Numerical computation of nonlinear oscillatory two-immiscible magnetohydrodynamic flow in dual porous media system : FTCS and FEM study

Beg, OA; Zaman, A; Ali, N; Gaffar, SA; Beg, TA

Abstract

The transient Hartmann magnetohydrodynamic (MHD) flow of two immiscible fluids flowing through a horizontal channel containing two porous media with oscillating lateral wall mass flux is studied. A two-dimensional spatial model is developed for the two fluids, one of which is electrically-conducting and the other electrically-insulating (as is the wall in the second region). Both fluid regimes are driven by a common pressure gradient. A Darcy-Forchheimer drag force model is used to simulate the porous medium effects on the flow in both fluid regions. Special boundary conditions are imposed at the interface. The governing second order nonlinear partial differential equations are non-dimensionalized for each region using a set of transformations. The resulting transport equations are shown to be controlled by the Hartmann hydromagnetic parameter (Ha), viscosity ratio parameter (α), two Darcy numbers (Da1, Da2), two Forchheimer numbers (Fs1, Fs2), two Reynolds numbers (Re1, Re2), frequency parameter (εA) associated with the transpiration (lateral wall flux) velocity and a periodic frequency parameter (ω*t*). Numerical FTCS finite difference solutions are obtained for a wide range of the governing parameters. Benchmarking is performed with a Galerkin finite element method code (MAGNETO-FEM) and the results are found to be in excellent agreement. Applications of the model include magnetic cleanup operations in coastal/ocean seabed oil spills and electromagnetic purification of petroleum reservoir fluids.

Citation

Beg, O., Zaman, A., Ali, N., Gaffar, S., & Beg, T. (2019). Numerical computation of nonlinear oscillatory two-immiscible magnetohydrodynamic flow in dual porous media system : FTCS and FEM study. Heat Transfer - Asian Research, 48(4), 1245-1263. https://doi.org/10.1002/htj.21429

• Journal Article Type: Article
• Acceptance Date: Jan 20, 2019
• Online Publication Date: Feb 3, 2019
• Publication Date: Feb 3, 2019
• Deposit Date: Jan 23, 2019
• Publicly Available Date: Feb 3, 2020
• Journal: Heat Transfer - Asian Research
• Print ISSN: 1099-2871
• Electronic ISSN: 1523-1496
• Publisher: Wiley
• Volume: 48
• Issue: 4
• Pages: 1245-1263
• DOI: https://doi.org/10.1002/htj.21429
• Publisher URL: https://doi.org/10.1002/htj.21429
• Related Public URLs: https://onlinelibrary.wiley.com/journal/15231496