Abstract In this study, the effect of magnetic field on the natural convection of Al2O3-water nanofluid inside a square enclosure with isothermal obstacles and sinusoidal wall temperature distribution has been numerically studied. The sidewalls were subject to sinusoidal boundary conditions, while the top and bottom walls were insulated. Two isothermal heat sources were implemented within the enclosure at the same distance from the center. The governing equations were transformed into the algebraic form using finite volume method and were then simultaneously solved using the SIMPLE algorithm. The proposed model by Vajjha was used to calculate the coefficient of thermal conductivity by taking Brownian motion of particles into account. In this study, the effect of Rayleigh number, aspect ratio, Hartmann number, direction change of applied magnetic field, and the volumetric percentage of nanoparticles was investigated. The results indicated that by increasing the Hartmann number, the fluid velocity as well as the Nusselt number decreased at all volumetric fractions of nanoparticles. An increase in the volumetric fraction of nanoparticles increased the Nusselt number, so that at a nanoparticle concentration of 6%, the mean Nusselt number increased by 9.04% compared to that of the base fluid. Moreover, the Nusselt number increased by increasing the magnetic field angle and the Rayleigh number, while it decreased as the aspect ratio was increased.

中文翻译：

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在具有正弦壁温分布的外壳内存在磁场的情况下，两个等温障碍对纳米流体自然对流的影响

摘要 在这项研究中，数值研究了磁场对具有等温障碍和正弦壁温分布的方形外壳内Al2O3-水纳米流体自然对流的影响。侧壁受正弦边界条件的影响，而顶壁和底壁是绝缘的。两个等温热源在外壳内与中心的距离相同。使用有限体积法将控制方程转换为代数形式，然后使用 SIMPLE 算法同时求解。Vajjha 提出的模型用于通过考虑粒子的布朗运动来计算导热系数。本研究中，瑞利数、纵横比、哈特曼数、研究了外加磁场的方向变化和纳米颗粒的体积百分比。结果表明，通过增加哈特曼数，流体速度以及努塞尔数在纳米颗粒的所有体积分数下都降低。纳米颗粒体积分数的增加增加了努塞尔数，因此在纳米颗粒浓度为 6% 时，平均努塞尔数与基液相比增加了 9.04%。此外，努塞尔数随着磁场角度和瑞利数的增加而增加，而随着纵横比的增加而减少。在纳米颗粒的所有体积分数下，流体速度和努塞尔数均降低。纳米颗粒体积分数的增加增加了努塞尔数，因此在纳米颗粒浓度为 6% 时，平均努塞尔数与基液相比增加了 9.04%。此外，努塞尔数随着磁场角度和瑞利数的增加而增加，而随着纵横比的增加而减少。在纳米颗粒的所有体积分数下，流体速度和努塞尔数均降低。纳米颗粒体积分数的增加增加了努塞尔数，因此在纳米颗粒浓度为 6% 时，平均努塞尔数与基液相比增加了 9.04%。此外，努塞尔数随着磁场角度和瑞利数的增加而增加，而随着纵横比的增加而减少。