This is a two-part paper, which proposes a new theory explaining the experimentally observed enhancement of the thermal conductivity, knf, of nanofluids (Part I) and discusses simulation results of nanofluid flow in a radial parallel-plate channel using different knf-models (Part II). Specifically, Part I provides the derivation of the new model as well as comparisons with benchmark experimental data sets and other theories, focusing mainly on aluminum and copper oxide nanoparticles in water. The new thermal conductivity expression consists of a base-fluid static part, kbf, and a new “micromixing” part, kmm, i.e., knf = kbf + kmm. While kbf relies on Maxwell’s theory, kmm encapsulates nanoparticle characteristics and liquid properties as well as Brownian-motion induced nanoparticle fluctuations, nanoparticle volume fractions, mixture-temperature changes, particle–particle interactions, and random temperature fluctuations causing liquid-particle interactions. Thus, fundamental physics principles include the Brownian-motion effect, an extended Langevin equation with scaled interaction forces, and a turbulence-inspired heat transfer equation. The new model predicts experimental data for several types of metal-oxide nanoparticles (20 < dp < 50 nm) in water with volume fractions up to 5% and mixture temperatures below 350 K. While the three competitive theories considered match selectively experimental data, their needs for curve-fitted functions and arbitrary parameters make these models not generally applicable. The new theory can be readily extended to accommodate other types of nanoparticle-liquid pairings and to include nonspherical nanomaterial.
On Estimation for Brownian Motion Governed by Telegraph Process with Multiple Off States