The most commonly used absorbers in flat-plate collectors are manufactured as finned tubes. In this article, an alternative design is investigated: the absorber consists of a rectangular, narrow duct, in which the fluid contacts the entire surface. Under the conditions of fully developed laminar flow and negligible heat resistance of the absorber plate material, relations are developed to calculate the temperature distribution within the fluid. These results are used to derive a formula for the collector efficiency factor F＇ of narrow-duct absorbers, which is then evaluated for water and a commonly used glycol antifreeze liquid as the collector fluid. Finally, the optimisation of narrow-duct absorbers is investigated with consideration of the thermal heat gained by the collector and primary energy consumed by the pump of the solar system due to the pressure drop in the absorber. It is concluded that duct heights in the range of 3-6 mm should be chosen. Collector efficiency factors F＇ around 0.98 may be expected.