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Magnetohydrodynamic effect on axisymmetric Stokes flow past a weakly permeable spheroid with a solid core

Prasad M. K., Bucha T.

Archives of Mechanics

2021

Vol. 73, nr 5-6

599--633

The current research is focused on the creeping motion of fluid past a permeable spheroidal particle that has an impermeable core under the magnetic forces. Motion in the permeable zone is proposed to be regulated by Darcy’s law. At the fluid-porous interface, the continuity of the normal velocity component is assumed together with the balance of pressure with normal stresses and the Beavers–Joseph–Saffman–Jones (BJSJ) slip boundary condition. Vanishing of the normal component of velocity is used at the surface of the impermeable core. The drag on the spheroidal particle is obtained in an analytical form. The reliability of the drag coefficient on significant physical parameters such as permeability, non-sphericity parameter, Hartmann numbers, separation parameter (the measure of closeness between the porous particle and the core), and slip parameters is examined. Comparisons of results are made with the cases having no magnetic effect and show that the applied magnetic field possesses the ability to reduce the rate of flow of fluid. Well-known previously published results are deduced from the current analysis.

Slow flow past a weakly permeable spheroidal particle in a hypothetical cell

Bucha Tina, Madasu Krishna Prasad

Archive of Mechanical Engineering

2021

LXVIII, nr 2

119--146

The perspective of the current analysis is to represent the incompressible viscous flow past a low permeable spheroid contained in a fictitious spheroidal cell. Stokes approximation and Darcy’s equation are adopted to govern the flow in the fluid and permeable zone, respectively. Happel’s and Kuwabara’s cell models are employed as the boundary conditions at the cell surface. At the fluid porous interface, we suppose the conditions of conservation of mass, balancing of pressure component at the permeable area with the normal stresses in the liquid area, and the slip condition, known as Beavers-Joseph-Saffman-Jones condition to be well suitable. A closed-form analytical expression for hydrodynamic drag on the bounded spheroidal particle is determined and therefore, mobility of the particle is also calculated, for both the case of a prolate as well as an oblate spheroid. Several graphs and tables are plotted to observe the dependence of normalized mobility on pertinent parameters including permeability, deformation, the volume fraction of the particle, slip parameter, and the aspect ratio. Significant results that influence the impact of the above parameters in the problem have been pointed out. Our work is validated by referring to previous results available in literature as reduction cases.