It has been more than two decades since the discovery of nanofluids-mixtures of common liquids and solid nanoparticles less than 100 nm in size. As a type of colloidal suspension, nanofluids are typically employed as heat transfer fluids due to their favorable thermal and fluid properties. There have been numerous numerical studies of nanofluids in recent years (more than 1000 in both 2016 and 2017, based on Scopus statistics). Due to the small size and large numbers of nanoparticles that interact with the surrounding fluid in nanofluid flows, it has been a major challenge to capture both the macro-scale and the nano-scale effects of these systems without incurring extraordinarily high computational costs.To help understand the state of the art in modeling nanofluids and to discuss the challenges that remain in this field, the present article reviews the latest developments in modeling of nanofluid flows and heat transfer with an emphasis on 3D simulations. In part I, a brief overview of nanofluids (fabrication, applications, and their achievable thermo-physical properties) will be presented first.Next, various forces that exist in particulate flows such as drag, lift (Magnus and Saffman), Brownian, thermophoretic, van der Waals, and electrostatic double layer forces and their significance in nanofluid flows are discussed. Afterwards, the main models used to calculate the thermophysical properties of nanofluids are reviewed. This will be followed with the description of the main physical models presented for nanofluid flows and heat transfer, from single-phase to Eulerian and Lagrangian two-phase models. In part II, various computational fluid dynamics (CFD) techniques will be presented. Next, the latest studies on 3D simulation of nanofluid flow in various regimes and configurations are reviewed. The present review is expected to be helpful for researchers working on numerical simulation of nanofluids and also for scholars who work on experimental aspects of nanofluids to understand the underlying physical phenomena occurring during their experiments.

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