The magnetic field effect on natural convection flow of power-law (PL) non-Newtonian fluid has been studied numerically using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). A two-dimensional rectangular enclosure with differentially heated at two vertical sides has been considered for the computational domain. Numerical simulations have been conducted for different pertinent parameters such as Hartmann number, [Formula: see text], Rayleigh number, [Formula: see text], PL indices, [Formula: see text]–1.4, Prandtl number, [Formula: see text], to study the flow physics and heat transfer phenomena inside the rectangular enclosure of aspect-ratio [Formula: see text]. Numerical results show that the heat transfer rate, quantified by the average Nusselt number, is attenuated with increasing the magnetic field, i.e. the Hartmann number (Ha). However, the average Nusselt number is increased by increasing the Rayleigh number, [Formula: see text] and decreasing the PL index, [Formula: see text]. Besides, the generation of entropy for non-Newtonian fluid flow under the magnetic field effect has been investigated in this study. Results show that in the absence of a magnetic field, [Formula: see text], fluid friction and heat transfer irreversibilities, the total entropy generation decreases and increases with increasing [Formula: see text] and [Formula: see text], respectively. In the presence of the magnetic field, [Formula: see text], the fluid friction irreversibility tends to decrease with increasing both the shear-thinning and shear thickening effect. It is noteworthy that strengthening the magnetic field leads to pulling down the total entropy generation and its corresponding components. All simulations have been performed on the Graphical Processing Unit (GPU) using NVIDIA CUDA and employing the High-Performance Computing (HPC) facility.

中文翻译：

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多重松弛时间格子玻尔兹曼方法对非牛顿流体自然对流和熵产生的磁场影响

采用多重松弛时间（MRT）格子玻尔兹曼方法（LBM）数值研究了磁场对幂律（PL）非牛顿流体自然对流流动的影响。计算域考虑了一个二维矩形外壳，在两个垂直侧有不同的加热。已经对不同的相关参数进行了数值模拟，例如哈特曼数、[公式：见文本]、瑞利数、[公式：见文本]、PL 指数、[公式：见文本]–1.4、普朗特数、[公式：见文本]，研究长宽比矩形外壳内的流动物理和传热现象[公式：见文本]。数值结果表明，由平均努塞尔数量化的传热速率随着磁场的增加而衰减，即 哈特曼数 (Ha)。然而，通过增加瑞利数[公式：见正文]和降低 PL 指数 [公式：见正文]，平均努塞尔数增加。此外，本研究还研究了磁场效应下非牛顿流体流动的熵的产生。结果表明，在没有磁场、[公式：见正文]、流体摩擦和传热不可逆性的情况下，总熵产生分别随着[公式：见正文]和[公式：见正文]的增加而减少和增加。在存在磁场的情况下，[公式：见正文]，流体摩擦不可逆性趋于随着剪切稀化和剪切增稠效应的增加而降低。值得注意的是，加强磁场会导致总熵产生及其相应分量的下降。所有模拟都是在图形处理单元 (GPU) 上使用 NVIDIA CUDA 和高性能计算 (HPC) 设施进行的。