Laminar air flow through a curved rectangular channel with a variable cross-section (c/s) area (diverging-converging) is numerically investigated. Such a flow passage is formed between the two fin walls of a 90° bend curved fin heat sink, used in avionics cooling. Simulations are carried out for two different configurations - (a) a curved channel with long, straight, constant c/s area inlet and outlet sections (entry and exit lengths), and (b) a short, curved channel with no entry and exit lengths. Formation of a complex, 3-D flow pattern and its evolution in space is studied through numerical flow visualization. Results show that a secondary motion sets in the radial direction in the curved section, which in combination with the axial (bulk) flow leads to the formation of a base vortex. In addition, under certain circumstances the axial and secondary flow separate from multiple locations on the channel walls, and create Dean vortices and separation bubbles. The role of variable c/s geometry is elucidated by comparing the results with those of a constant c/s area, curved channel. Investigation of the dimensionless friction factor reveals that the overall channel pressure drop is governed by both the curvature effect as well as the area expansion effect. Due to the combined effect pressure drop for developing flow in a short, curved channel can be even less than that of a straight channel.