Numerical solution of a singular integral equation appearing in magnetohydrodynamics

Singh, B.; Agarwal, Pooja

doi:10.1007/bf00945441

Cited by 21 publications

(8 citation statements)

References 6 publications

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“…Alternatively, BEM have been applied for solving MHD duct flow, however several problems have risen from the difficulties of solving huge systems and high computational costs due to the domain discretization. Papers at [13][14][15][16][17] are representative studies on the BEM solutions of MHD duct flow problems. All these BEM solutions have been obtained for small and moderate values of Hartmann number (M ≤ 50).…”

Section: Introductionmentioning

confidence: 99%

Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions

et al. 2010

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In this article a numerical solution of the time dependent, coupled system equations of magnetohydrodynamics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method. The approximation of the field variables is obtained with the moving least squares (MLS) approximation. Regular and irregular nodal distributions are used. Thus, a numerical solver is developed for the unsteady coupled MHD problems, using the collocation formulation, for regular and irregular cross sections, as are the rectangular, triangular and circular. Arbitrary wall conductivity conditions are applied when a uniform magnetic field is imposed at characteristic directions relative to the flow one. Velocity and induced magnetic field across the section have been evaluated at various time intervals for several Hartmann numbers (up to 10 5 ) and wall conductivities. The numerical results of the strong-form MPC method are compared with those obtained using two weak-form meshless methods, that is, the local boundary integral equation (LBIE) meshless method and the meshless local PetrovGalerkin (MLPG) method, and with the analytical solutions, where they are available. Furthermore, the accuracy of the method is assessed in terms of the error norms L 2 and L ∞ , the number of nodes in the domain of influence and the time step length depicting the convergence rate of the method. Run time results are also presented demonstrating the efficiency and the applicability of the method for real world problems.

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Section: Introductionmentioning

confidence: 99%

Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions

et al. 2010

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“…Helliwell [37] studied the Couette magnetohydrodynamic compressible flow with thermal radiation, between flat walls of arbitrary electrical conductivity, radiative emissivity and temperature, computing profiles of velocity, induced magnetic field, radiative flux and temperature. Singh and Agarwal [38] presented computational solutions for the velocity and induced magnetic field based on a singular integral equation describing MHD flow through a rectangular pipe with perfectly conducting electrodes. An increase in Hartmann number caused a flattening of the velocity profile and reduced flux through a section.…”

Section: Introductionmentioning

confidence: 99%

Nonsimilar, laminar, steady, electrically-conducting forced convection liquid metal boundary layer flow with induced magnetic field effects

Bég

Bakier

Prasad³

et al. 2009

International Journal of Thermal Sciences

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“…Now, the use of (BEM) based methods has been favored as a way to deal with the difficulties of managing large system sizes due to the need to increase domain discretization accuracy. Examples for Hartmann numbers of 1 ( 10 ) O  are given by Singh and Agarwal (1984), Tezer-Sezgin (1994), Liu and Zhu (2002), Tezer-Sezgin and Aydin (2002), Carabineanu et al (1995), and Bozkaya and . Particularly, Liu and Zhu (2002), and Bozkaya and Tezer-Sezgin (2008), applied a (BEM) based methodology variant referred as dual reciprocity boundary element method (DRBEM) for non-conducting walls, and also another one referred as time-domain (BEM) for arbitrary wall conductivity unsteady MHD duct flow.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study on the Magnetohydrodynamics of a Liquid Metal Oscillatory Flow under Inductionless Approximation

Sierra¹

2017

JAFM

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A harmonically-driven, incompressible, electrically conducting, and viscous liquid metal magnetohydrodynamic flow through a thin walled duct of rectangular cross section interacting with a uniform magnetic field traverse to its motion direction is numerically investigated. Chebyshev spectral collocation method is used to solve the Navier-Stokes equation under the inductionless approximation for the magnetic field in the gradient formulation for the electric field. Flow is considered fully developed in the direction perpendicular to the applied magnetic field and laminar in regime. Validation of numerical calculations respect to analytical calculations is established. Flow structure and key magnetohydrodynamic features regarding eventual alternating power generation application in a rectangular channel liquid metal magnetohydrodynamic generator setup are numerically inquired. Influence of pertinent parameters such as Hartmann number, oscillatory interaction parameter and wall conductance ratio on magnetohydrodynamic flow characteristics is illustrated. Particularly, it is found that in the side layer and its vicinity the emerging flow structures/patterns depend mainly on the Hartmann number and oscillatory interaction parameter ratio, while the situation for the Hartmann layer and its vicinity is less eventful. A similar feature has been discussed in the literature for the steady liquid metal flow case and served as rationale for developing the composite core-side-layer approximation to study the magnetohydrodynamics of liquid metal flows usable in direct power generation. In this study that approximation is not considered and the analysis is performed on liquid metal oscillatory (i., e., unsteady) flows usable in alternating power generation. Conversely, in terms of prospective practical applicability the formulation developed and tested with these calculations admits the implementation of a load resistance and walls conductivity optimization. That means that besides representing a numerical study on the magnetohydrodynamics of the oscillatory flow under consideration, absent in the literature for the parametric ranges reported, the formulation presently implemented can also be applicable to study the performance of an alternating liquid metal magnetohydrodynamic generator in the rectangular channel configuration.

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Numerical solution of a singular integral equation appearing in magnetohydrodynamics

Cited by 21 publications

References 6 publications

Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions

Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions

Nonsimilar, laminar, steady, electrically-conducting forced convection liquid metal boundary layer flow with induced magnetic field effects

Numerical Study on the Magnetohydrodynamics of a Liquid Metal Oscillatory Flow under Inductionless Approximation

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