Exploiting nanofluids in thermal systems is growing day by day. Nanofluids having ultrafine solid particles promise new working fluids for application in energy devices. Many studies have been conducted on thermophysical properties as well as heat and fluid flow characteristics of nanofluids in various systems to discover their advantages compared to conventional working fluids. The main aim of this study is to present the latest developments and progress in the mathematical modeling of nanofluids flow. For this purpose, a comprehensive review of different nanofluid computational fluid dynamics CFD approaches is carried out. This study provides detailed information about the commonly used formulations as well as techniques for mathematical modeling of nanofluids. In addition, advantages and disadvantages of each method are rendered to find the most appropriate approach, which can give valid results.Keywords: nanofluid, CFD, numerical simulation, mathematical modeling, singleand two-phase methods . IntroductionIn general, the assessment of the thermal performance of a system through numerical simulations is much affordable compared to experimental studies with high expenses of material and equipment. The significance of a numerical study is highlighted when a nanofluid is utilized as the working fluid. High costs for the production of nanofluids and difficulties in preparing stable nanofluids are the main barriers to perform experiments with nanofluids. Therefore, numerical modeling of nanofluids, where a suitable approach is selected to simulate the flow, could be the best solution for problems involved with nanoparticle suspensions.However, in spite of considerable developments in computing power and methods, literature review reveals that there is no comprehensive study to conclude the best technique for the modeling of nanofluids. In particular, due to the ultrafine size of nanoparticles, the governing terms in multiphase models are still not entirely identified. In the present work, latest studies on numerical simulations of nanofluid flow are reviewed with a particular focus on different multiphase schemes. . Numerical methods for nanofluids' flow simulationNanofluid computational fluid dynamic CFD modeling can be classified into two main groups single-phase and two-phase models. However, there are few other models that may not be included in these categories, such as Lattice-Boltzmann method LBM . Moreover, different numerical approaches have been employed to solve models mentioned above to predict thermal and hydraulic characteristics of nanofluids flow. Finite volume method FVM and finite element method FEM are two main approaches for solving the governing equations of nanofluid problems. However, finite difference method FDM , control volume-based finite element method, and some novel numerical approaches such as homotopy analysis method HAM and smoothed particle hydrodynamics SPH methods have also been utilized in the previous studies. In this study, a comprehensive review of various numerical ...

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