Two-dimensional laminar magneto-hydrodynamic (MHD) natural convection flow of non-Newtonian ferrofluid has been investigated to understand the characteristics of heat transfer, streamlines, isotherms, and entropy generation in a wavy enclosure using the finite volume method (FVM). The horizontal boundaries of the cavity are assumed to be thermally adiabatic, while the temperatures of the left and right vertical walls are presumed to be $T_H$ and $T_C,$ respectively. The rheology of the nanofluid is represented through the power-law model, and the density variations due to thermal expansion lie within the framework of the Boussinesq approximation. Numerical simulations have been carried out for a range of dimensionless parameters such as Rayleigh number ($Ra={10}^3,{10}^4,{10}^5$), Hartmann number ($Ha=0,10,20$), power-law index ($n=0.6,0.8,1.0,1.2,1.4$), volume fraction ($\varphi =0,0.05,0.1$), and Prandtl number $Pr$ = 6.8377. Results indicate that the isotherms of the shear-thinning fluid are dominated by thermal convection, whereas conduction is more pronounced for shear-thickening fluids. The average Nusselt number of the non-Newtonian ferrofluid increases with the attenuation of the Hartmann number and augmentation of the Rayleigh number, and in our entire simulation, the maximum value of $\overline{Nu},$ due to the addition of ferro-particles, is found to be 8.07. The power-law index has a remarkable influence on the streamlines, and ${\psi }_{max}$ tends to decrease when $n$ is increased gradually from shear-thinning to shear-thickening fluid behavior. Moreover, it is revealed that the heat transfer rate of ferrofluid ($\varphi$=10%) increases up to 26% for the shear-thinning case and 25% for the shear-thickening case, under the influence of the magnetic field. Further, it is inferred that the irreversibility due to heat transfer, fluid friction, and magnetic field for the shear-thinning, Newtonian and shear-thickening ferrofluids, can be minimized based on the optimal parametric combination. The increment of Hartmann number results in 60% attenuation of total entropy for shear-thinning fluid and 9% diminution for the shear-thickening case. With the augmentation of the power-law index, the entropy generation is found to decrease by 80% in the absence of the magnetic field effect and by 54% in the presence of it. A new correlation for the average Nusselt number is proposed for the shear-thinning fluids and shows a good agreement between the computed and predicted results.

已经研究了非牛顿铁磁流体的二维层流磁流体动力学（MHD）自然对流，以了解使用有限体积法（FVM）在波浪形外壳中的传热，流线，等温线和熵产生的特征。腔的水平边界假定是绝热的，而左右垂直壁的温度假定为${Ť}_H$ 和 ${Ť}_C，$分别。纳米流体的流变性通过幂律模型表示，并且由于热膨胀引起的密度变化在Boussinesq近似的框架内。已对一系列无量纲参数（例如瑞利数（$\mathrm{[R}\mathrm{一种}={10}^3，{10}^4，{10}^5$），哈特曼数（$H\mathrm{一种}=0，10，20$），幂律指数（$ñ=0.6，0.8，1.0，1.2，1.4$）， 体积分数 （$\varphi =0，0.05，0.1$）和Prandtl号 $P\mathrm{[R}$= 6.8377。结果表明，剪切稀化流体的等温线以热对流为主，而剪切稀化流体的传导更为明显。非牛顿铁磁流体的平均Nusselt数随Hartmann数的衰减和Rayleigh数的增加而增加，在我们的整个模拟中，$\overline{ñü}，$由于添加了铁颗粒，发现为8.07。幂律指数对流线有显着影响，并且${\psi }_{米\mathrm{一种}X}$ 在以下情况下趋于减少 $ñ$从剪切稀化到剪切稠化的流体行为逐渐增加。此外，揭示了铁磁流体的传热速率（$\varphi$= 10％）在磁场的影响下，剪切变稀的情况增加到26％，剪切变稠的情况增加到25％。此外，可以推断出，基于最佳参数组合，可将因剪切稀化，牛顿和剪切增稠的铁磁流体的传热，流体摩擦和磁场引起的不可逆性降至最低。Hartmann数的增加会导致剪切稀化流体的总熵衰减60％，而剪切稀化情况的总熵减小9％。随着幂律指数的增加，发现在没有磁场效应的情况下，熵的产生减少了80％，在存在磁场效应的情况下，熵的产生减少了54％。针对剪切稀化流体提出了一种新的平均努塞尔数相关性，并显示出计算结果与预测结果之间的良好一致性。