Abbas Amir, Ashraf Muhammad, Ahmad Hafeez, Ghachem Kaouther, Ullah Zia, Hussanan Abid, Labidi Taher, Kolsi Lioua
Department of Mathematics, Faculty of Science, University of Gujrat, Sub-Campus, Mandi Bahauddin, 50400, Pakistan.
Department of Mathematics, Faculty of Science, University of Sargodha, Sargodha, 40100, Pakistan.
Heliyon. 2023 Apr 25;9(5):e15696. doi: 10.1016/j.heliyon.2023.e15696. eCollection 2023 May.
The study of radiation, Darcy-Forchheimer relation, and reduced gravity, effects on magnetohydrodynamic flow across a solid sphere immersed in porous material, is the focus of the current work. Coupled and nonlinear partial differential governing equations, are established to model the studied configuration. By using appropriate scaling variables, the resultant set of governing equations is converted to its dimensionless form. Based on these established equations, a numerical algorithm is written based on the finite element approach to solve the considered problem. A verification of the validity of the proposed model is done by comparing with already published results. Furthermore, to check the precision of solutions, a grid independence test has been accomplished. The unknown variables, such as fluid velocity and temperature, and their gradients are evaluated. This investigation's main objective is to demonstrate how the Darcy-Forchheimer law and reduced gravity due to density difference affect the natural convective heat transfer across a solid sphere immersed in a porous medium. Results show that the flow intensity decreases with the magnetic field parameter, local inertial coefficient, Prandtl number, and porosity parameter and becomes more important by increasing the reduced gravity and radiation parameters. In addition, the temperature increases with the inertial coefficient, porosity parameter, Prandtl number, radiation parameter, and magnetic field parameter and get declined with the reduced gravity parameter.
本研究聚焦于辐射、达西 - 福希海默关系以及重力减小对浸没在多孔材料中的实心球体周围磁流体动力学流动的影响。建立了耦合的非线性偏微分控制方程来模拟所研究的结构。通过使用适当的标度变量，将所得的控制方程组转化为无量纲形式。基于这些已建立的方程，编写了一种基于有限元方法的数值算法来解决所考虑的问题。通过与已发表的结果进行比较，验证了所提出模型的有效性。此外，为了检验解的精度，完成了网格独立性测试。对诸如流体速度和温度等未知变量及其梯度进行了评估。本研究的主要目的是展示达西 - 福希海默定律以及由于密度差异导致的重力减小如何影响浸没在多孔介质中的实心球体的自然对流换热。结果表明，流动强度随磁场参数、局部惯性系数、普朗特数和孔隙率参数的增加而减小，而随着重力减小参数和辐射参数的增加而变得更加显著。此外，温度随惯性系数、孔隙率参数、普朗特数、辐射参数和磁场参数的增加而升高，随重力减小参数的增加而降低。
