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

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 DarcyForchheimer 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.

Automated summary

The current work focuses on studying the effects of radiation, Darcy-Forchheimer relation, and reduced gravity on magnetohydrodynamic flow across a solid sphere in porous material. The study establishes coupled and nonlinear partial differential equations to model the configuration and converts them to dimensionless form using appropriate scaling variables. A numerical algorithm based on the finite element approach is developed to solve the problem, and the proposed model is validated by comparing with published results. The study aims to demonstrate the impact of Darcy-Forchheimer law and reduced gravity on natural convective heat transfer, and the results show that flow intensity decreases with certain parameters while temperature increases with others.