# Stabilized FEM solution of MHD duct flow with conducting cracks in the insulation

2023-05-15
Tezer, Münevver
AYDIN, SALİM TUTGUN
© 2022 Elsevier B.V.In this paper, the numerical solution of the fully developed liquid–metal magnetohydrodynamic (MHD) flow is given in a rectangular duct under an external oblique magnetic field with no-slip and insulated walls containing crack regions. The coupled MHD flow equations are transformed first into decoupled convection–diffusion equations in terms of the velocity and induced magnetic field. Thus, we apply the SUPG stabilization in the finite element method (FEM) solution procedure for high values of Hartmann number which determine the convection dominant case. Numerical solutions for high values of Hartmann number and several orientation angles of external magnetic field as well as different crack configurations depict the effects of these parameters on the flow, flowrate and induced current. The SUPG in the FEM solution of MHD equations enables one to display the well-known characteristics of MHD pipe flow for large values of Hartmann number in which wall insulation is faced to several cracks. It is found that, the flowrate drops with an increase in the Hartmann number, and the increase in the number and lengths of the cracks which are located on one Hartmann wall. The flowrate is minimum if the crack is located at the center of the Hartmann wall. If the crack is located on the side layer, it does not significantly affect the flowrate. The case of each Hartmann wall contains one crack, significantly drops the flowrate compared to two cracks on the same Hartmann wall. Also, the breakdowns and peaks are sharpened when the Hartmann wall is a curved boundary. The FEM with SUPG stabilization is capable of capturing flow changes for high values of Hartmann number even in the vicinity of small-sized crack regions.
Journal of Computational and Applied Mathematics

# Suggestions

 Stabilizing subgrid FEM solution of the natural convection flow under high magnitude magnetic field on sinusoidal corrugated enclosure Aydın, S. H.; Tezer, Münevver (Informa UK Limited, 2019-7-7) This study deals with the stabilized finite element solution of the steady, natural convection flow in an enclosure under a magnetic field applied perpendicular to the sinusoidal corrugated vertical walls of the enclosure, in terms of primitive variables. Several vertical sinusoidal functions are selected for the comparison. A stabilized FEM scheme called SSM is proposed in order to obtain a stable solution for the high values of problem parameters with a cheap computational cost. Proposed numerical scheme ...
 A DRBEM solution for MHD pipe flow in a conducting medium Han Aydın, S.; Tezer, Münevver (Elsevier BV, 2014-3) Numerical solutions are given for magnetohydrodynamic (MHD) pipe flow under the influence of a transverse magnetic field when the outside medium is also electrically conducting. Convection-diffusion-type MHD equations for inside the pipe are coupled with the Laplace equation defined in the exterior region, and the continuity requirements for the induced magnetic fields are also coupled on the pipe wall. The most general problem of a conducting pipe wall with thickness, which also has magnetic induction gene...
 Controlling the power law fluid flow and heat transfer under the external magnetic field using the flow index and the Hartmann number Evcin, Cansu; Uğur, Ömür; Tezer, Münevver (2018-10-01) The direct and optimal control solution of laminar fully developed, steady Magnetohydrodynamics (MHD) flow of an incompressible, electrically conducting power-law non-Newtonian fluid in a square duct is considered with the heat transfer. The fluid is subjected to an external uniform magnetic field as well as a constant pressure gradient. The apparent fluid viscosity is both a function of the unknown velocity and the flow index which makes the momentum equation nonlinear. Viscous and Joule dissipation terms ...
 Controlling the power law fluid flow and heat transfer under the external magnetic field using the flow index and the Hartmann number Evcin, Cansu; Uğur, Ömür; Tezer, Münevver (2018-10-01) The direct and optimal control solution of laminar fully developed, steady Magnetohydrodynamics (MHD) flow of an incompressible, electrically conducting power-law non-Newtonian fluid in a square duct is considered with the heat transfer. The fluid is subjected to an external uniform magnetic field as well as a constant pressure gradient. The apparent fluid viscosity is both a function of the unknown velocity and the flow index which makes the momentum equation nonlinear. Viscous and Joule dissipation terms ...
 Numerical solution of magnetohydrodynamic flow problems using the boundary element method Tezer, Münevver (2005-03-18) A boundary element solution is given for a magnetohydrodynamic (MHD) flow problem in a rectangular duct having insulating walls, in terms of velocity and induced magnetic field. The coupled velocity and magnetic field equations are first transformed into decoupled nonhomogeneous convection-diffusion type equations and then finding particular solutions, the homogeneous equations are solved using the boundary element method (BEM). The fundamental solutions of the decoupled homogeneous equations themselves are...
Citation Formats
M. Tezer and S. T. AYDIN, “Stabilized FEM solution of MHD duct flow with conducting cracks in the insulation,” Journal of Computational and Applied Mathematics, vol. 423, pp. 0–0, 2023, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85142894649&origin=inward. 