## FHD flow in an irregular cavity subjected to a non-uniform magnetic field

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.72, no.2, pp.530-550, 2023 (ESCI)

• Publication Type: Article / Article
• Volume: 72 Issue: 2
• Publication Date: 2023
• Doi Number: 10.31801/cfsuasmas.1087827
• Journal Name:
• Journal Indexes: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
• Page Numbers: pp.530-550
• Karadeniz Technical University Affiliated: Yes

#### Abstract

In this paper FHD flow in a rectangular pipe constricted by two analogous semi-cylinders attached to the left and the bottom walls is investigated. The laminar, axial flow is produced by a constant pressure gradient, and the flow is affected by a spatially varying non-uniform magnetic field caused by two electric wires. The current-carrying wires are placed along the axes of the semi-cylinders. The fully developed flow is studied on the 2D cross-section of the pipe, a cavity, where the wires act as point magnetic sources. The pressure equation is added to the mathematical model, and the velocity-pressure form governing equations are numerically solved by the dual reciprocity boundary element method (DRBEM). The Dirichlet type pressure boundary conditions are approximated through a process using the radial basis functions and a finite difference. The flow, velocity, and pressure variations are investigated for different magnetic field strengths and current ratios. The grid independence study is also carried out. The proposed iterative scheme is capable of generating numerical results by performing a non-uniform discretization for the boundary. Dense discretizations are applied at the places where the flow shows a sudden fluctuation. It is shown by the numerical results that the flow and the pressure variations are dominated by the strong magnetic source. With an increment in the magnetic number, the planar flow is accelerated, the axial flow is decelerated, and the pressure increases, especially around the strong point magnetic source.