RBF Solution of Incompressible MHD Convection Flow in a Pipe

2016-10-12
Gürbüz, Merve
Tezer, Münevver
The steady convection flow of a viscous, incompressible and electrically conducting fluid is considered in a lid-driven cavity under the effect of a uniform horizontally applied magnetic field. The governing equations are the Navier-Stokes equations of fluid dynamics including buoyancy and Lorentz forces and the energy equation including Joule heating and viscous dissipation. These coupled equations are solved iteratively in terms of velocity components, stream function, vorticity, pressure and temperature by using radial basis function (RBF) approximation. Particular solution which is approximated by RBF to satisfy both differential equation and boundary conditions becomes the solution of the differential equation. The results are given for several values of Hartmann (M), Grashof (Gr) and the Reynolds (Re) numbers to visualize the effects on the solution. An increase in Gr moves the central vortex of the flow trough the center of the cavity emphasizing the movement of the top lid. Re increases the circulation of the fluid throughout the cavity. Heat is also circulated between the adiabatic walls when Gr or Re increases. The effect of increasing M is the boundary layer formation close to the moving lid for the flow and isotherms. The solution is obtained in a considerably low computational cost through the use of RBF approximation.
11. Workshop on Mathematical Modeling of Environmental and Life Sciences Problems

Suggestions

MHD Stokes flow and heat transfer in a lid-driven square cavity under horizontal magnetic field
Gurbuz, Merve; Tezer, Münevver (2018-04-01)
This study considers the steady flow of a viscous, incompressible and electrically conducting fluid in a lid-driven square cavity under the effect of a uniform horizontally applied magnetic field. The governing equations are obtained from the Navier-Stokes equations including buoyancy and Lorentz force terms and the energy equation including Joule heating and viscous dissipation terms. These equations are solved iteratively in terms of velocity components, stream function, vorticity, temperature, and pressu...
FEM solution to natural convection flow of a micropolar nanofluid in the presence of a magnetic field
TÜRK, ÖNDER; Tezer, Münevver (2017-03-01)
The two-dimensional, laminar, unsteady natural convection flow in a square enclosure filled with aluminum oxide ()-water nanofluid under the influence of a magnetic field, is considered numerically. The nanofluid is considered as Newtonian and incompressible, the nanoparticles and water are assumed to be in thermal equilibrium. The mathematical modelling results in a coupled nonlinear system of partial differential equations. The equations are solved using finite element method (FEM) in space, whereas, the ...
MHD natural convection flow in a porous cavity
Bozkaya, Canan (null; 2018-09-13)
A numerical investigation of natural convection flow in a cavity filled with a fluid-saturated porous medium in the presence of uniform magnetic field is performed. The steady, viscous, incompressible flow inside the porous medium is assumed to obey the Darcy law. The fluid physical properties are constant except the density in the body force term which is treated according to Boussinesq approximation. The fluid and porous medium are in thermal equilibrium. The governing equations subject to appropriate bou...
Radial basis function and dual reciprocity boundary element solutions of fluid dynamics problems
Gürbüz, Merve; Tezer Sezgin, Münevver; Department of Mathematics (2017)
In this thesis, the two-dimensional, laminar steady or unsteady flow of a viscous, incompressible, electrically conducting fluid is considered in channels of several geometries under the impact of a uniform magnetic field with different orientations. Magnetohydrodynamic (MHD) flow governed by the hydrodynamic and electromagnetic equations is solved numerically with or without Stokes approximation and with or without magnetic induction due to the large or small values of Reynolds and magnetic Reynolds number...
Magnetohydrodynamic convection of Cu-water nanofluid in a square cavity with a circular cylinder
Bozkaya, Canan (2016-01-01)
The hydromagnetic free convection of a Cu-water nanofluid in a square cavity involving an adiabatic circular cylinder is numerically investigated in the presence of an inclined uniform magnetic field. The left and right walls of the cavity are kept at constant hot and cold temperatures, respectively, while the horizontal walls are assumed to be adiabatic. The coupled nonlinear equations of mass, momentum and energy governing the present problem are discretized using the dual reciprocity boundary element met...
Citation Formats
M. Gürbüz and M. Tezer, “RBF Solution of Incompressible MHD Convection Flow in a Pipe,” presented at the 11. Workshop on Mathematical Modeling of Environmental and Life Sciences Problems, Constanta, Romanya, 2016, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/77132.