In this paper, the natural convection flow in a square cavity filled with nanofluid water-Al2O3 with a hot circular cylinder in the center of the cavity is numerically analyzed. All the walls are in lower temperatures than the circular cylinder. The Navier–Stokes and energy equations in the primitive variable form are discretized and solved by the finite element method (FEM). The effect of the volume fraction, the radius of the circular cylinder, the temperature and Rayleigh number is considered on the average Nusselt number. For the calculation of the viscosity coefficient and thermal conductivity coefficient of water-Al2O3 nanofluid, an experimental model is used which is the function of the volume fraction, temperature and nanoparticles diameter. This model is compared to the Brinkman model for viscosity and Maxwell model for thermal conductivity which are only the functions of volume fraction and are used by many researchers. The results show the experimental model leads to different results in comparison with the Brinkman model and Maxwell model, and indicate that the rate of the heat transfer can increase or decrease with the increase in volume fraction and temperature.

中文翻译：

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方腔充水-Al2O3纳米流体中温度变化对传热速率影响的数值研究

在本文中，充满纳米流体水的方形空腔中的自然对流流动——铝2○3对位于型腔中心的热圆柱进行数值分析。所有壁的温度都低于圆柱体。原始变量形式的 Navier-Stokes 和能量方程通过有限元法 (FEM) 离散化和求解。在平均努塞尔数上考虑了体积分数、圆柱半径、温度和瑞利数的影响。用于计算水的粘度系数和导热系数-铝2○3纳米流体，使用的是体积分数、温度和纳米粒子直径的函数的实验模型。该模型与粘度的 Brinkman 模型和热导率的 Maxwell 模型进行了比较，后者只是体积分数的函数，并被许多研究人员使用。结果表明，与布林克曼模型和麦克斯韦模型相比，实验模型得出了不同的结果，并表明传热速率可以随着体积分数和温度的增加而增加或减少。