The BEM Solutions of MHD Flow and Heat Transfer in a Rectangular Duct with Temperature Dependent Viscosity

Authors

  • Elif Ebren Kaya Department of Mathematics, Middle East Technical University, Ankara, Turkey
  • Münevver Tezer-Sezgin Department of Mathematics, Middle East Technical University, Ankara, Turkey

Keywords:

BEM, DRBEM, MHD duct flow, variable viscosity.

Abstract

The steady, laminar, fully developed magnetohydrodynamic (MHD) flow of an incompressible, electrically conducting fluid with temperature dependent viscosity is studied in a rectangular duct together with its heat transfer. Although the induced magnetic field is neglected due to the small Reynolds number, the Hall effect, viscous and Joule dissipations are taken into consideration. The momentum and the energy equations are solved iteratively. Firstly, the momentum equation is solved by using the boundary element method with a parametrix since the diffusion term contains variable viscosity parameter depending on the temperature exponentially. Next, the momentum equation is also solved by using the dual reciprocity boundary element method (DRBEM) for comparison. The energy equation is solved by using the DRBEM keeping all the terms containing the velocity as inhomogeneity. The temperature and the velocity behaviours are examined for several values of Hartmann number, dimensionless viscosity parameter, Brinkmann number and the Hall parameter. As Hartmann number is increasing, the velocity magnitude drops which is a well known property of the MHD duct flow. Increasing viscosity parameter reduces both the flow and the temperature magnitudes whereas the increase in the Hall parameter accelerates the flow and increases the fluid temperature.

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Author Biographies

Elif Ebren Kaya, Department of Mathematics, Middle East Technical University, Ankara, Turkey

Elif Ebren Kaya received her BSc in Mathematics from the Middle East Technical University, Turkey in 2013. She has been a PhD student and a Research Asistant in the Department of Mathematics, Middle East Technical University, Turkey since 2013.

Münevver Tezer-Sezgin, Department of Mathematics, Middle East Technical University, Ankara, Turkey

M¨unevver Tezer-Sezgin received her BSc in Mathematics from the Middle East Technical University, Turkey in 1974. She received her MSc and PhD degrees in Applied Mathematics in 1978 and 1980 from the University of Saskatchewan, Canada and the University of Calgary, Canada, respectively. She is retired and currently working as a part time Professor in the Department of Mathematics, Middle East Technical University, Turkey. She also has held one year visiting position at the University ofVictoria, Canada, and short term visiting position at the Technical University of Darmstadt, Germany. She is the holder of Mustafa N. Parlar 1990 Research and 2014 Science Awards in applied mathematics and engineering.

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Published

2019-08-07

How to Cite

Kaya, E. E., & Tezer-Sezgin, M. (2019). The BEM Solutions of MHD Flow and Heat Transfer in a Rectangular Duct with Temperature Dependent Viscosity. European Journal of Computational Mechanics, 28(1-2), 97–122. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/930

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Original Article