Boundary layers from constructal law

This article communicates a new problem and solution: Fluid is initially motionless in a rectangular space the shape of which is free to vary. A blade enters along one of the sides of the rectangle, moves at constant speed, and sets the fluid in motion by viscous diffusion. If the constructal law of design evolution is invoked, then the evolutionary direction is toward the shape of the rectangular space such that the entire fluid is set in laminar flow more easily, during the shortest time. The shape is found via scale analysis, and, coincidentally, it matches the shape of the boundary layer known from classical boundary layer theory. The difference between the two methods is fundamental: with the constructal law, the shape comes from the evolution of all the possible shapes toward greater access for the flow of momentum; with boundary layer theory, the shape is unique and comes from solving the simplified momentum equations for an assumed slender flow region.