Alotaibi Hammad, Eid Mohamed R
Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.
Department of Mathematics, Faculty of Science, New Valley University, Al-Kharga 72511, Al-Wadi Al-Gadid, Egypt.
Micromachines (Basel). 2021 Nov 13;12(11):1395. doi: 10.3390/mi12111395.
This paper discusses the Darcy-Forchheimer three dimensional (3D) flow of a permeable nanofluid through a convectively heated porous extending surface under the influences of the magnetic field and nonlinear radiation. The higher-order chemical reactions with activation energy and heat source (sink) impacts are considered. We integrate the nanofluid model by using Brownian diffusion and thermophoresis. To convert PDEs (partial differential equations) into non-linear ODEs (ordinary differential equations), an effective, self-similar transformation is used. With the fourth-fifth order Runge-Kutta-Fehlberg (RKF45) approach using the shooting technique, the consequent differential system set is numerically solved. The influence of dimensionless parameters on velocity, temperature, and nanoparticle volume fraction profiles is revealed via graphs. Results of nanofluid flow and heat as well as the convective heat transport coefficient, drag force coefficient, and Nusselt and Sherwood numbers under the impact of the studied parameters are discussed and presented through graphs and tables. Numerical simulations show that the increment in activation energy and the order of the chemical reaction boosts the concentration, and the reverse happens with thermal radiation. Applications of such attractive nanofluids include plastic and rubber sheet production, oil production, metalworking processes such as hot rolling, water in reservoirs, melt spinning as a metal forming technique, elastic polymer substances, heat exchangers, emollient production, paints, catalytic reactors, and glass fiber production.
本文讨论了在磁场和非线性辐射影响下，可渗透纳米流体通过对流加热多孔延伸表面的达西 - 福希海默三维（3D）流动。考虑了具有活化能和热源（汇）影响的高阶化学反应。我们通过布朗扩散和热泳来整合纳米流体模型。为了将偏微分方程（PDEs）转换为非线性常微分方程（ODEs），使用了一种有效的自相似变换。采用打靶技术的四 - 五阶龙格 - 库塔 - 费尔贝格（RKF45）方法对所得的微分方程组进行数值求解。通过图表揭示了无量纲参数对速度、温度和纳米颗粒体积分数分布的影响。讨论了纳米流体流动和传热以及在所研究参数影响下的对流热传输系数、阻力系数、努塞尔数和舍伍德数的结果，并通过图表和表格呈现。数值模拟表明，活化能的增加和化学反应的阶数会提高浓度，而热辐射则相反。这种有吸引力的纳米流体的应用包括塑料和橡胶片材生产、石油生产、金属加工过程如热轧、水库中的水、作为金属成型技术的熔体纺丝、弹性聚合物物质、热交换器、润肤剂生产、涂料、催化反应器和玻璃纤维生产。
