The present communication aims to investigate Marangoni based convective Casson modeled nanofluid flow influenced by the presence of Lorentz forces instigated into the model by an aligned array of magnets in the form of Riga pattern. The exponentially decaying Lorentz force is considered using the Grinberg term. On the liquid - gas or liquid - liquid interface, a realistic temperature and concentration distribution is considered with the assumption that temperature and concentration distributions are variable functions of $ x $. The set of so-formulated governing problems under the umbrella of Navier Stokes equations is transformed into nonlinear ODEs using suitable transformations. Homotopy approach is implemented to achieve convergent series solutions for the said problem. Influence of active fluid parameters such as Casson parameter, Brownian diffusion, Prandtl number, Thermophoresis and others on flow profiles is analyzed graphically. The fluctuation in local physical quantities such as heat and mass flux rates, is noticed to check the significance of current fluid model in many industrial as well as engineering procedures using nanofluids. The outcomes indicate that the effective Lorentz force assists the fluid motion that results in an augmented velocity profile with incremental values of modified Hartman number. Furthermore, incremental data of Casson parameter motivates significant reduction in velocity profile.

中文翻译：

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在里加板产生洛伦兹力的情况下，Marangoni 强迫对流卡松型纳米流体流动

本通讯旨在研究基于 Marangoni 的对流 Casson 模拟纳米流体流动，该流动受洛伦兹力的存在影响，这些力是由以里加图案形式的对齐磁铁阵列激发到模型中的。使用格林伯格项考虑指数衰减的洛伦兹力。在液体 - 气体或液体 - 液体界面上，假设温度和浓度分布是 $ x $ 的变量函数，则考虑现实的温度和浓度分布。使用合适的变换将 Navier Stokes 方程组下的一组如此制定的控制问题转换为非线性 ODE。实施同伦方法以实现上述问题的收敛级数解。Casson 参数等主动流体参数的影响，布朗扩散、普朗特数、热泳和其他关于流动剖面的图形分析。注意到局部物理量（例如热量和质量通量率）的波动，以检查当前流体模型在许多使用纳米流体的工业和工程程序中的重要性。结果表明，有效的洛伦兹力有助于流体运动，从而导致具有修正哈特曼数增量值的增强速度剖面。此外，Casson 参数的增量数据促使速度剖面显着降低。注意到在许多使用纳米流体的工业和工程程序中检查当前流体模型的重要性。结果表明，有效的洛伦兹力有助于流体运动，从而导致具有修正哈特曼数增量值的增强速度剖面。此外，Casson 参数的增量数据促使速度剖面显着降低。注意到在许多使用纳米流体的工业和工程程序中检查当前流体模型的重要性。结果表明，有效的洛伦兹力有助于流体运动，从而导致具有修正哈特曼数增量值的增强速度剖面。此外，Casson 参数的增量数据促使速度剖面显着降低。