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Research Papers: Natural and Mixed Convection

The Joule Heating Effects on Natural Convection of Participating Magnetohydrodynamics Under Different Levels of Thermal Radiation in a Cavity

[+] Author and Article Information
Jing-Kui Zhang

The State Key Laboratory
of Refractories and Metallurgy,
Wuhan University of Science and Technology,
Wuhan 430081, China
e-mail: zhangjingky@gmail.com

Ben-Wen Li

The State Key Laboratory
of Refractories and Metallurgy,
Wuhan University of Science and Technology,
Wuhan 430081, China
e-mail: heatli@hotmail.com; heatli@dlut.edu.cn

Yuan-Yuan Chen

The State Key Laboratory
of Refractories and Metallurgy,
Wuhan University of Science and Technology,
Wuhan 430081, China
e-mail: chenyuanyuan@wust.edu.cn

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 23, 2013; final manuscript received January 21, 2015; published online February 18, 2015. Assoc. Editor: Robert D. Tzou.

J. Heat Transfer 137(5), 052502 (May 01, 2015) (10 pages) Paper No: HT-13-1432; doi: 10.1115/1.4029681 History: Received August 23, 2013; Revised January 21, 2015; Online February 18, 2015

A numerical study is conducted for the Joule heating effects on fluid flow and heat transfer of radiatively participating magnetohydrodynamics (MHD) under different levels of thermal radiation considering the Hall effects in a square cavity. In the cavity, the vertical walls are isothermal with constant but different temperatures, while the horizontal walls are adiabatic. The absorption, emission, and scattering of the fluid and the reflection, absorption, and emission of the walls are all taken into account. The governing equations for momentum and energy together with the boundary conditions are solved by the finite volume method (FVM), while the governing equation for radiative transfer is solved by the discrete ordinates method (DOM). Tabular and graphical results are presented in terms of streamlines, isotherms, Nusselt number, and the average temperature of the fluid. After detailed analysis, we found that the Joule heating has notable effects on fluid flow and heat transfer in the cavity and Joule heating cannot be neglected in certain range of parameters.

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Figures

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Fig. 1

Physical model with coordinate system and boundary conditions

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Fig. 2

Comparison of radiative heat flux

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Fig. 5

Streamlines for J = 0 (the left plots), J = 1 (the middle plots), and J = 3 (the right plots) with Ha = 10, Re = 200, Ri = 3, Pr = 0.733, and m = 1. (a) Pl = 0.02, (b) Pl = 0.2, and (c) Pl = 2.

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Fig. 6

Isotherms for J = 0 (the left plots), J = 1 (the middle plots), and J = 3 (the right plots) with Ha = 10, Re = 200, Ri = 3, Pr = 0.733, and m = 1. (a) Pl = 0.02, (b) Pl = 0.2, and (c) Pl = 2.

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Fig. 7

The local Nusselt number on the isothermal walls: (a) the convective Nusselt number, (b) the radiative Nusselt number, and (c) the total Nusselt number for Pl = 0.02, Ha = 10, Re = 200, Ri = 3, Pr = 0.733, and m = 1

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Fig. 8

The local Nusselt number on the isothermal walls: (a) the convective Nusselt number, (b) the radiative Nusselt number, and (c) the total Nusselt number for Pl = 0.2, Ha = 10, Re = 200, Ri = 3, Pr = 0.733, and m = 1

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Fig. 9

The local Nusselt number on the isothermal walls: (a) the convective Nusselt number, (b) the radiative Nusselt number, and (c) the total Nusselt number for Pl = 2, Ha = 10, Re = 200, Ri = 3, Pr = 0.733, and m = 1

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Fig. 3

Streamlines for J = 0 (the left plots), J = 1 (the middle plots), and J = 3 (the right plots) with Pl = 0.2, Re = 200, Ri = 3, Pr = 0.733 and m = 1. (a) Ha = 10, (b) Ha = 20, and (c) Ha = 50.

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Fig. 4

Isotherms for J=0 (the left plots), J = 1 (the middle plots), and J = 3 (the right plots) with Pl = 0.2, Re = 200, Ri = 3, Pr = 0.733, and m = 1. (a) Ha = 10, (b) Ha = 20, and (c) Ha = 50.

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