An analytical study is made of the laminar flow and heat transfer in ducts whose cross section is bounded by a wall with periodic corrugations distributed across the span; the other bounding wall is parallel to the corrugated wall and is plane. The study consists of two parts, the first of which is aimed at providing basic heat transfer and fluid flow results while the second utilizes and illuminates these results by means of performance evaluations and comparisons. The basic results, determined numerically, encompass Nusselt numbers, friction factors, isovels and isotherms, and cross sectional mass flow distributions. For the performance evaluations, comparisons were made between the corrugated-wall duct and the parallel plate channel. It was demonstrated that if the temperature of the duet wall is to be minimized, as in an air-operated solar collector, a corrugated duet can be highly effective, but at the price of additional surface area and greater duet height.