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Research Papers: Natural and Mixed Convection

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

[+] Author and Article Information
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

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

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

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 138(6), 062501 (Mar 08, 2016) (13 pages) Paper No: HT-14-1825; doi: 10.1115/1.4032609 History: Received December 21, 2014; Revised December 27, 2015

## Abstract

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 $0≤Ha≤100$, $0.1≤τL≤10$, $0≤ω≤1$, and $0.2≤εW≤1$. 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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## Figures

Fig. 2

Radial and axial velocity profiles at the centerlines calculated with four grids at Ha=100, τL=1, ω=0.5, and εW=1

Fig. 1

Physical model with coordinate system and boundary conditions

Fig. 3

Comparisons of streamlines ((a) and (b)), +Δψ=6.8,−Δψ=0.11 and isotherms ((c) and (d)), ΔT=0.1 for Ri=1: (a) and (c) result of Ref. [34] and (b) and (d) this study

Fig. 4

Comparisons of streamlines ((a) and (b)), +Δψ=1.3,−Δψ=0.89 and isotherms ((c) and (d)), ΔT=0.1 for Ri=0.05: (a) and (c) result of Ref. [34] and (b) and (d) this study

Fig. 7

Streamlines with τL=0.1, ω=0.5, and εW=1: (a) Ha=0, (b) Ha=10, (c) Ha=50, and (d) Ha=100

Fig. 8

Isotherms with τL=0.1, ω=0.5, and εW=1: (a) Ha=0, (b) Ha=10, (c) Ha=50, and (d) Ha=100

Fig. 9

Streamlines (top row) and isotherms (bottom row) with Ha=100, ω=0.5, and εW=1: (i) τL=0.1, (ii) τL=1.0, and (iii) τL=10

Fig. 5

Comparison of mean equivalent conductivity variation with Richardson number for Re=100

Fig. 6

Comparisons of nondimensional radial heat flux distribution at the outer wall of a finite concentric cylindrical enclosure

Fig. 10

Streamlines (top row) and isotherms (bottom row) with Ha=100, τL=1.0, and εW=1: (i) ω=0, (ii) ω=0.5, and (iii) ω=1.0

Fig. 11

Streamlines (top row) and isotherms (bottom row) with Ha=100, τL=1.0, and ω=0.5: (i) εW=0.2, (ii) εW=0.6, and (iii) εW=1.0

Fig. 12

Effects of Hartmann number on Nusselt number for τL=0.1, ω=0.5, and εW=1

Fig. 14

Effects of scattering albedo on Nusselt number for Ha=100, τL=1.0, and εW=1

Fig. 15

Effects of emissivity of walls on Nusselt number for Ha=100, τL=1.0, and ω=0.5

Fig. 13

Effects of optical thickness on Nusselt number for Ha=100, ω=0.5, and εW=1

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