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

Date

2019-05-01

Author

Tezer, Münevver
Bozkaya, Canan

Metadata

Show full item record

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

Item Usage Stats

263
views

0
downloads

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.

Subject Keywords

General Engineering, General Mathematics

URI

https://hdl.handle.net/11511/40830

Journal

MATHEMATICAL METHODS IN THE APPLIED SCIENCES

DOI

https://doi.org/10.1002/mma.5518

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Numerical investigation of flow and scour around a vertical circular cylinder Baykal, Cüneyt; Fuhrman, D. R.; Jacobsen, N. G.; Fredsoe, J. (The Royal Society, 2015-01-28) Flow and scour around a vertical cylinder exposed to current are investigated by using a three-dimensional numerical model based on incompressible Reynolds-averaged Navier-Stokes equations. The model incorporates (i) k-omega turbulence closure, (ii) vortex-shedding processes, (iii) sediment transport (both bed and suspended load), as well as (iv) bed morphology. The influence of vortex shedding and suspended load on the scour are specifically investigated. For the selected geometry and flow conditions, it i...
A computational procedure for estimating residual stresses and secondary plastic flow limits in nonlinearly strain hardening rotating shafts Eraslan, Ahmet Nedim (Springer Science and Business Media LLC, 2005-03-01) A computational procedure to estimate the residual stress distributions and the limit angular speeds for avoiding secondary plastic deformation in nonlinearly strain hardening rotating elastic-plastic shafts is given. The model is based on von Mises yield condition, J(2) deformation theory and a Swift-type hardening law. The boundary value problem for the governing nonlinear differential equation is solved by a shooting method using Newton iterations with numerically approximated tangent. Solid as well as h...
NONCOMMUTATIVE MACKEY THEOREM Dosi, Anar (World Scientific Pub Co Pte Lt, 2011-04-01) In this note we investigate quantizations of the weak topology associated with a pair of dual linear spaces. We prove that the weak topology admits only one quantization called the weak quantum topology, and that weakly matrix bounded sets are precisely the min-bounded sets with respect to any polynormed topology compatible with the given duality. The technique of this paper allows us to obtain an operator space proof of the noncommutative bipolar theorem.
Relative topology of real algebraic varieties in their complexifications Ozan, Yıldıray (Mathematical Sciences Publishers, 2004-12-01) We investigate, for a given smooth closed manifold M, the existence of an algebraic model X for M (i.e., a nonsingular real algebraic variety diffeomorphic to M) such that some nonsingular projective complexification i:X-->X-C of X admits a retraction r:X-C-->X. If such an X exists, we show that M must be formal in the sense of Sullivan's minimal models, and that all rational Massey products on M are trivial.
THERMAL-STRESSES IN A HEAT GENERATING ELASTIC-PLASTIC CYLINDER WITH FREE ENDS ORCAN, Y (Elsevier BV, 1994-06-01) The exact solution of the distribution of stress and deformation in an elastic-perfectly plastic cylindrical rod with uniform internal heat generation under generalized plane strain condition is presented. The treatment is based on Tresca's yield condition and the associated flow rule. The stress image points of the outer and inner plastic regions lie on two different edges of Tresca prism. With increasing heat generation parameter, the image points of the intermediate regions spread out through two side re...

Citation Formats

M. Tezer and C. Bozkaya, “Semi-analytical solution of MHD flow through boundary integrals on the pipe wall,” MATHEMATICAL METHODS IN THE APPLIED SCIENCES, pp. 2404–2416, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40830.