Magnetohydrodynamic (MHD, also for magnetohydrodynamics) mixed convection of electrically conducting and radiative participating fluid is studied in a differentially heated vertical annulus. The outer cylinder is stationary, and the inner cylinder is rotating at a constant angular speed around its axis. The temperature difference between the two cylindrical walls creates buoyancy force, due to the density variation. A constant axial magnetic field is also imposed to resist the fluid motion. The nonlinear integro-differential equation, which characterizes the radiation transfer, is solved by the discrete ordinates method (DOM). The MHD equations, which describe the magnetic and transport phenomena, are solved by the collocation spectral method (CSM). Detailed numerical results of heat transfer rate, velocity, and temperature fields are presented for $0\u2264Ha\u2264100$, $0.1\u2264\tau L\u226410$, $0\u2264\omega \u22641$, and $0.2\u2264\epsilon W\u22641$. The computational results reveal that the fluid flow and heat transfer are effectively suppressed by the magnetic field as expected. Substantial changes occur in flow patterns as well as in isotherms, when the optical thickness and emissivity of the walls vary in the specified ranges. However, the flow structure and the temperature distribution change slightly when the scattering albedo increases from 0 to 0.5, but a substantial change is observed when it increases to 1.

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June 2016

Research-Article

# Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus

Ben-Wen Li,

Ben-Wen Li

Institute of Thermal Engineering,

School of Energy and Power Engineering,

Dalian University of Technology,

Dalian 116024, China

e-mails: heatli@hotmail.com; heatli@dlut.edu.cn

School of Energy and Power Engineering,

Dalian University of Technology,

Dalian 116024, China

e-mails: heatli@hotmail.com; heatli@dlut.edu.cn

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Wei Wang,

Wei Wang

Key Laboratory of National Education Ministry

for Electromagnetic Processing of Materials,

Northeastern University,

Shenyang 110819, China

e-mail: wangwei_neu_china@hotmail.com

for Electromagnetic Processing of Materials,

Northeastern University,

Shenyang 110819, China

e-mail: wangwei_neu_china@hotmail.com

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Jing-Kui Zhang

Jing-Kui Zhang

The State key Laboratory of Refractories and

Metallurgy,

Wuhan University of Science and Technology,

Wuhan 430081, China

e-mail: zk_neu@163.com

Metallurgy,

Wuhan University of Science and Technology,

Wuhan 430081, China

e-mail: zk_neu@163.com

Search for other works by this author on:

Ben-Wen Li

School of Energy and Power Engineering,

Dalian University of Technology,

Dalian 116024, China

e-mails: heatli@hotmail.com; heatli@dlut.edu.cn

Wei Wang

for Electromagnetic Processing of Materials,

Northeastern University,

Shenyang 110819, China

e-mail: wangwei_neu_china@hotmail.com

Jing-Kui Zhang

Metallurgy,

Wuhan University of Science and Technology,

Wuhan 430081, China

e-mail: zk_neu@163.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 21, 2014; final manuscript received December 27, 2015; published online March 8, 2016. Assoc. Editor: Sujoy Kumar Saha.

*J. Heat Transfer*. Jun 2016, 138(6): 062501 (13 pages)

**Published Online:**March 8, 2016

Article history

Received:

December 21, 2014

Revised:

December 27, 2015

Citation

Li, B., Wang, W., and Zhang, J. (March 8, 2016). "Combined Effects of Magnetic Field and Thermal Radiation on Fluid Flow and Heat Transfer of Mixed Convection in a Vertical Cylindrical Annulus." ASME. *J. Heat Transfer*. June 2016; 138(6): 062501. https://doi.org/10.1115/1.4032609

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