DRBEM solution of singularly perturbed coupled MHD flow equations

Date

2023-10-01

Author

Arslan, Sinem
Tezer, Münevver

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In this study, the numerical solution of singularly perturbed magnetohydrodynamic (MHD) flow in a square duct with no-slip, and insulated or perfectly conducting walls is investigated by using the Dual Reciprocity Boundary Element Method (DRBEM). The steady, laminar and fully-developed MHD flow of an incompressible, viscous, and electrically conducting fluid in a long channel of square cross-section (duct) is driven by a pressure gradient. The governing MHD flow equations are convection–diffusion type and coupled in terms of the velocity V(x,y) and induced magnetic field B(x,y). When the intensity of horizontally applied external magnetic field is high, the Hartmann number (Ha) which is the coefficient of convection terms becomes large, that is, the coupled MHD flow equations become convection dominated. In other words, the coefficient of the diffusion terms is very small giving singularly perturbed MHD duct flow which exhibits thin boundary layers. The numerical scheme uses Shishkin mesh which depends on the number of points on one side and Ha. Numerical results obtained by DRBEM reveal that the well-known characteristics of the MHD flow problem are found as Ha increases and it is possible to obtain V(x,y) and B(x,y) for large values of Hartmann number up to Ha=1000.

Subject Keywords

Boundary layer, DRBEM, Hartmann number, MHD flow, Singular perturbation, Transition point

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85164705588&origin=inward
https://hdl.handle.net/11511/104704

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Department of Mathematics, Article