Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations

Önder Türk

Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations

Abstract

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.

Keywords

MHD,CSCM; Heat transfer

References

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Details

Primary Language

Turkish

Subjects

-

Journal Section

-

Authors

Önder Türk This is me

Publication Date

October 5, 2018

Submission Date

May 14, 2018

Acceptance Date

-

Published in Issue

Year 2018 Volume: 22

IZ

https://izlik.org/JA66DD45BW

Cite

RIS / Bibtex

APA

Türk, Ö. (2018). Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22, 355-366. https://izlik.org/JA66DD45BW

AMA

1.Türk Ö. Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations. J. Nat. Appl. Sci. 2018;22:355-366. https://izlik.org/JA66DD45BW

Chicago

Türk, Önder. 2018. “Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 (October): 355-66. https://izlik.org/JA66DD45BW.

EndNote

Türk Ö (October 1, 2018) Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 355–366.

IEEE

[1]Ö. Türk, “Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations”, J. Nat. Appl. Sci., vol. 22, pp. 355–366, Oct. 2018, [Online]. Available: https://izlik.org/JA66DD45BW

ISNAD

Türk, Önder. “Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 (October 1, 2018): 355-366. https://izlik.org/JA66DD45BW.

JAMA

1.Türk Ö. Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations. J. Nat. Appl. Sci. 2018;22:355–366.

MLA

Türk, Önder. “Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, Oct. 2018, pp. 355-66, https://izlik.org/JA66DD45BW.

Vancouver

1.Önder Türk. Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations. J. Nat. Appl. Sci. [Internet]. 2018 Oct. 1;22:355-66. Available from: https://izlik.org/JA66DD45BW