In this article, the heat transfer of magnetic nanofluids over a sphere has been considered in the presence of an external oscillating uniform magnetic field for a wide range of Reynolds number values (Re). This study incorporates the effect of magnetic permeability and purposes the optimal operating condition for the first time. The significant difference between the magnetic property of the nanofluid and the heated sphere makes a non-uniform magnetic field around the sphere resulting in a significant alteration in the distribution of velocity and temperature around sphere. The variations of average Nusselt number (Nu_avg) and drag coefficient (C_d) have been studied to demonstrate the influence of magnetic field frequency and intensity, Re, and the relative magnetic permeability of the sphere. It has been found that the magnetic field causes the vortices to appear or grow behind the sphere. This leads to fluid separation even for low Re values in the presence of magnetic field. Local Nu value is minimum at the separation point. This point moves towards the front of sphere as the magnetic field intensity increases. These vortices lead to boundary layer distortion, thereby increasing heat-transfer rate and drag force. In addition, the obtained results clearly indicate that there is an optimal frequency at which Nu_avg and C_d can be maximized. The dimensionless optimal frequency (Ωτ) is about 0.6 regardless of Re value or magnetic field intensity. Moreover, the influence of the applied magnetic field is more noticeable for low Re values and/or frequencies near the optimum value. For instance, Nu_avg and C_d increase by 150% and 50%, respectively, for Re value of 30 while they are three times smaller for Re value of 200. Increase in the magnetic permeability of sphere enhances the Nu_avg up to 170% (at Re = 50) close to the optimal frequency, whereas its effect is almost negligible for frequencies far away from the optimal one. Furthermore, the obtained results clearly demonstrate that the heat-transfer increase is much larger than the penalty due to the drag force increase for frequencies close to the optimal value.

中文翻译：

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振荡磁场对球体周围流体流动和强制对流传热影响的研究

在这篇文章中，在存在广泛雷诺数值 (Re) 的外部振荡均匀磁场的情况下，考虑了磁性纳米流体在球体上的热传递。这项研究首次纳入了磁导率的影响，并确定了最佳运行条件。纳米流体和加热球体的磁性之间的显着差异使得球体周围的磁场不均匀，导致球体周围的速度和温度分布发生显着变化。平均努塞尔数（Nu _avg）和阻力系数（C _d) 进行了研究，以证明磁场频率和强度、Re 以及球体的相对磁导率的影响。已经发现磁场导致涡流在球体后面出现或增长。即使在存在磁场的情况下，对于低 Re 值，这也会导致流体分离。局部 Nu 值在分离点处最小。随着磁场强度的增加，该点向球体前方移动。这些涡流导致边界层变形，从而增加传热速率和阻力。此外，所获得的结果清楚地表明，存在一个最佳频率，在该频率下 Nu _avg和 C _d可以最大化。无论 Re 值或磁场强度如何，无量纲最佳频率 (Ωτ) 约为 0.6。此外，对于低 Re 值和/或接近最佳值的频率，施加磁场的影响更为明显。例如，当 Re 值为 30 时，Nu avg 和 C _d分别_{增加了 150% 和 50%，而当 Re 值为 200 时，Nu avg 和 C d 分别减小了三倍。球体磁导率的增加增强了 Nu avg}高达 170%（在 Re = 50 时）接近最佳频率，而对于远离最佳频率的频率，其影响几乎可以忽略不计。此外，所获得的结果清楚地表明，对于接近最佳值的频率，由于阻力增加，传热增加远大于惩罚。