smooth wall and the modules yielded slightly higher coefficients than did heating at the smooth wall alone. The enhancement of the smooth-wall heat transfer by barriers seated in the space between successive rows of modules was investigated. Substantial enhancement was achieved at the lower Reynolds numbers and for the higher barriers. The major enhancement did not occur immediately after a barrier but, rather, farther downstream, at the point where the barrier-induced separated flow reattached to the smooth wall.