Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations

Önder Türk

Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations

Öz

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.

Anahtar Kelimeler

MHD,CSCM; Heat transfer

Kaynakça

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Ayrıntılar

Birincil Dil

Türkçe

Konular

-

Bölüm

-

Yazarlar

Önder Türk Bu kişi benim

Yayımlanma Tarihi

5 Ekim 2018

Gönderilme Tarihi

14 Mayıs 2018

Kabul Tarihi

-

Yayımlandığı Sayı

Yıl 2018 Cilt: 22

IZ

https://izlik.org/JA66DD45BW

Kaynak Göster

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. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 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 (Ekim): 355-66. https://izlik.org/JA66DD45BW.

EndNote

Türk Ö (01 Ekim 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”, Süleyman Demirel Üniv. Fen Bilim. Enst. Derg., c. 22, ss. 355–366, Eki. 2018, [çevrimiçi]. Erişim adresi: 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 (01 Ekim 2018): 355-366. https://izlik.org/JA66DD45BW.

JAMA

1.Türk Ö. Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2018;22:355–366.

MLA

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

Vancouver

1.Önder Türk. Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. [Internet]. 01 Ekim 2018;22:355-66. Erişim adresi: https://izlik.org/JA66DD45BW