Computational analysis of Darcy-Forchheimer relation, reduced gravity, and external applied magnetic field influence on radiative fluid flow and heat transfer past a sphere: Finite difference method

Amir Abbas; Muhammad Ashraf; Hafeez Ahmad; Kaouther Ghachem; Zia Ullah; Abid Hussanan; Taher Labidi; Lioua Kolsi

doi:10.1016/j.heliyon.2023.e15696

Computational analysis of Darcy-Forchheimer relation, reduced gravity, and external applied magnetic field influence on radiative fluid flow and heat transfer past a sphere: Finite difference method

Heliyon. 2023 Apr 25;9(5):e15696. doi: 10.1016/j.heliyon.2023.e15696. eCollection 2023 May.

Authors

Amir Abbas¹, Muhammad Ashraf², Hafeez Ahmad³, Kaouther Ghachem⁴, Zia Ullah⁵, Abid Hussanan⁶, Taher Labidi⁷, Lioua Kolsi^{8

9}

Affiliations

¹ Department of Mathematics, Faculty of Science, University of Gujrat, Sub-Campus, Mandi Bahauddin, 50400, Pakistan.
² Department of Mathematics, Faculty of Science, University of Sargodha, Sargodha, 40100, Pakistan.
³ Department of Statistics, School of Quantitative Sciences, University of Utara, Malaysia.
⁴ Department of Industrial Engineering and Systems, College of Engineering, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia.
⁵ Department of Mathematics and Statistics, Faculty of Science, Sargodha-Campus, The University of Lahore, Sargodha, 40100, Pakistan.
⁶ Department of Mathematics, Division of Science and Technology, University of Education, Lahore, 54000, Pakistan.
⁷ Department of Software Engineering, College of Computer Engineering and Sciences, Prince Sattam bin Abdulaziz University, P.O. Box 151,Al-Kharj, 11942, Saudi Arabia.
⁸ Department of Mechanical Engineering, College of Engineering, University of Ha'il, Ha'il City, 81451, Saudi Arabia.
⁹ Laboratory of Metrology and Energy Systems, Department of Energy Engineering, University of Monastir, Monastir, 5000, Tunisia.

Abstract

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.

Keywords: Darcy-Forchheimer relation; Finite difference method; Magnetohydrodynamics; Porous-medium; Reduced-gravity; Solar-radiation; Sphere.