Abstract In this paper, two new empirical equations for calculating the effective dynamic viscosity and thermal conductivity of nanofluids are presented based on a high number of experimental data available in the literature. These two equations present the effective dynamic viscosity and thermal conductivity of nanofluids as a function of the volume fraction (0 ≤ ϕ ≤ 12%), size (10nm ≤ dp ≤ 5μm) and type (Ag, Cu, Al2O3, TiO2, CuO, SiO2, ZnO, MgO, Fe, Fe3O4, Al, AlN, CaCO3) of the nanoparticles, temperature and thermo-physical properties of the base fluid. The proposed models are compared with frequent used models in literature (Brinkman and Maxwell-Garnett models) and found that these classical models severely underestimate the effective viscosity and thermal conductivity of nanofluids. Two proposed models are also compared with some other theoretical models, as those of Chon, Patel, Corcione, Prasher, Koo, Maiga, Masoumi, etc. The results showed that, present models for spherical nanoparticle are in excellent agreement with experimental data and provide more accurate character predictions for thermos-physical properties of nanofluid in comparison with existing models. In addition, five new equations are also proposed using the least squares method for calculating the viscosity of five common working fluids (Water, Glycerol, Ethylene glycol (EG), Propylene glycol (PG) and Ethanol) as a function of the temperature. Beside the pure comparison between these models, two well-known benchmark cases of conjugate natural (Differentially Heated Cavity) and mixed convection (Two-sided Lid-driven Cavity) of nanofluid are chosen in order to investigate the effects of the volume fraction, size and type of the nanoparticles on the fluid flow and heat transfer performance of nanofluids. Easy to use for numerical simulation purposes, covering a wide range of the solid particle size and having high accuracy in predicting thermos-physical properties of nanofluids make these equations useful and practical for the design of various thermal engineering systems such as heat exchangers.

中文翻译：

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提出两个新的经验模型来计算纳米流体的有效动态粘度和热导率

摘要 在本文中，基于大量文献中可用的实验数据，提出了两个用于计算纳米流体的有效动态粘度和热导率的新经验方程。这两个方程表示纳米流体的有效动态粘度和热导率与体积分数 (0 ≤ φ ≤ 12%)、尺寸 (10nm ≤ dp ≤ 5μm) 和类型 (Ag、Cu、Al2O3、TiO2、CuO、 SiO2、ZnO、MgO、Fe、Fe3O4、Al、AlN、CaCO3）、基液的温度和热物理性质。将所提出的模型与文献中常用的模型（Brinkman 和 Maxwell-Garnett 模型）进行比较，发现这些经典模型严重低估了纳米流体的有效粘度和热导率。两个提出的模型还与其他一些理论模型进行了比较，如 Chon、Patel、Corcione、Prasher、Koo、Maiga、Masoumi 等。结果表明，现有的球形纳米颗粒模型与实验数据非常吻合，并提供了与现有模型相比，对纳米流体的热物理特性进行更准确的特征预测。此外，还提出了使用最小二乘法计算五种常见工作流体（水、甘油、乙二醇 (EG)、丙二醇 (PG) 和乙醇）作为温度函数的粘度的五个新方程。除了这些模型之间的纯粹比较之外，选择了纳米流体的共轭自然（差热腔）和混合对流（双侧盖驱动腔）两个著名的基准案例，以研究纳米粒子的体积分数、尺寸和类型对流体的影响纳米流体的流动和传热性能。易于用于数值模拟目的，涵盖了广泛的固体颗粒尺寸范围，并且在预测纳米流体的热物理特性方面具有高精度，使得这些方程对于各种热工程系统（如热交换器）的设计非常有用和实用。