Abstract Taking a more complex engineering geometry into account, magnetohydrodynamic natural convection of nanofluid (Cu-water) in a wavy walled enclosure having a circular hot cylinder inside is investigated by employing Galerkin-weighted residual formulation. In order to investigate the flow and heat transfer characteristics from several perspectives and increase the ability of adaptation to various engineering applications, the influences of the Hartmann number, Ha, Rayleigh number, Ra, and nanoparticle concentration are examined in detail. In addition to that, heat generation and heat absorption situations are also considered within the present work, which are simulated by a heat coefficient in a range of −10 ≤ q ≤ +10. The results revealed that increasing Ha has an insignificant effect on Nusselt number, Nu, at low Ra, however, it significantly pulls Nu down up to 33% for higher Ra, because of restricting convection. It is found that the heat coefficient, q, has a remarkable impact on Nu at low Ra, while its significance is diminished when Ra is increased. For q 0) conversely reduces Nu up to 48%. Besides, variation in heat coefficient does not considerably affect the improvement impact of nanoparticles.

中文翻译：

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磁场作用下发热和吸热对波状外壳中Cu-水纳米流体自然对流的影响

摘要 考虑到更复杂的工程几何形状，采用伽辽金加权残差公式研究了纳米流体（Cu-水）在内部具有圆形热圆柱体的波浪壁外壳中的磁流体动力学自然对流。为了从多个角度研究流动和传热特性并提高对各种工程应用的适应能力，详细研究了哈特曼数、Ha、瑞利数、Ra 和纳米颗粒浓度的影响。除此之外，在目前的工作中还考虑了发热和吸热情况，这些情况通过-10 ≤ q ≤ +10 范围内的热系数进行模拟。结果表明，在低 Ra 时，增加 Ha 对 Nusselt 数 Nu 的影响不显着，但是，由于对流的限制，它显着将 Nu 降低到 33%，以获得更高的 Ra。发现热系数 q 在低 Ra 时对 Nu 有显着影响，而当 Ra 增加时其显着性减弱。对于 q 0) 相反，Nu 最多可减少 48%。此外，热系数的变化不会显着影响纳米粒子的改进效果。