Constructal multi-scale structure for maximal heat transfer density

 This paper presents a new concept for generating the multi-scale structure of a finite-size flow system that has maximum heat transfer density–maximum heat transfer rate installed in a fixed volume. Laminar forced convection and parallel isothermal blades fill the volume. The spacings between adjacent blades of progressively smaller scales are optimized based on constructal theory: the goal is maximum heat transfer density. The smaller blades are installed in the fresh-fluid regions that sandwich the tips of the boundary layers of longer blades. The overall pressure difference is constrained. As the number of length scales increases, the flow rate decreases and the volume averaged heat transfer density increases. There exists a smallest (cutoff) length scale below which heat transfer surfaces are no longer lined by distinct (slender) boundary layers. Multi-scale flow structures for maximum heat transfer rate density can be developed in an analogous fashion for natural convection. The constructal multi-scale algorithms are deduced from principles, unlike in fractal geometry where algorithms are assumed.