This paper presents a mathematical model for bi-directional convection magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow from the upper horizontal subsurface of a stretching parabolic surface to a non-Darcian porous medium, as a simulation of nanocoating. Chemical reaction, activation energy and thermo solutal buoyancy effects are included. The Darcy–Brinkman–Forchheimer model is deployed which permits the analysis of inertial (second order) porous drag effects. The Buongiorno nanoscale model is deployed which includes Brownian motion and thermophoresis effects. The dimensionless, transformed, nonlinear, coupled ordinary differential equations are solved by implementing the spectral relaxation method (SRM). Validation with previous studies is included. The numerical influence of key parameters on transport characteristics is evaluated and visualized graphically. Velocity is elevated (and momentum boundary layer thickness is reduced) with increasing wall thickness parameter, permeability parameter, Forchheimer parameter, Weissenberg (rheological) parameter and modified Hartmann (magnetic body force) number. Velocity enhancement is also computed with increment in stretching rate parameter, rheological power-law index, thermal Grashof number, and species (solutal) Grashof number, and momentum boundary layer thickness diminishes. Temperature is suppressed with increasing stretching rate index and Prandtl number whereas it is substantially elevated with increasing Brownian motion and thermophoresis parameters. Velocity and temperature profiles are reduced adjacent to the parabolic surface with larger wall thickness parameter for stretching rate index <1, whereas the reverse behavior is observed for stretching rate index >1. Nanoparticle concentration magnitude is depleted with larger numeric of Lewis number and the Brownian motion parameter, whereas it is enhanced with greater values of the stretching index and thermophoresis parameter. The nanoparticle concentration magnitude is reduced with an increase in chemical reaction rate parameter whereas it is boosted with activation energy parameter. Skin friction, Nusselt number and Sherwood number are also computed. The study is relevant to electromagnetic nanomaterials coating processes with complex chemical reactions.

中文翻译：

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非达西多孔介质中拉伸上抛物面的反应双向水磁非牛顿对流的光谱计算

本文提出了双向对流磁流体动力学 (MHD) 正切双曲线纳米流体从拉伸抛物面的上部水平次表面流到非达西多孔介质的数学模型，作为纳米涂层的模拟。包括化学反应、活化能和热溶浮力效应。部署了 Darcy-Brinkman-Forchheimer 模型，该模型允许分析惯性（二阶）多孔阻力效应。部署了 Buongiorno 纳米级模型，其中包括布朗运动和热泳效应。通过实施谱弛豫方法 (SRM) 求解无量纲、变换、非线性、耦合常微分方程。包括与先前研究的验证。以图形方式评估和可视化关键参数对传输特性的数值影响。随着壁厚参数、磁导率参数、Forchheimer 参数、Weissenberg（流变）参数和修正的 Hartmann（磁体力）数的增加，速度增加（动量边界层厚度减小）。速度增强也随着拉伸速率参数、流变幂律指数、热 Grashof 数和物种（溶质）Grashof 数的增加而计算，并且动量边界层厚度减小。温度随着拉伸速率指数和普朗特数的增加而受到抑制，而随着布朗运动和热泳参数的增加而显着升高。 <1，而对于拉伸率指数观察到相反的行为 >1. 纳米粒子浓度大小随着路易斯数和布朗运动参数的增大而减少，而随着拉伸指数和热泳参数的增大而增强。纳米粒子浓度大小随着化学反应速率参数的增加而降低，而随着活化能参数的增加而增加。还计算了皮肤摩擦、努塞尔数和舍伍德数。该研究与具有复杂化学反应的电磁纳米材料涂层工艺有关。