Multiscale modeling of nanofluid flow and enhanced heat transfer via a computational fluid dynamics–discrete element coupled approach

A new multiscale model, which directly considers the interaction between the macroscopic continuous base fluid phase and the microscopic discrete nanoparticle phase, is proposed to analyze the nanofluid flow and enhanced heat transfer. At the macroscale, the flow and heat transfer of nanofluids are modeled by the nonisothermal Navier–Stokes equations under the Eulerian framework. At the microscale, the motion and thermal state of each nanoparticle are governed by a group of ordinary differential equations derived from the Newton's second law and energy balance law under the Lagrangian framework. The models at different scales are coupled together through both interaction force and thermal parameters. To reduce the cost in calculating the interaction force between the two phases, the discrete element method is used. Compared to the existing models, the primary novelties of the present model are twofold. First, the collisions between nanoparticles and between nanoparticles and solid walls are considered to count the heat migration and exchange caused by collisions. Second, the effective thermal conductivity is calculated locally, which establishes the dependence of thermal conductivity on the local spatial distribution of nanoparticles. It is no doubt that these considerations will make the new model more realistic and accurate. To solve the model efficiently, a stable, accurate and decoupled numerical solver is designed by using the finite element method and characteristic-based split scheme. Numerical results show good accuracy of the proposed model and corresponding solver. In particularly, for the nonuniform nanoparticle distribution, the new method has an incomparable advantage over other methods.