A theoretical model is developed for steady magnetohydrodynamic viscous flow resulting from a moving semi-infinite flat plate in an electrically conducting nanofluid. Thermal radiation and magnetic induction effects are included in addition to thermal convective boundary conditions. Buongiorno’s two-component nanoscale model is deployed, which features Brownian motion and thermophoresis effects. The governing nonlinear boundary layer equations are converted to nonlinear ordinary differential equations by using suitable similarity transformations. The transformed system of differential equations is solved numerically, employing the spectral relaxation method (SRM) via the MATLAB R2018a software. SRM is a simple iteration scheme that does not require any evaluation of derivatives, perturbation, and linearization for solving a nonlinear system of equations. Effects of embedded parameters such as sheet velocity parameter|$\lambda$|⁠, magnetic field parameter|$\beta$|⁠, Prandtl number|$Pr$|⁠, magnetic Prandtl number|$Prm$|⁠, thermal radiation parameter|$Rd$|⁠, Lewis number|$Le$|⁠, Brownian motion parameter|$Nb$|⁠, and thermophoresis parameter|$Nt$| on velocity, induced magnetic field, temperature, and nanoparticle concentration profiles are investigated. The skin-friction results, local Nusselt number, and Sherwood number are also discussed for various values of governing physical parameters. To show the convergence rate against iteration, residual error analysis has also been performed. The flow is strongly decelerated, and magnetic induction is suppressed with greater magnetic body force parameter, whereas temperature is elevated due to extra work expended as heat in dragging the magnetic nanofluid. Temperatures are also boosted with increment in nanoscale thermophoresis parameter and radiative parameter, whereas they are reduced with higher wall velocity, Brownian motion, and Prandtl numbers. Both hydrodynamic and magnetic boundary layer thicknesses are reduced with greater reciprocal values of the magnetic Prandtl number Pr_m. Nanoparticle (concentration) boundary layer thickness is boosted with higher values of thermophoresis and Prandtl number, whereas it is diminished with increasing wall velocity, nanoscale Brownian motion parameter, radiative parameter, and Lewis number. The simulations are relevant to electroconductive nanomaterial processing.

中文翻译：

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具有辐射通量和磁感应的移动表面导电纳米流体对流的光谱弛豫计算

开发了一种理论模型，用于在导电纳米流体中由移动的半无限平板引起的稳定磁流体动力学粘性流。除了热对流边界条件外，还包括热辐射和磁感应效应。部署了 Buongiorno 的双组分纳米级模型，该模型具有布朗运动和热泳效应。通过使用合适的相似变换，控制非线性边界层方程被转换为非线性常微分方程。通过 MATLAB R2018a 软件采用谱松弛法 (SRM) 对微分方程的变换系统进行数值求解。SRM 是一种简单的迭代方案，不需要对导数、扰动、和用于求解非线性方程组的线性化。嵌入参数的影响，例如片速度参数|$\lambda$|⁠，磁场参数|$\beta$|⁠，普朗特数|$Pr$|⁠，磁普朗特数|$Prm$|⁠，热辐射参数|$Rd$|⁠，刘易斯号| $ $乐|⁠，布朗运动参数| $铌$ |⁠，和热泳参数| $ Nt个$ |对速度、感应磁场、温度和纳米颗粒浓度分布进行了研究。还针对控制物理参数的各种值讨论了皮肤摩擦结果、局部 Nusselt 数和 Sherwood 数。为了显示针对迭代的收敛速度，还进行了残差分析。流动被强烈减速，并且磁感应被更大的磁体力参数抑制，而温度由于在拖动磁性纳米流体时作为热量消耗的额外功而升高。随着纳米级热泳参数和辐射参数的增加，温度也会升高，而随着壁速度、布朗运动和普朗特数的增加，温度会降低。镨_米。纳米粒子（浓度）边界层厚度随着热泳和普朗特数的升高而增加，而随着壁速度、纳米级布朗运动参数、辐射参数和路易斯数的增加而减小。模拟与导电纳米材料加工有关。