In the present research, the numerical investigation of the nanofluid flow inside the circular cavity with the presence of fractal barriers has been done using the finite volume method (FVM). This investigation is done for Richardson numbers (Ri) = 0.1 to 1, solid nanoparticle volume fraction (φ) = 0 to 0.6 and for three shapes of fractal barrier in the two-dimensional (2D) cavity. The results of this research show that the presence of an obstacle with a special shape causes the components of the flow paths, creates weaker vortices in parts of the cavity and finally increases the contact of the fluid with hot surfaces. The behavior of the flow lines in the cavity is affected by two main stimulating factors. The main factor in the movement of the flow is the mobility of the cap (lid-driven), which, as a result, due to the viscosity of the fluid, the layered transfer of movement continues to the lower layers of the fluid. This factor forces the flow field to move. An increase in Ri increases the speed of the cap, which will result in better heat penetration and mixing between the fluid layers in different parts of the cavity. If this is accompanied by an increase in the disturbance of the flow due to the presence of obstacles, it will have a greater effect on the uniform temperature distribution. It seems that in addition to the forced convection, the conduction mechanism will also play a significant role in heat distribution. Adding solid nanoparticles in a higher φ, this behavior makes the heat distribution uniform to a small extent. Moreover, changing the shape of the fractal barrier will cause changes in fluid circulation behavior and reduce the slope of constant temperature lines. The thermal conductivity of the fluid will also improve through the addition of solid nanoparticles and consequently, the local Nusselt number (Nu) increases. Changes in the average Nusselt number at Ri = 0.1 in different volume fractions and for the cases studied can cause an increase in the Nusselt number between 10 and 16 percent. The above behavior for Ri = 1 improves the Nusselt number by less than 13 percent and for Ri = 10 this is less than 4 percent.

中文翻译：

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在充满纳米流体的圆形腔中使用分形势垒进行联合对流传热的数值研究


在本研究中，使用有限体积法 （FVM） 对存在分形势垒的圆腔内纳米流体流动进行了数值研究。这项研究是针对理查森数 （Ri） = 0.1 到 1、固体纳米粒子体积分数 （φ） = 0 到 0.6 以及二维 （2D） 腔中的三种形状的分形势垒进行的。这项研究的结果表明，具有特殊形状的障碍物的存在会导致流路的组成部分，在腔体的某些部分产生较弱的涡流，并最终增加流体与热表面的接触。型腔中流线的行为受两个主要刺激因素的影响。流动运动的主要因素是盖子的移动性（盖子驱动），因此，由于流体的粘度，运动的分层转移继续到流体的下层。这个因子迫使流场移动。Ri 的增加会增加帽的速度，这将导致更好的热渗透和腔体不同部分的流体层之间的混合。如果这伴随着由于障碍物的存在而引起的流动扰动增加，它将对均匀的温度分布产生更大的影响。看来，除了强制对流之外，传导机制也将在热量分布中发挥重要作用。以更高的φ添加固体纳米颗粒，这种行为使热量分布在很小程度上均匀。此外，改变分形势垒的形状会导致流体循环行为发生变化，并减小恒温线的斜率。 流体的导热性也将通过添加固体纳米颗粒而提高，因此，局部努塞尔数 （Nu） 增加。在不同体积分数中，Ri = 0.1 时平均努塞尔数的变化以及所研究的案例会导致努塞尔数增加 10% 到 16%。Ri = 1 的上述行为使 Nusselt 数提高了不到 13%，而 Ri = 10 时，这小于 4%。