DRBEM solution of the Cauchy MHD duct flow with a slipping perturbed boundary

Date

2018-08-01

Author

Aydin, Cemre
Tezer, Münevver

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

198
views

0
downloads

In this study, the MHD flow direct and Cauchy problems are solved in a rectangular duct with a perturbed, curved, and slip upper boundary. The aim is to recompute the slipping velocity and the slip length by using the asymptotic analysis with respect to the perturbation parameter e and solving MHD flow equations for the first order and the corrector solutions in the rectangular duct. Hence, without discretizing the curved boundary, we are able to obtain the solution of MHD flow in the duct with curved perturbed boundary. The dual reciprocity boundary element method (DRBEM) is utilized for solving the coupled MHD equations as a whole. The discretization of Cauchy problems leads ill-conditioned systems of linear algebraic equations, hence a regularization technique is necessary. In this study, the Tikhonov regularization is used to obtain the solution of the Cauchy MHD problems. The main advantage of the DRBEM is discretizing only the boundary and providing both the velocity and its normal derivative values on the boundary. This enables us to recover the slip length on the perturbed boundary through the slip boundary condition.

Subject Keywords

General Engineering, Applied Mathematics, Analysis, Computational Mathematics

URI

https://hdl.handle.net/11511/44574

Journal

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

DOI

https://doi.org/10.1016/j.enganabound.2018.04.007

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

DRBEM solution of exterior nonlinear wave problem using FDM and LSM time integrations Meral, Guelnihal; Tezer, Münevver (Elsevier BV, 2010-06-01) The nonlinear wave equation is solved numerically in an exterior region For the discretization of the space derivatives dual reciprocity boundary element method (DRBEM) is applied using the fundamental solution of Laplace equation. The time derivative and the nonlinearity are treated as the nonhomogenity. The boundary integrals coming from the far boundary are eliminated using rational and exponential interpolation functions which have decay properties far away from the region of Interest. The resulting sys...
DRBEM solution of natural convection flow of nanofluids with a heat source Gumgum, S.; Tezer, Münevver (Elsevier BV, 2010-08-01) This paper presents the dual reciprocity boundary element method (DRBEM) solution of the unsteady natural convective flow of nanofluids in enclosures with a heat source. The implicit Euler scheme is used for time integration. All the convective terms are evaluated in terms of DRBEM coordinate matrix. The vorticity boundary conditions are obtained from the Taylor series expansion of stream function equation. The results report that the average Nusselt number increases with the increase in both volume fractio...
DRBEM solution to MHD flow in ducts with thin slipping side walls and separated by conducting thick Hartmann walls Senel, P.; Tezer-Sezgin, M. (Elsevier BV, 2019-11-01) In this study, the dual reciprocity boundary element method (DRBEM) solution to magnetohydrodynamic (MHD) flow is given in a single and two ducts stacked in the direction of external magnetic field. The duct walls perpendicular to the applied magnetic field (Hartmann walls) are conducting, thick and no-slip whereas the horizontal walls (side walls) are insulated, thin and allow the velocity slip. The DRBEM transforms the convection diffusion type MHD equations in the duct and Laplace equation in the thick w...
DRBEM Solution of MHD flow in a rectangular duct with time-varied external magnetic field Ebren Kaya, Elif; Tezer, Münevver (Elsevier BV, 2020-08-01) This paper investigates the flow behavior of a viscous, incompressible and electrically conducting fluid in a long channel subjected to a time-varied oblique magnetic field B-0(t) = B(0)f(t). The time-dependent MHD equations are solved by using the dual reciprocity boundary element method (DRBEM). The transient level velocity and induced magnetic field profiles are presented for moderate Hartmann number values, several direction of applied magnetic field and for several functions f(t) as polynomial, exponen...
Solution of magnetohydrodynamic flow problems using the boundary element method Tezer, Münevver (Elsevier BV, 2006-05-01) A boundary element solution is implemented for magnetohydrodynamic (MHD) flow problem in ducts with several geometrical cross-section with insulating walls when a uniform magnetic field is imposed perpendicular to the flow direction. The coupled velocity and induced magnetic field equations are first transformed into uncoupled inhomogeneous convection-diffusion type equations. After introducing particular solutions, only the homogeneous equations are solved by using boundary element method (BEM). The fundam...

Citation Formats

C. Aydin and M. Tezer, “DRBEM solution of the Cauchy MHD duct flow with a slipping perturbed boundary,” ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, pp. 94–104, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/44574.