# Numerical solutions of boundary value problems; applications in ferrohydrodynamics and magnetohydrodynamics

2017
Şenel, Pelin
In this thesis, steady, laminar, fully developed flows in pipes subjected to a point magnetic source or uniform magnetic field are simulated by the dual reciprocity boundary element method (DRBEM). The Navier-Stokes and energy equations are solved in terms of the velocity, pressure and the temperature of the fluid which are all of the original variables of the problem. The missing pressure equation is derived and pressure boundary conditions are generated by a finite difference approximation and the DRBEM coordinate matrix. Fundamental solution of Laplace equation is made use of to convert the nonlinear partial differential equations into the boundary integral equations. The terms other than Laplacian are approximated by a series of radial basis functions. The nonlinearities in the governing equations are easily handled by the use of the DRBEM coordinate matrix. The influence of the point source magnetic field on the Ferrohydrodynamics (FHD) Stokes, incompressible, and forced convection flows are investigated first. The interaction between the buoyancy force, magnetization force and the viscous dissipation is discussed. Then, the effect of multiple point magnetic sources on the FHD incompressible flow is studied. DRBEM simulations of Magnetohydrodynamics (MHD) pipe flow and the flow between parallel infinite plates with slip velocity conditions are also presented. The coupled momentum and magnetic induction equations are combined and solved without an iteration. This process provides the nodal solutions in one stroke both on the boundary and inside the problem domain. The importance of the thesis study is in the fact that it is the first DRBEM application to FHD flow under point magnetic source and MHD flow with slip walls.

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Citation Formats
P. Şenel, “Numerical solutions of boundary value problems; applications in ferrohydrodynamics and magnetohydrodynamics,” Ph.D. - Doctoral Program, Middle East Technical University, 2017. 