The Application of the Boundary Element Method to the Theory of MHD Faraday Generators

Carabineanu, Adrian

doi:10.1007/978-3-319-39929-4_7

Cited by 1 publication

(1 citation statement)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Magnetohydrodynamic flow through pipes has many practical applications in the design of cooling systems with liquid metals for nuclear reactors, MHD generators, electromagnetic pumps, MHD flow‐meters measuring blood pressure, and biomedical instruments using magnetic sources . Carabineanu gives boundary element method (BEM) application to the theory of MHD Faraday generators. The flow of an incompressible, viscous, electrically conducting fluid inside the pipe gives rise to an induced magnetic field with the interaction of an external transverse magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Semi‐analytical solution of MHD flow through boundary integrals on the pipe wall

Tezer‐Sezgin

Bozkaya

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

A mathematical model is given for the magnetohydrodynamic (MHD) pipe flow as an inner Dirichlet problem in a 2D circular cross section of the pipe, coupled with an outer Dirichlet or Neumann magnetic problem. Inner Dirichlet problem is given as the coupled convection‐diffusion equations for the velocity and the induced current of the fluid coupling also to the outer problem, which is defined with the Laplace equation for the induced magnetic field of the exterior region with either Dirichlet or Neumann boundary condition. Unique solution of inner Dirichlet problem is obtained theoretically reducing it into two boundary integral equations defined on the boundary by using the corresponding fundamental solutions. Exterior solution is also given theoretically on the pipe wall with Poisson integral, and it is unique with Dirichlet boundary condition but exists with an additive constant obtained through coupled boundary and solvability conditions in Neumann wall condition. The collocation method is used to discretize these boundary integrals on the pipe wall. Thus, the proposed procedure is an improved theoretical analysis for combining the solution methods for the interior and exterior regions, which are consolidated numerically showing the flow behavior. The solution is simulated for several values of problem parameters, and the well‐known MHD characteristics are observed inside the pipe for increasing values of Hartmann number maintaining the continuity of induced currents on the pipe wall.

show abstract

Section: Introductionmentioning

confidence: 99%