Constructal design of particle volume fraction in nanofluids

We perform a constructal design of particle volume fraction of four types of nanofluids used for heat conduction in four systems: a circular disk, a sphere, a plane slab, and a circular annulus. The constructal volume fraction is obtained to minimize system overall temperature difference and overall thermal resistance. Also included are the features of the constructal volume fraction and the corresponding constructal thermal resistance, which is the minimal overall resistance to the heat flow. The constructal nanofluids that maximize the system performance are not necessarily the ones with uniformly dispersed particles in base fluids. Nanofluids research and development should thus focus on not only nanofluids but also systems that use them. The march toward micro- and nanoscales must also be with the sobering reminder that useful devices are always macroscopic, and that larger and larger numbers of small-scale components must be assembled and connected by flows that keep them alive.