Numerical solutions of liquid metal flows by incompressible magneto‐hydrodynamics with heat transfer

Şentürk, Kenan; Tessarotto, Massimo; Aslan, Necdet

doi:10.1002/fld.1928

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…Their results set forth that for large values of Hartmann number, the magnetic induction equations should be taken into consideration in the mathematical model. There are several studies, implementing different numerical methods, where the full model for liquid metal flows is considered, and the existence of external and internal magnetic fields is taken into account.Şentürk et al proposed a two-dimensional scheme in [8] to simulate the natural convection with internal heat generation and absorption in addition to non-linear time dependent evolution of heated and magnetized liquid metals exposed to external fields. The algorithm consists of a Lax-Wendroftype matrix distribution together with a dual time-stepping scheme employing third-order Runge-Kutta steps.…”

Section: Introductionmentioning

confidence: 99%

Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations

Türk¹

2018

SDÜ Fen Bil Enst Der

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In this study, a Chebyshev spectral collocation method (CSCM) approximation is proposed for solving the full magnetohydrodynamics (MHD) equations coupled with energy equation. The MHD flow is two-dimensional, unsteady, laminar and incompressible, and the heat transfer is considered using the Boussinesq approximation for thermal coupling. The flow takes place in a square cavity which is subjected to a vertically applied external magnetic field, and the presence of the induced magnetic field is also taken into account due to the electrical conductivity of the fluid. The governing equations given in terms of stream function, vorticity, temperature, magnetic stream function, and current density, are solved iteratively using CSCM for the spatial discretisation, and an unconditionally stable backward difference scheme for the time integration. The induced magnetic field is obtained by means of its relation to the magnetic stream function. The behaviours of the flow and the heat transfer are investigated for varying values of Reynolds (Re), magnetic Reynolds (Rem), Rayleigh (Ra) and Hartmann (Ha) numbers.

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Section: Introductionmentioning

confidence: 99%

Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations

Türk¹

2018

SDÜ Fen Bil Enst Der

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“…The MHD system is coupled with the temperature effect through gravitational force by means of the Bousinessq approximation. As a consequence, flow and temperature fields are adjusted by the application of external magnetic field, and in turn, fluid flow contributes to the magnetic field distribution in the fluid (Senturk et al, 2009). Karcher et al (2002) and Kakarantzas et al (2009) investigated the effect of a vertical magnetic field on the convective heat transfer in a cylindrical container filled by a liquid metal heated locally from above.…”

Section: Introductionmentioning

confidence: 99%

FEM solution of natural convection flow in square enclosures under magnetic field

Türk

Tezer‐Sezgin

2013

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -The purpose of the paper is to obtain finite element method (FEM) solution of steady, laminar, natural convection flow in inclined enclosures in the presence of an oblique magnetic field. The momentum equations include the magnetic effect, and the induced magnetic field due to the motion of the electrically conducting fluid is neglected. Quadratic triangular elements are used to ensure accurate approximation for second order derivatives of stream function appearing in the vorticity equation. Design/methodology/approach -Governing equations in terms of stream function and vorticity are solved by FEM using quadratic triangular elements. Vorticity boundary conditions are obtained through Taylor series expansion of stream function equation by using more interior stream function values to improve the accuracy. Isothermally heated or cooled and/or adiabatic conditions for the temperature are imposed. Results are obtained for Rayleigh number values and Hartmann number values up to 1000000 and 100, respectively. Findings -It is observed that streamlines form a thin boundary layer close to the heated walls as Ha increases. The same effect is seen in the vorticity contours, and isotherms are not affected much. As Ra increases streamlines are deformed moving from the heated walls through cooled walls. Vorticity starts to develop boundary layers close to heated and adjacent walls. Isotherms are pushed towards the sinusoidally heated wall whereas in the case of linearly heated left and bottom walls they expand towards cooled part of the cavity as Ra increases. Originality/value -The application of FEM with quadratic elements for solving natural convection flow problem under the effect of a magnetic field is new in the sense that the results are obtained for large values of Rayleigh and Hartmann numbers.

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Prediction of Better Flow Control Parameters in MHD Flows Using a High Accuracy Finite Difference Scheme

Rejeesh¹,

Udhayakumar²,

Sekhar³

et al. 2017

AJCM

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We have successfully attempted to solve the equations of full-MHD model within the framework of ψ ω − formulation with an objective to evaluate the performance of a new higher order scheme to predict better values of control parameters of the flow. In particular for MHD flows, magnetic field and electrical conductivity are the control parameters. In this work, the results from our efficient high order accurate scheme are compared with the results of second order method and significant discrepancies are noted in separation length, drag coefficient and mean Nusselt number. The governing Navier-Stokes equation is fully nonlinear due to its coupling with Maxwell's equations. The momentum equation has several highly nonlinear body-force terms due to full-MHD model in cylindrical polar system. Our high accuracy results predict that a relatively lower magnetic field is sufficient to achieve full suppression of boundary layer and this is a favorable result for practical applications. The present computational scheme predicts that a drag-coefficient minimum can be achieved when , it is found that the heat transfer rate is independent of electrical conductivity of the fluid. From the numerical values of physical quantities, we establish that the order of accuracy of the computed numerical results is fourth order accurate by using the method of divided differences.

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Numerical solutions of liquid metal flows by incompressible magneto‐hydrodynamics with heat transfer

Cited by 3 publications

References 12 publications

Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations

Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations

FEM solution of natural convection flow in square enclosures under magnetic field

Prediction of Better Flow Control Parameters in MHD Flows Using a High Accuracy Finite Difference Scheme

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